# Does the sun have a vertical movment?

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As the Sun moves along with the planets does the sun exhibit vertical movement? That is, does it traverse in different planes?

Does the sun have a vertical movment?

## Sure it does!

People who follow solar system bodies with the highest accuracy, including NASA's JPL, use the solar system barycenter (center of mass) for the origin of the plane of the ecliptic.

Since the big planets (Jupiter et al.) have some inclination, they pull the Sun up and down out of the plane of the Ecliptic by tens of thousands of kilometers. It's a small fraction of it's 600,000 kilometer radius, but it certainly happens.

You can see the data from the JPL Horizons website, or if you like Python, you can get virtually the same numbers by running the Skyfield package.

From Horizions I downloaded the position of the Sun and the four major planets of the solar system in 10 day steps from the years 1900 to 2100. Below I plot the three components X, Y and Z in the J2000.0 Solar system barycentric coordinates using the ecliptic as the reference frame. The black line is the motion of the Sun, and the color lines are for the four planets, but I have multiplied each by the the mass of the planet divided by the Mass of the Sun.

In the second plot, I added the four together, and you can see that together they mirror the motion of the Sun.

The last two show the movement of the Sun in 3D (two views). Note that the vertical scale is much smaller than the horizontal scale.

Horizons setup:

below: Black thick line: motion of the Sun in barycentric coordinates in the J2000.0 X, Y and Z directions, relative to the ecliptic. Four thinner color lines: motions of the four largest planets, each weighted by its mass relative to the Sun's mass. Short period lines are Jupiter and Saturn with Jupiter the largest amplitude, long periods are Uranus and Neptune, with Neptune the largest amplitude.

below: Black thick line: motion of the Sun in barycentric coordinates in the J2000.0 X, Y and Z directions, relative to the ecliptic. Thin red line: sum of the motions of the four largest planets, each weighted by its mass relative to the Sun's mass.

below: Two views of the 3D motion of the Sun in barycentric coordinates between the years 1900 and 2100. Units are kilometers, and note that the scales are different for each axis.

class Body(object): def __init__(self, name): self.name = name import numpy as np import matplotlib.pyplot as plt from mpl_toolkits.mplot3d import Axes3D names = ('Sun', 'Jupiter', 'Saturn', 'Uranus', 'Neptune') bodies = [] for name in names: fname = 'sun motion ' + name + ' horizons_results.txt' body = Body(name) bodies.append(body) with open(fname, "r") as infile: lines = infile.read().splitlines() iSOE = [i for i, line in enumerate(lines) if "$$SOE" in line][0] iEOE = [i for i, line in enumerate(lines) if "$$EOE" in line][0] print (name, iSOE, iEOE, lines[iSOE], lines[iEOE]) lines = [line.split(',') for line in lines[iSOE+1:iEOE]] JD = np.array([float(line[0]) for line in lines]) pos = np.array([[float(item) for item in line[2:5]] for line in lines]) body.lines = lines body.JD = JD body.pos = pos.T.copy() years = 2000 + (JD - JD[3652])/365.2564 Sun, Jupiter, Saturn, Uranus, Neptune = bodies for body in bodies: body.rsun = np.sqrt(((body.pos - Sun.pos)**2).sum(axis=0)) planets = [b for b in bodies if 'sun' not in b.name.lower()] massdict = {'Jupiter':1.898E+27, 'Saturn':5.683E+26, 'Uranus':8.681E+25, 'Neptune':1.024E+26, 'Sun':1.989E+30} for b in bodies: b.mass = massdict[b.name] if True: plt.figure() for i, thing in enumerate(Sun.pos): plt.subplot(3, 1, i+1) plt.plot(years, thing, '-k', linewidth=1.5) for p in planets: for i, thing in enumerate(p.pos): plt.subplot(3, 1, i+1) thing = thing * (p.mass/Sun.mass) plt.plot(years, thing) plt.show() all_four = Body('all_four') all_four.pos = np.array([p.pos*(p.mass/Sun.mass) for p in planets]).sum(axis=0) if True: plt.figure() for i, thing in enumerate(Sun.pos): plt.subplot(3, 1, i+1) plt.plot(years, thing, '-k', linewidth=1.5) for i, thing in enumerate(all_four.pos): plt.subplot(3, 1, i+1) plt.plot(years, thing, '-r') plt.show() if True: fig = plt.figure(figsize=[12, 10]) # [12, 10] ax = fig.add_subplot(1, 1, 1, projection="3d") x, y, z = Sun.pos ax.plot(x, y, z) plt.show()

## Does the sun have a vertical movment? - Astronomy

• The human eye can see about 6000 stars without aid.

The stars are grouped into constellations .

Most of these are the same ones described by the ancient Greeks and Babylonians, although the southern hemisphere has many that were "created" by European explorers a few centuries ago.

• Nowadays we often think of constellations as "stick figures", consisting of lines connecting the major stars.

These figures leave out many stars and other objects, including those that require telescopes to be seen.

So, astronomers now think of a constellation as one of 88 regions that divide up the sky and completely cover it.

Many stars have names from Arabic or Greek, e.g. Betelgeuse means "armpit" in Arabic.

The stars are also given names such as "Alpha Orionis", using letters from the Greek alphabet followed by the constellation name.

After that, numbers are typically used, e.g. "37 Orionis".

This ordering is typically (but not always) according to brightness.

Extra: an extensive listing of common Star Names and their meanings.

#### 2.2 The Celestial Sphere

##### (Discovering the Universe, 5th ed., §1-3)

• An important characteristic of the stars is that they have relatively fixed positions with respect to each other, i.e. the constellations do not change with time.

The stars do actually move, but this motion is only noticeable to the unaided eye after a long time, tens of thousands of years or more.

We cannot detect this motion, however, so it appears to us as if the stars (and Sun and Moon and planets) are rotating around us : they rise in the east and set in the west, once a day.

This is called diurnal motion .

Picture Information

• This motion can be seen in the time-lapse photograph at the right, centered on the north pole of the celestial sphere.

#### 2.3 Latitude and Longitude

##### (Discovering the Universe, 5th ed., §1-4)

• It is useful to be able to precisely specify positions on the celestial sphere.

So, a set of coordinates is used that is similar to latitude and longitude on the Earth.

The system of latitude and longitude was first suggested by Hipparchus, a Greek astronomer in the 2nd C. B.C.

