Astronomy - The Solar System

Mercury	Gaspra	Saturn	Iapetus	Comet Wild 2
Venus	Ida	Mimas	Uranus
Earth	Mathilde	Enceladus	Miranda
Earth's Moon (Luna)	Jupiter	Tethys	Ariel
Mars	Io	Dione	Titania
Phobos	Europa	Rhea	Neptune
Deimos	Ganymede	Titan	Triton
Eros	Callisto	Hyperion	Comet Tempel 1

Pay attention to atmospheric features such as density, coloration and movement.

Yellow and orange coloration are largely due to sulfur compounds, although in Titan's case its coloration comes from a heavy hydrocarbon haze. Jupiter's ammonia content also affects its color, and can be seen in the greenish tints reflected from the night sides of the Galilean moons. Methane absorbs light in the red and yellow wavelengths, leading to Uranus' (with less methane) and Neptune's (with more methane) coloration.

To get a feel for how difficult this business is, read this analysis of Europa.

This image shows the planets to scale:

(source), and this one shows some of the moons to scale:

(source). This image shows the orbits of the outer planets:

(source).

Have you ever seen the far side of the Moon? (source)

(View GOES 2/26/98 eclipse images (source).)

(View Cosmos DVD 4, episode 6, on Voyager at Europa.)

(View Cosmos DVD 3, episode 4, comet simulations, on the Tunguska Event.)

(View Solar System Animations from the Minor Planet Center.)

Some of the smallest constituents of the Solar System are dust particles.

Portfolio Exercise 4: Categorize each body in the list above as to the distinguishing feature(s) of its landscape: tectonic, volcanic, geyser or meteoric. You may have some bodies in which multiple features are present.

For any characterization other than meteoric, find NASA images which support your categories; include them (with source references) in your portfolio. Annotate the pictures, circling and identifying the features which support your categorization.

Solar System Observation

Body	Perihelion	Aphelion	Ang. Diam. @	Orbital	Orbital	Rotational	Axial Tilt
	(AU)	(AU)	ca. (as)	Period (Yrs)	Inclination	Period (Days)
Sun			1918	2.2 * 108		25.38	7.25
Mercury	0.3075	0.4667	13.03	0.241	7	58.65	0
Venus	0.718	0.728	65.44	0.615	3.39	-243	177.3
Earth	0.983	1.017		1	5. * 10-5	0.9973	23.45
The Moon	0.00243	0.00271	1968	0.075	5.145	27.32	6.68
Mars	1.381	1.666	25.73	1.881	1.8	1.026	25.19
Phobos	6.175 * 10-5	6.363 * 10-5	0.1047	8.731 * 10-4	1	1.026
Deimos	1.567 * 10-4	1.569 * 10-4	0.05824	0.003456	1.8	1.026
Gaspra						0.2917
Ida						0.193
Jupiter	4.952	5.455	50.1	11.86	1.305	0.4135	3.12
Io	0.00281	0.002832	1.2761	0.004844	0.04	1.769
Europa	0.004445	0.004526	1.097	0.009723	0.47	3.551
Ganymede	0.007138	0.007167	1.846	0.01959	0.21	7.155
Callisto	0.0125	0.01268	1.684	0.04569	0.51	16.69
Saturn	9.021	10.05	20.76	29.4	2.484	0.444	26.73
Mimas	0.001215	0.001265	0.06753	0.00258	1.53	0.9424
Enceladus	0.001584	0.001598	0.0851	0.003751	0	1.37
Tethys	0.00197	0.00197	0.1826	0.005169	1.86	1.888
Dione	0.002517	0.002528	0.1929	0.007493	0.02	2.737
Rhea	0.00352	0.003527	0.2632	0.01237	0.35	4.518
Titan	0.007929	0.008406	0.8871	0.04366	0.33	15.95
Hyperion	0.00887	0.01093	0.03062	0.0583	0.43	13	(chaotic)
Iaepetus	0.02313	0.02448	0.2474	0.2172	14.72	79.33
Uranus	18.29	20.1	4.086	84.02	0.77	-0.7196	97.86
Miranda	8.658 * 10-4	8.705 * 10-4	0.03769	0.00387	4.2	1.413
Ariel	0.001272	0.001281	0.09246	0.0069	0.3	2.52
Titania	0.00291	0.002923	0.126	0.02384	0.14	8.706
Neptune	29.81	30.33	2.372	164.8	1.769	0.6712	29.58
Triton	0.002371	0.002371	0.1295	-0.01609	157.3	-5.877

("ca." stands for "closest approach".)