The Earth rotates around this axis, leaving the poles fixed.

The angle (with vertex at the center of the Earth) between a given circle of latitude and the equator describes that circle and any point on it.

So, the North Pole is at 90° north latitude, the equator itself is 0° latitude, and Johannesburg, South Africa is roughly 30° south latitude.

The angle (with vertex at the center of the Earth) between a given meridian and the prime meridian describes that meridian and any point on it.

So, Johannesburg is at 30° east longitude.

#### 2.4 Celestial Coordinates

##### (Discovering the Universe, 5th ed., §1-2)

• We describe the celestial sphere using a similar geographical notation:

The North Celestial Pole is the point on the celestial sphere directly above the Earth's North Pole .

Similarly, the South Celestial Pole is directly above the Earth's South Pole.

Polaris is therefore also called the North Star.

The north celestial pole is at 90° north declination (+90° dec). The south celestial pole is at 90° south declination (-90° dec).

Circles of constant declination are all parallel to the celestial equator.

Since the Earth and the celestial sphere are concentric, simple geometry shows that the zenith will always have a declination equal to the latitude of the observer (such as for Atlanta in the picture).

Right ascension corresponds to longitude, but different units are used.

Instead of 360°, a circle is broken into 24 hours of right ascension.

So, 360° = 24 h R.A., 15° = 1 h R.A., and 1° = 4 min R.A.

Note that hours of right ascension is a unit of angle , not time, although there is an obvious connection due to the daily rotation of the celestial sphere.

The celestial meridian is a semicircle connecting the celestial poles and passing through a particular point on the celestial equator called the vernal equinox (defined below).

Question: to what position on Earth is the vernal equinox analogous?

Right ascension increases from west to east (note that we are looking at the exterior of the celestial sphere in the above picture).

#### 2.5 The Motion of the Sun

##### (Discovering the Universe, 5th ed., §1-6)

• Although the stars are fixed relative to each other, the Sun moves relative to the stars.

Once a year, the Sun traces out a circle on the celestial sphere called the ecliptic .

The ecliptic is tilted at an angle of 23.5° with respect to the celestial equator.

(The Moon and planets also move near the ecliptic.)

The vernal equinox is chosen to be 0 h R.A.

This position is called the autumnal equinox because the Sun is there on September 23.

This position is called the summer solstice because the Sun is there on June 21.

The Sun then has a declination of +23.5°.

This position is called the winter solstice because the Sun is there on December 21.

#### 2.6 The Local Horizon

##### (Discovering the Universe, 5th ed., §1-6)

• To an observer on the Earth, only one half of the celestial sphere can be observed at a time.

As a result, in Atlanta the sky appears roughly as shown at the right.

The compass directions north, south, east, and west are marked along the horizon.

North will be underneath the north celestial pole.

When we face north, east is on our right and west is on our left.

The horizon has an altitude of 0° and the zenith has an altitude of 90°.

The azimuth of an object is the angle between it and north, measured clockwise along the horizon.

North has an azimuth of 0°, east has an azimuth of 90°, south has an azimuth of 180°, and west has an azimuth of 270°.

Question: the local meridian is a projection onto the celestial sphere of what previously described item on the Earth?

Question: what happens to these items when the observer moves to a different location on the Earth?

Since the zenith's declination is equal to one's latitude, Columbus was always able to determine his latitude when he crossed the Atlantic Ocean by measuring the altitude of Polaris.

In Atlanta, it therefore appears high in the sky at transit, 33.7° - 23.5° = 10.2° away from the zenith.

In Atlanta, it therefore appears low in the sky at transit, 33.7° + 23.5° = 57.2° away from the zenith.

At 23.5° S, the tropic of Capricorn , it just reaches the zenith on the winter solstice.

Between these latitudes (the tropics ), the Sun crosses the zenith twice during the year.

Tropic is from the Greek for "turning", again describing the Sun's motion at the solstice.

Cancer and Capricorn are the constellations where the Sun is located at the solstices (or rather where it was located in 500 B.C. ).

#### 2.7 Day and Night

##### (Discovering the Universe, 5th ed., §1-4)

• We define the synodic day as the time for the Sun to transit twice .

The synodic day is defined to be exactly 24 hours long, i.e. it is the "day" you are familiar with.

Since this can only happen at one longitude at a time, it used to be that every town had its own "time zone".

This was a nightmare for the railroads to keep track of, so in the 19th century they convinced Congress to implement time zones, breaking up the country into four broad areas that shared the same clock time.

This meant that, for most places, noon no longer occurred when the Sun was at transit, but it simplified scheduling, especially when broadcast radio and TV came along.

Atlanta is on the western edge of the Eastern Time Zone, so the Sun doesn't transit until 12:40 P.M. EST (1:40 P.M. EDT).

As the Sun sets toward the horizon, it is "after the meridian" or post meridian (P.M.).

These are the stars on the opposite side of the celestial sphere from the location of the Sun.

But which stars we see depends on the time of the year, because the Sun moves along the ecliptic!

The Sun moves about one degree, or about 4 minutes of RA, along the ecliptic every day (360°/365 d).

This solar motion means that a particular star will rise (or transit, or set) about 4 min earlier on each subsequent night.

The sidereal day is defined as the time for a star to cross the meridian twice.

## Does The Sun Move?

[/caption]Does the Sun Move? What an interesting question. We mainly talk about everything in the solar system orbiting the Sun and celestial objects outside the solar system being in relation to the Sun. The answer to the question is : Yes. The Sun and the entire solar system orbits around the center of the Milky Way galaxy. The average velocity of the solar system is 828,000 km/hr. At that rate it will take about 230 million years to make one complete orbit around the galaxy.

The Milky Way is a spiral galaxy. It is believed that it consists of a central bulge, 4 major arms, and several shorter arm segments. The Sun and the rest of our solar system is located near the Orion arm, between two major arms, Perseus and Sagittarius. The diameter of the Milky Way is about 100,000 light years and the Sun is located about 28,000 light-years from the Galactic Center. It has been suggested fairly recently that ours is actually a barred spiral galaxy. That means that instead of a bulge of gas and stars at the center, there is probably a bar of stars crossing the central bulge.

Everything in the known universe rotates on an axis and orbits something else in space. The Sun is no exception. Here is the NASA webpage about the sun’s movements through space. Astronomy Cast offers two good episodes: one is about the mysteries of the solar system and the other is about solar system movements.

## Lesson 1: Light and Shadows: The Sun Moves in the Sky

The class record observations of the Sun's apparent motion or path through the daytime sky from East to West. This activity of tracking the Sun's path along the Southern horizon should be repeated 3 times a year during three different seasons.

### After this activity, students should be able to:

• Describe the shape of the Sun's path throughout the day.
• Describe the Sun's movement and its relation to other objects each hour.
• Use landmarks to record and make predictions of the Sun's changing positions.
• Compare the class' Sun's path observations and recording during each season.
• Understand that the Sun rises in the East and sets in the West.
• Predict where the Sun is before they arrive at and after they leave school.

### Science:

• Objective 3.01 Observe that light travels in a straight line until it strikes and object and is reflected and or/absorbed.
• Objective 3.02 Observe that objects in the sky have patterns of movement including: Sun, Moon, Stars.
• Objective 3.03 Using shadows, follow and record the apparent movement of the Sun in the sky during the day.
• Objective 3.01 Use the appropriate vocabulary to compare, describe, classify two and three-dimensional figures.

Panoramic photo labeling in Science Notebook during Activity: Part 1 Intro

Activity Assessment
Panoramic photo data recorded in Science Notebook with follow up questions:

1. If you were to draw the Sun at 6PM tonight where would it be?
2. Where would the Sun's position be at 12 AM or midnight?
3. Can you count on the Sun to be in the same positions tomorrow? In three months? In a year? Explain why or why not?
4. So, what will the position of the Sun in the sky tell you about the time of day?
5. Why do you think they call noon the middle of the day or midpoint of the day?
6. How will daylight savings affect our recordings?
7. How does the Sun's path in winter compare with the Sun's path in fall?
8. How or why do you think the Sun's path effects or controls your town's weather? Or how late you get to play outside after school?

Post-Activity Assessment
Computer generated illustrated model of the Sun's path with written explanation using computer graphics software (i.e. KidPix) to illustrate and answer the following questions:

1. Draw the southern horizon with East, South, West and at least 4 landmarks labeled.
2. Illustrate the Sun's path as it changes position each hour.
3. Describe the Sun's path's shape? What is the shape similar to?
4. What do you notice about the Sun's path's pattern each hour?
5. What happens to the Sun after it sets? Why can't we see it?
6. Some people say the Sun's path across the sky is not a real motion. The Sun appears to us to move because the Earth is spinning and we are spinning with it. Do your observations agree with this idea? Do they contradict it? What observations could you use to try to distinguish the two hypotheses.

### Background

The apparent motion of the Sun across the sky from East to West, as well as the similar motion of all celestial objects, is explained as a result of the motion of the Earth and us with it. In fact, as we shall see later (in Activity 7) the actual path of the Sun's apparent motion reflects a somewhat complex interplay of the Earth's rotation, the resultant change in our orientation depending upon our latitude, and the position of the Earth in its orbit (Activity 9).

Our purpose in this activity is not to discuss any of this. Rather, we wish to create a baseline of concrete observations common to the entire class, to which we will refer as we work through our understanding of the motions of the Earth/Sun/Moon system. This activity is also an excellent opportunity to introduce the importance of careful, systematic observation and of presenting and sharing the results of observation in a clear and accurate way. It also invites students to realize that underlying our ability to comprehend nature is the fact that our observations reveal repeating, predictable patterns. In essence, science is the process of discerning, describing, and explaining these patterns.

There is a somewhat subtle point here, on which educated adults have been known to be unclear. The issue may not come up in class until later activities, but we chose to address it early here. We typically describe the apparent motion of the Sun, as mentioned above, as a result of the Earth's spinning motion about its axis. The idea that the Sun is in fact moving around the Earth, it is thought, was overthrown by the Copernican revolution of the 17th century. This is, in fact, false. Indeed, all of our observations suggest the Earth is spinning about its axis, completing one rotation every 24 hours or so. These observations include the apparent motion not only of the Sun but also of all other celestial objects, essentially anything in the Universe that is not on Earth. One can, without contradiction with observations, say that the Earth is not spinning. But one then has to claim that the entire Universe is in fact spinning about the Earth as a center. One also has to posit some rather unnatural causes for the (weak, but certainly measurable) centrifugal forces that we ascribe to our motion as the Earth rotates. Most unnaturally, one will note that all the other planets in the Solar system, and indeed all other celestial bodies, rotate about their own axis in addition to their apparent motion about Earth. It is thus far more natural to assume Earth is also in constant rotation about its axis. But fundamentally, taking the point of view of an Earth-bound person, describing the Universe as revolving around the Earth, is consistent if not simple.

The revolution engendered by Copernicus was not associated to this question at all. Instead, it addressed the fact that planets appear to be moving relative to the stars, in addition to the apparent uniform motion of everything that is explained by the Earth's rotation. This motion of the planets is far slower than the daily rotation of the entire sky, taking months or years to complete a cycle, depending on the planet in question. Before Copernicus, these apparent motions of the planets relative to the stars were explained by having planets move along complicated trajectories about the Earth (epicycles). Copernicus showed that the same apparent motion resulted from far simpler, essentially circular, motion of the planets around the Sun, provided we allow that we observe this from an Earth which itself orbits the Sun. The complicated apparent motions are the result of viewing simple motion from a moving platform. One can maintain the point of view of a stationary Earth even after Copernicus, at the cost of having the entire Universe perform a yearly compensating motion, but the level of complexity involved in this choice becomes so high that is is rarely attempted by scientists.

## The sun's clock: New calculations support and expand planetary hypothesis

The sun sported about a dozen active regions over a five-day period in May 2015. The bright, spindly strands that extend out of these active regions are particles spinning along magnetic field lines that connect areas of opposite polarity. Credit: Solar Dynamics Observatory, NASA

Solar physicists around the world have long been searching for satisfactory explanations for the sun's many cyclical, overlapping activity fluctuations. In addition to the most famous, approximately 11-year "Schwabe cycle", the sun also exhibits longer fluctuations, ranging from hundreds to thousands of years. It follows, for example, the "Gleissberg cycle" (about 85 years), the "Suess-de Vries cycle" (about 200 years) and the quasi-cycle of "Bond events" (about 1500 years), each named after their discoverers. It is undisputed that the solar magnetic field controls these activity fluctuations.

Explanations and models in expert circles partly diverge widely as to why the magnetic field changes at all. Is the sun controlled externally or does the reason for the many cycles lie in special peculiarities of the solar dynamo itself? HZDR researcher Frank Stefani and his colleagues have been searching for answers for years—mainly to the very controversial question as to whether the planets play a role in solar activity.

Rosette-shaped movement of the sun can produce a 193-year cycle

The researchers have most recently taken a closer look at the sun's orbital movement. The sun does not remain fixed at the center of the solar system: It performs a kind of dance in the common gravitational field with the massive planets Jupiter and Saturn—at a rate of 19.86 years. We know from the Earth that spinning around in its orbit triggers small motions in the Earth's liquid core. Something similar also occurs within the sun, but this has so far been neglected with regard to its magnetic field.

The researchers came up with the idea that part of the sun's angular orbital momentum could be transferred to its rotation and thus affect the internal dynamo process that produces the solar magnetic field. Such coupling would be sufficient to change the extremely sensitive magnetic storage capacity of the tachocline, a transition region between different types of energy transport in the sun's interior. "The coiled magnetic fields could then more easily snap to the sun's surface," says Stefani.

The researchers integrated one such rhythmic perturbation of the tachocline into their previous model calculations of a typical solar dynamo, and they were thus able to reproduce several cyclical phenomena that were known from observations. What was most remarkable was that, in addition to the 11.07-year Schwabe cycle they had already modeled in previous work, the strength of the magnetic field now also changed at a rate of 193 years—this could be the sun's Suess-de Vries cycle, which from observations has been reported to be 180 to 230 years. Mathematically, the 193 years arise as what is known as a beat period between the 19.86-year cycle and the twofold Schwabe cycle, also called the Hale cycle. The Suess-de Vries cycle would thus be the result of a combination of two external "clocks": the planets' tidal forces and the sun's own movement in the solar system's gravitational field.

Planets as a metronome

For the 11.07-year cycle, Stefani and his researchers had previously found strong statistical evidence that it must follow an external clock. They linked this "clock" to the tidal forces of the planets Venus, Earth and Jupiter. Their effect is greatest when the planets are aligned: a constellation that occurs every 11.07 years. As for the 193-year cycle, a sensitive physical effect was also decisive here in order to trigger a sufficient effect of the weak tidal forces of the planets on the solar dynamo.

After initial skepticism toward the planetary hypothesis, Stefani now assumes that these connections are not coincidental. "If the sun was playing a trick on us here, then it would be with incredible perfection. Or, in fact, we have a first inkling of a complete picture of the short and long solar activity cycles." In fact, the current results also retroactively reaffirm that the 11-year cycle must be a timed process. Otherwise, the occurrence of a beat period would be mathematically impossible.

Tipping into chaos: 1000-2000-year collapses are not more accurately predictable

In addition to the rather shorter activity cycles, the sun also exhibits long-term trends in the thousand-year range. These are characterized by prolonged drops in activity, known as "minima", such as the most recent "Maunder Minimum", which occurred between 1645 and 1715 during the "Little Ice Age". By statistically analyzing the observed minima, the researchers could show that these are not cyclical processes, but that their occurrence at intervals of approximately one to two thousand years follows a mathematical random process.

To verify this in a model, the researchers expanded their solar dynamo simulations to a longer period of 30,000 years. In fact, in addition to the shorter cycles, there were irregular, sudden drops in magnetic activity every 1000 to 2000 years. "We see in our simulations how a north-south asymmetry forms, which eventually becomes too strong and goes out of sync until everything collapses. The system tips into chaos and then takes a while to get back into sync again," says Stefani. But this result also means that very long-term solar activity forecasts—for example, to determine influence on climate developments—are almost impossible.

## The Sun Dagger

The 2-3 meter sandstone slabs, at Fajada Butte in Chaco Canyon, cast shadows of the late morning and midday sun to indicate both solstices and equinoxes.The first, clearly visible on this photograph, is a large spiral, 34 cm high and 41 cm wide. The spiral numbers nine and a half turns, moving outwards and counterclockwise from its center. The second, much smaller petroglyph is a coiled snake form, located higher and to the left of the large spiral, and is hidden from view here.

At the summer solstice, before midday, the shafts of light illuminating the cliff face interact with the large spiral in a visually striking manner. Shortly past 11:00am local solar time, a small spot of sunlight first appears above the large spiral. It lengthens vertically into a very narrow, downward pointing elongated triangle (or "dagger"). The dagger continues growing and moving downward until, around 11:15am, it cleanly bisects the spiral almost over its entire height. At this point the Sun is high enough in the sky for the overhang above site to begin casting a shadow on the slabs, and in doing so cuts off the upper end of the dagger. This leads to the dagger as a whole moving downwards while maintaining approximately the same length, until it slips off the cliff face and disappears completely. The whole event lasts a little over 20 minutes. On the winter solstice a = similar sequence of events unfolds, except that this time two light shafts illuminate the cliff face. Once again the shafts start off as small light spots above the spiral, and subsequently stretch downward until they bracket the large spiral. At the equinoxes a long, thin shaft of light illuminates the large spiral off center, but a second, smaller shaft bisects the coil on the smaller snake petroglyph.

Recall from page "Horizon Calendars" that shortly before local solar noon the Sun is moving almost horizontally across the sky. To produce a downward moving light pattern then requires the interaction of two inclined or curved surfaces. Here the needed surfaces are situated near the top of the slabs. It has been suggested that those critical surfaces were further shaped by the Anasazi, but the faint pecking marks noted as supporting evidence for this hypothesis are effectively impossible to distinguish from naturally occurring sandstone weathering patterns.

In 1982 the National Park Service restricted public access to the site, for fear of accelerating erosion and soil loss around the slabs caused by increased visitor volume. Those fears were unfortunately well-founded. In 1989 it was noted that the summer solstice light pattern was altered, due to slight shifting of two of the sandstone slabs. The Sun dagger, as seen on this slide, is now considerably thicker than it was when first studied in the late 1970s. In addition, rather than moving vertically downward, the dagger now forms slightly left of a vertical line bisecting the spiral, and drifts towards center as it moves downward. Subsequent observations revealed that the winter solstice and equinox patterns were severely altered, as compared to the patterns recorded when the site was first studied. A retaining wall was built around the base of the slabs to prevent further erosion and slab movement, and at this writing access to the site is only allowed for yearly site monitoring.

## Ep. 171: Solar System Movements and Positions

Even in ancient times, astronomers realized there was something different about the planets – they move! The movement of the planets and their moons are governed by gravity. And as we all know, gravity can do some funny things.

### Transcript: Solar System Movements

Fraser: Even in ancient times astronomers realized there was something different about the planets–they move! The movement of the planets and their moons are governed by gravity, and as we all know, gravity can do some funny things. So, let’s kind of go back to ancient history and sort of get an idea of what the ancient people thought… the way the universe worked.
Pamela: Well, originally it was all based on philosophy, looking up and imagining how the pieces fit together and, using philosophy, it was Aristotle who led the idea that all the planets orbited on perfect circles and the stars were embedded on a perfect sphere that embraced the planet Earth. And so it was all nested circles with the earth at the center moving outwards and outwards.
Fraser: And standing on the surface of the earth, that’s the natural conclusion that you would come to. You look up into the sky and the stars seem to be moving and so it seems like the stars are moving around you, the sun is moving, the moon is moving, the planets are moving…
Pamela: And from one season to the next you don’t see the stars move relative to one another, which is what you kind of expect if we were in a little tiny system where stars weren’t that far away. Since the stars didn’t seem to move, they just seemed to rotate around and around and around, it seemed natural… ok, they’re just embedded on a flat… well they’re embedded on the inside of a sphere that’s not too big that embraces the planet
earth.
Fraser: Right. And how well were astronomers able to use this model to do astronomy?
Pamela: It made some predictions, but they weren’t particularly accurate. You couldn’t, for instance, using simply descriptions of… well, here’s the sun on a circle, here’s the moon on a circle, come up with a precise day and time for when an eclipse would be visible on the surface of the earth. You couldn’t accurately say this planet was going to be right next to this star at this moment in time. So we had a theory, we just didn’t have a way to back it up with evidence.
Fraser: Right. And then along came Copernicus.
Pamela: Well, Copernicus was one of the first ones to move that we should instead of having the earth at the center, have the sun at the center. Now this was again in part for philosophy and religious reasons. Unfortunately, his theory, while having at least the sun in the right place, it didn’t do anything to really improve our ability to predict where things are located. And sadly at about the same time we had Ptolemy’s theory with his earth-centered system and his epicycles that circles on circles trying to control the planets’ positions… his theory was able to make much more accurate, but not completely accurate, predictions for where things would be located.
Fraser: Right. So Ptolemy’s got these circles within circles, Copernicus’s got just circles… but Ptolemy’s math actually works out better?
Pamela: Right. Because he was able to correct for things by simply adding in extra cycles, adding in extra corrections, moving things around until everything worked out just right. He still wasn’t able to make precise predictions, but he was better than Copernicus at being able to say where things would be at a given point in time.
Fraser: So when did the astronomy finally get accurate?
Pamela: Well, we finally figured out the math thanks to Kepler. He was working about the same time as Galileo� years ago. He was working with a man called Tycho Brahe who was the observationalist behind the team. Kepler was very much a theorist. So, Tycho Brahe had taken books and books and books worth of observational measurements of exactly where the planets were located. Kepler poured through these patterns looking for ways to mathematically match what had been seen on the sky. He tried all sorts of things… nesting circles mathematically within invisible geometric solids in the sky, and none of it worked. After a lot of mathematical head beating, he came to the realization that it’s not circles that the planets are orbiting on, but instead… the ellipse. It’s a slightly flattened circle in some cases, and by just making this minor change, by saying ellipses instead of circles, he was able to very accurately, within the ability of us to make measurements 400 years ago, he was able to finally predict where things would be located in the sky and when.
Fraser: And I guess part of the problem is that as a planet or some object’s following an elliptical path around the sun, the speed that they’re orbiting changes, so as they get very close to one of the nodes of this ellipse, they’re going to go very fast, while when they’re at the very far point of it, away from the sun, they’re going to go slower. So, any time you’re looking at the speed of the planet moving and trying to use that to predict where it’s going to be, you have to know the shape of that ellipse or it doesn’t do you any good.
Pamela: And for the planets that they were able to see back then–Mercury, Venus, Mars, Jupiter, and Saturn–they were very close to circles… with the exception of Mercury. It was just that slight difference that kept doing them in, mathematically, and he was able to overcome that slight difference. Now the problem is, the differences between Kepler’s predictions, which only used the sun, even though he didn’t quite know that at the time, differences between Kepler’s predictions and reality slowly began to crop up. It wasn’t until Newton came along that we were finally able to start understanding the differences and where they came from, thanks to understanding gravity.
Fraser: Right, apple dropping on his head… there’s gravity.
Pamela: Right. And it turns out that you can use the exact same mathematics to understand that apple falling that you use to understand the moon falling around the planet earth.
Fraser: Now, I don’t want any more mail about how that’s probably never really happened.
Pamela: But the original documents describing how Newton told that story to one of his colleagues are now posted online and we’ll try to link to them. So there is original documentation about this bit of gossip…
Fraser: Right. He saw an apple fall, yeah… so he said… but ok, please continue…
Pamela: Newton came along and he realized that it’s forces that are controlling the motion, that the planet Earth… it gravitationally tugs on the moon and the moon tugs back. Our mass and the moon’s mass, we orbit the sun and our planet is tugging on the moon, we’re tugging on Venus, all the different bodies are gravitationally tugging on one another. And some of the variances we see in planets’ behavior year after year after year, they’re coming up from… well, Jupiter’s giving Mars a good tug here and there, and Earth is giving Mars a good tug here and there, and together we’re slowly evolving its obit, causing its orbit to change over time. In fact, all the planets’ orbits are slowly changing over time.
Fraser: Ok, so let’s then take a look at sort of the big picture here… all the planets orbit the sun…
Pamela: Yes.
Fraser: Why?
Pamela: The best way to imagine this is that all the planets are basically racing around the gravitational equivalent of a cyclodrome, where you have essentially a dimple in space-time. And if you have enough velocity racing around the inside of this bowl, you’re just going to keep going in a circle. Now, not all of these bowls are perfect circles. The sun’s gravity essentially creates a pit in space-time, and as long as the planets keep moving, they keep staying on the wall of this hole in the continuum. There’s other descriptions where we mathematically start saying there’s gravitons flying back and forth, and it’s the gravitons that are communicating, “hey, there’s gravity… you need to stay where you are.” But the basic idea is the planets are trying to move in a perfectly straight line, and the gravity from the sun is going, “no… come to me.” So as they try and go in a straight line, the constant yanking of the sun going “no… come to me” bends that straight line. So, they move a little bit forward, they move a little bit towards the sun… they move a little bit forward, they move a little bit toward the sun. And if any of you ever used the Logo computer language back in the 󈨔s, this is how you draw a circle… you move forward… you turn. You move forward… you turn. And that’s exactly how an orbit works.
Fraser: Right, and in this situation those forces are in perfect balance. If you made the sun more massive, the planets would all spiral inward and be destroyed. And if you made the sun less massive, the planets would all spiral outward into space and be lost forever. If you made the planets move any slower in their orbits, they would all spiral inward and be destroyed, and if you made the planets any faster they would all spiral outward. It’s this exact, perfect balance. And that’s leftover from the creation of the solar system way back when…
Pamela: It’s not quite that deadly… if you varied something slightly, it would just move to a stable larger or smaller orbit. This is happening all the time because the sun is constantly losing mass due to its stellar wind, and at very miniscule levels the planets are slowly migrating away from the sun… and this is good! Because when the sun bloats itself up in a few billion years and leaves the main sequence, the earth will have migrated to a possibly safe distance away. But yeah, slight variations in any parameter cause the orbits to change.
Fraser: Alright, so let’s take one planet, let’s take a look at say Mercury, for example…
Pamela: Mercury, of course, is one of the completely…
Fraser: It’s one of the more complicated ones, but sure… so then what way is it going around the sun… what direction…
Pamela: If you look down on the solar system in such a way that all the planets are moving in a clockwise direction, then this is said to be looking down on the north poles of every thing except for Venus which believes in standing on its head. So, looking down from the north at the solar system, Mercury appears to be going around and around and around in an anticlockwise direction. But its orbit is fairly elliptical. If you speak eccentricities, it has an eccentricity a little over 0.2 and this means you can actually see how flattened that circle is with your eye. On one side of its orbit it’s a lot closer to the sun than on the other side of its orbit. And when it’s closest to the sun, tidal forces… these are the same forces that cause us to always see the exact same side of the moon… tidal forces make it not want to rotate. So, during that period of time when it’s closest to the sun, the sun pretty much stands still in the Mercurial sky. It’s only as Mercury gets further and further away from the sun that it’s able to orbit a little bit more freely. Luckily, it’s moving really fast when it’s close to the sun. It’s moving really slowly when it’s far away from the sun. So, the rate at which it rotates on its axis actually stays completely constant, it’s just relative to where it is in its orbit, at that point when it’s closest to the sun, the sun appears to completely stand still in the sky.
Fraser: So then if I could stand on the surface of Mercury and watch the sun, over the course of a day, or a year, what would I see?
Pamela: Well, you’d have to do a whole lot of waiting to see very much. A day on Mercury relative to its year is a fairly long, long thing to wait through. In fact, for every three times the planet experiences a day, it goes all the way around the sun twice. This is what’s called a spin-orbit resonance. For the longest time, astronomers actually thought that Mercury was completely tidally locked. It’s really hard to try to image the surface of Mercury from here, and it wasn’t until the 1960s when we started imaging Mercury using radar that was sent from big radar dishes here on the planet that we realized oh… it is rotating, and realized over years… Mercury years… of watching it that it has this resonance in how long it takes to rotate and how long it takes to experience a year.
Fraser: And this is where I think we should distinguish between solar days and sidereal days…
Pamela: Right.
Fraser: A solar day is how long it takes the sun to return to the same position in the sky, while a sidereal day is how long would it take if you could look above the planet and not really think about the sun… how long does it take for it to turn back to the same spot. And here on earth, those are fairly similar… which we’ll get to in a second, but on Mercury, they’re totally different.
Pamela: They’re totally different. And this is because we do have this strange rotation rate, where in order to get the sun geometrically in the same place in the sky, back to exactly noon straight overhead, you have to keep going and going and going around the sun, whereas well before you get the sun back in the same place, you’ve already gotten the stars back in the same place.
Fraser: Right. Now Venus… let’s move on out, Venus is even weirder. I mean it’s going around the sun in the same direction… all the planets in the same direction. They’re all going in that counterclockwise direction, right?
Pamela: Right. Now the problem with Venus is when you look at… well where’s its north pole? Its north pole, if you define the north pole as where your standing such that when you look at your feet everything is going around in an anticlockwise direction, its north pole is actually opposite of everything else in the solar system. In fact, when you look down, you see all the rest of the planets, happily you can see, for the most part–we have another problem when we get to Uranus–you can look down and see all their clouds going around in the same anticlockwise direction that they’re orbiting around the sun. But with Venus, you look down and its clouds are going about in a clockwise direction as it orbits in that anticlockwise direction about the sun.
Fraser: Right. So imagine… look at the whole solar system from above, you’re going to see all the planets all moving in the same direction… so Venus is obeying that rule. But yet, if you actually look at the planet itself, from the position of the stars, you would see it turning slowly backwards. And of course Venus is even more weird because a day on Venus is longer than its year… it’s backwards day is longer than its year.
Pamela: Right. Yeah, so Venus is even weirder. First of all you have this upside-down motion, but then when you start looking at how long it takes for the sun and the stars to get back to where they started, well it’s year… let’s start with what it’s year is. To get all the way around the sun is 224 earth days. And to an observer standing on the surface of Venus, you have the sun rising in the west and setting in the east, and from one noon to the next noon, that’s going to be 116 days. So, that’s most of the time that it takes you to get all the way around the sun. But because everything’s going from west to east, the amount of time it takes to get the stars back in the same place that’s actually going to be longer than an entire year. So, to get the stars back to where they started out at the beginning of the year takes 243 days. This is kind of weird and kind of special to Venus.
Fraser: Now I think we’re fairly familiar and comfortable with our days here on Earth, right…
Pamela: I hope so…
Fraser: We’ve got the earth… well we say that a day takes 24 hours, and I think we’ve mentioned that that’s a solar day. So it takes 24 hours for the sun to come back to the same place, while a sidereal day is shorter than that.
Pamela: Right, and that’s to get the stars back to the exact same place they were in the sky.
Fraser: And that’s actually the true rotational speed of the earth.
Pamela: Right. It’s just not useful for when you’re trying to make plans for the future because the stars vary a little bit too much from one point in the year to the next.
Fraser: Mars is similar to Earth, right… just a little over 24 hours. Jupiter has a crazy-fast rotation speed.
Pamela: Jupiter… it has an amazing speed of 9.9 hours to get the sun back to where it started. And then Saturn we don’t know. Saturn’s a bit problematic. Its atmosphere refuses to let us understand what’s going on down in the center. We’re trying to understand it using magnetic fields, but I’ll just leave it at… we don’t know.
Fraser: Right. We kind of approximately sorta think it’s about 10 1/2 hours, but…
Pamela: We don’t know.
Fraser: We don’t know for sure…. because there’s many ways to measure that. But I think, you know, the really interesting one is Uranus.
Pamela: Right. And this is the planet that apparently had a very bad life in the past. It’s tilted completely on its side. And there’s really only two ways to have a planet have that particular fate. One is that you just hit it with something about the size of the planet Earth, and if I were Uranus, I certainly wouldn’t want to get hit with something the size of the planet Earth. And the other way is to be a victim of gravitational abuse from Saturn and Jupiter going through a weird resonance period during the early part of the solar system. We’re not sure which one happened… it also could have been a combination of Uranus getting knocked about gravitationally by Saturn and Jupiter and getting hit by something smaller. We don’t know. All we know is it’s 97 degrees tilted over.
Fraser: Right. Which is essentially tilted over on its side.
Pamela: Right. So for all intents and purposes, its pole points at the sun when it has its winter solstice and when it has its summer solstice.
Fraser: Right. And this is where you sort of got to think about it. Imagine Uranus tilted over on its side, but it’s not like it’s rolling around the sun.
Pamela: No, it always keeps its pole pointed at the same set of stars.
Fraser: Right. So sometimes that pole has to go through the sun first to get to those stars, and other times the sun is on the opposite side of the planet, but still… Now, Pluto is not a planet anymore, but it used to have… I guess it still has a highly eccentric orbit.
Pamela: Right. And the thing is, though, we talk about it having a highly eccentric orbit, but its eccentricity isn’t mathematically all that different from Mercury’s. Mercury’s eccentricity is 0.206 and Pluto’s is 0.248, so those are pretty similar. The reason we notice Pluto’s eccentricity is because its orbit cuts back and forth in front of Neptune. So sometimes Pluto is closer to the sun than Neptune is and sometimes Neptune is closer to the sun than Pluto is.
Fraser: And that difference in distance actually has a fairly interesting effect on Pluto which is that at its closest point it warms up to the point that its atmosphere pops up. Then when it’s further away, its atmosphere freezes back down onto the surface.
Pamela: Right. So we have a planet that sometimes has an atmosphere and sometimes doesn’t. This actually led Mario Livio to make a quote that I will forever love and that’s “if you took Pluto and brought it in close to the sun it would turn into a comet, and that’s no way for a planet to behave.” So, what we’re seeing is as Pluto gets closer to the sun it starts to “fuzz up” the same way a comet does as it gets closer and closer to the sun.
Fraser: It’s exhibiting very comet-like behaviors. That’s pretty funny. Ok, so now we’ve talked about the planets, and talked about how they’re rotating… I want to talk a bit then… if we imagine the solar system as a flat… like a record… that is the plane of the ecliptic. And the planets are mostly orbiting on that, but not quite.
Pamela: Each of the planets’ orbits is (relative to the earth’s) a little bit tilted in one way or another. Exactly how much they’re tilted varies. And for the most part, they aren’t tilted very much. So we have for Mercury the orbital inclination–it’s the most–it has a 7 degree tilt, Venus has about 3.4. All the rest are tilted less than 3 degrees. This is very slight and not the type of thing that’s going to be very easy for you to get out and start measuring with your protractor.
Fraser: But this is why we don’t see Venus pass in front of the sun…
Pamela: All the time…
Fraser: All the time… right. It’s sometimes above the sun from our vantage point and sometimes it’s below the sun.
Pamela: So the slight tilts that are out there do create a much less interesting observational universe. But what’s neat is when we start looking out at the dwarf planets, at all the trans-Neptunian objects. They do have all sorts of different crazy tilts, where we see that Pluto is tilted 17 degrees and Himae is 28 degrees, so is Mak-mak, and Eros is 44 degrees tilted. We also start seeing the asteroids with tilts… where Ceres has an 11 degree tilt relative to the earth’s orbit. So it’s just the planets that seem to be locked in to this disk where we start looking at asteroids and comets and dwarf planets, these small-mass leftover bits in the solar system, they sort of end up on much more catawampus orbits around the sun.
Fraser: That is the first time you’ve used that word in this podcast, I think… catawampus…
Pamela: It’s the best way to describe these objects…
Fraser: But still, if you were going to go look to discover new planets… this is Mike Brown’s approach, the best place to look is on the plane of the ecliptic. That’s where you’re going to see them all. You’re not going to look straight up above the solar system and see them, or down below. You’re going to see them somewhere in that zone… helps you constrain your search.
Pamela: And every one of these objects crosses the ecliptic, so no matter what you’re looking at, at some point it’s going to be in the disk of the solar system.
Fraser: Now, what about the comets and the asteroids? I mean, the asteroids have kind of weirder… some weirder orbits and the comets can have really bizarre ones.
Pamela: The asteroids have a bunch of varied orbits, and for the most part they constrain themselves to being between Mars and Jupiter. But within all of these orbits we see occasional collisions… we think we just saw the remnants of one recently out in the asteroid belt. We also see asteroids that periodically decide that they’re going to come in and start crossing our own Earth’s orbit periodically. These are more of the Near Earth Objects. For the most part, yes… they do have more elliptical orbits but they’re not ranging over the entire solar system the way comets do. Comets in many cases will start out in the Kuiper Belt, so they’re starting out at a distance, in many cases, at a distance greater than Neptune’s orbit, and then plunging all the way in… in some cases to plunge straight into the sun, but often to come in and dance between the orbits of Mercury and the sun or Venus or Earth and just coming right in to the inner part of the solar system and growing huge tails as they melt away in the heat.
Fraser: And when they’re at their closest point, they’re moving very quickly and then they slow back down. That’s why we’ll see them accelerate as they approach the sun and then slow back down as they’re heading back out into deep space. They can go in orbits that last tens of thousands of years.
Pamela: And many of them will have, the one’s that we’re happy to keep observing over and over and over again, like Halley’s comet, will have orbits that are measured in tens of years, but the period of time that they’re in the inner solar system is a very small fraction.
Fraser: I guess the last thing to talk about is how the movement of the moons is governed as well by gravity.
Pamela: And again, we start seeing these interesting resonances, these interesting beat frequencies, when we start looking out at systems that have multiple moons. There’re people that believe that the reason that Venus has such a really long day is it’s in resonance with the planet Earth so that we’re pretty much always seeing, when we’re on closest approach, the same part of Venus. When we start getting out and looking at Jupiter’s moons, we see different orbital resonances that keep its moons coming in so that they line up the same way every few orbits. We see this in particular with Io and Europa which are both being tidally heated leading to, on Europa, liquid water beneath its surface and on Io, massive amounts of volcanism.
Fraser: There’s a resonance between those two moons, so every time Io goes around Jupiter twice for every time Europa goes around once?
Pamela: There’s actually a really neat 1 to 2 to 4 resonance between Jupiter’s moons Ganymede, Europa, and Io, leading to Ganymede goes around once for every 2 times Europa goes around for every 4 times Io goes around. We also see a 2 to 3 resonance with Pluto and Neptune. Resonances like this happen all over the solar system. And what’s great is we can see the exact same mathematics applied to Jupiter and its moons that we see with the planets. This was one of the things that really made it clear that Kepler’s physics and Newton’s physics were right was we had Galileo looking at Jupiter’s moons at the same–relatively, in the grand scheme of human history–that Kepler was coming up with his orbital mathematic equations… Kepler’s three laws. Scientists in the following decades were able to say, oh… this applies to Jupiter as well. So we can look out and we can apply the same mathematics to Jupiter, we can see it at Saturn, we can see it orbiting all of the planets. We know that these gravitational tugs tend to lead to things ending up in resonant orbits.
Fraser: Of course, that story is going on at even larger scales with the movements of the galaxies and the interactions of the galaxies in the whole large-scale structure of the universe. But that’s another story… that we’ve already told, I think. Alright, well thanks a lot, Pamela.
Pamela: It’s been my pleasure, Fraser.
Fraser: Talk to you again…
Pamela: Bye bye.

## Motion of the Moon against the Starry Vault

The Sun goes around the starry vault once a year, the Moon goes completely around every month.

Does it follow the same path as the Sun?

The answer is no, but it's close. It always stays within 5 degrees of the ecliptic, so it goes through the same set of constellations, "the Moon is in the Seventh House" and all that. In fact, the "houses"--the signs of the Zodiac--are defined to occupy a band of the stars that stretches eight degrees either way from the ecliptic, because that turns out to be wide enough that the Sun, Moon and all the planets lie within it.

How can we understand the Moon's motion from our present perspective? If the Earth, the Moon and the Sun were all in the same plane, in other words, if the moon's orbit was in the same plane as the Earth's orbit around the Sun, the Moon would follow the ecliptic. In fact, the Moon's orbit is tilted at 5 degrees to the Earth's orbit around the Sun.

This also explains why eclipses of the Moon (and Sun) don't happen every month, which they would if everything was in the same plane. In fact, they only occur when the moon's path crosses the ecliptic, hence the name.

A nice three-dimensional representation, published by Cellario in 1627, can be found at //www.atlascoelestis.com/Cell%2009.htm : here it is:

Figure 1. Portrait of Leonardo da Vinci by the painter Francesco Melzi.

While many of Leonardo's statements proved eventually to be wrong, some of them do demonstrate his immense intellectual curiosity, his unusually keen power of observation, and his ability to distill simple conclusions even from complex data.

Take, for instance, his crisp description of the Sun: "The Sun has substance, shape, movement, radiance, heat and generative power and these qualities all emanate from itself without its diminution." Indeed, the timescale on which the Sun evolves (about ten billion years) is so long, that it would appear unchanged during a human lifetime. Similarly, Leonardo addressed the question of whether the Sun is hot: "Some say that the Sun is not hot because it is not the color of fire is much paler and clearer. To these we may reply that when liquified bronze is at its maximum of heat it most resembles the Sun in color, and when it is less hot it has more the color of fire."

Generally, Leonardo's interest in astronomy stemmed primarily from his attentiveness to vision and to optics. Still, he owned a copy of Ptolemy's "Cosmography", as well as a book by the medieval Persian astronomer Abu Mashar.

One area in which Leonardo anticipated the later findings by Galileo, and clearly departed from the Aristotelian views of his time, concerned the nature of the Moon. Unlike Aristotle, who made a clear distinction between the "terrestrial" and the "celestial", Leonardo concluded that there is no real difference between the Earth and the Moon: "If you were on the Moon. , our Earth would appear to you to make the same effect as does the Moon." He further stated that: "The Moon is not luminous in itself. It does not shine without the Sun."

Leonardo also pointed out contradictions in the many erroneous ideas that existed about the spots seen on the lunar surface. Thus he declared, for instance, "some have said that vapors are given off from the Moon after the manner of clouds, and are interposed between the Moon and our eyes. If this were the case these spots would never be fixed either as to position or shape and when the Moon was seen from different points, even although these spots did not alter their position, they would change their shape."

Figure 2. A page from Leonardo's notebook, showing a sketch and accompanying text that may be related to the design of a telescope.

A question that has intrigued many Leonardo scholars was whether or not he had ever attempted to design a telescope. After examining much of the evidence, my personal (non-professional) conclusion is that while Leonardo certainly explored some of the theoretical aspects involved in the construction of telescopes (and he even made such statements as: "Construct glasses to see the Moon magnified"), he never actually built one. Figure 2 presents a sketch from Leonardo's notebook, accompanied by text part of which reads: "eyeglass of crystal thick at the sizes at ounce of an ounce." Leonardo researcher Domenico Argentieri found the full text to be suggestive of a design of a telescope.

To conclude, Leonardo was definitely not an astronomer, but he was fascinated by nature, and he did not hesitate to attempt to provide explanations for natural phenomena, or to suggest tools that could help decipher nature's secrets.