Since we telescopically measure only angular positions in the sky, we cannot measure perihelion and aphelion directly; we require an independent measurement of distance. This is done, for example, by radar ranging of Venus at closest approach. Thus the perihelion and aphelion values are actually computed and not directly observed. Planetary orbits are elliptical, and orbital parameters such as perihelion and aphelion are obtained by fitting careful measurements to elliptical orbits.

The data in the tables in this section come from NASA. There is an Excel spreadsheet available containing some of this information. It will serve as a starting point for your efforts to duplicate the conclusions below.

Orbits

In this plot, the sum of the lengths of the two red lines is a constant for every point on the ellipse.

• perihelion = semimajor axis * (1 - eccentricity)
• aphelion = semimajor axis * (1 + eccentricity)

and

• radians = p * degrees / 180
• diameter = distance * angular diameter_radians

we can compute the following parameters:

Body	a(AU)	Eccentricity	R(m)	R(Earth)
Sun	1.62 * 109		6.955 * 108	109
Mercury	0.3871	0.2056	2.44 * 106	0.3825
Venus	0.7233	0.0068	6.052 * 106	0.9488
Earth	1	0.01671	6.378 * 106	1
The Moon	0.00257	0.0549	1.734 * 106	0.2719
Mars	1.524	0.0934	3.397 * 106	0.5326
Phobos	6.269 * 10-5	0.015	1.3816 * 104	0.002166
Deimos	1.568 * 10-4	5. * 10-4	7688	0.001205
Gaspra			8428	0.001321
Ida			1.57 * 104	0.002462
Mathilde			2.971 * 104	0.004658
Jupiter	5.203	0.04839	7.149 * 107	11.21
Io	0.002821	0.004	1.821 * 106	0.2855
Europa	0.004485	0.009	1.565 * 106	0.2454
Ganymede	0.007153	0.002	2.634 * 106	0.413
Callisto	0.01259	0.007	2.403 * 106	0.3768
Saturn	9.537	0.05415	6.027 * 107	9.449
Mimas	0.00124	0.0202	1.96 * 105	0.03073
Enceladus	0.001591	0.00452	2.47 * 105	0.03873
Tethys	0.00197	0	5.3 * 105	0.0831
Dione	0.002523	0.00223	5.6 * 105	0.0878
Rhea	0.003523	0.001	7.64 * 105	0.1198
Titan	0.008167	0.02919	2.575 * 106	0.4037
Hyperion	0.0099	0.104	8.878 * 104	0.01392
Iaepetus	0.02381	0.02828	7.18 * 105	0.1126
Uranus	19.19	0.04717	2.559 * 107	4.012
Miranda	8.681 * 10-4	0.0027	2.36 * 105	0.037
Ariel	0.001276	0.0034	5.79 * 105	0.09078
Titania	0.002916	0.0022	7.889 * 105	0.1237
Neptune	30.07	0.00859	2.476 * 107	3.883
Triton	0.002371	1.6 * 10-5	1.352 * 106	0.212
Tempel 1			3103	4.865 * 10-4
Wild 2			2750	4.312 * 10-4

(Here and in the following, "(Earth)" means the values are multiples of that value for the Earth.)

• the orientation of the ellipse with respect to, for instance, the direction of the galactic center;
• the angle of inclination of the plane of the ellipse with respect to the plane of the Earth's orbit;
• the angle of the twist of the plane of the ellipse (around the semimajor axis), and
• the position of the planet on its ellipse at a specific time.

Together these 6 values are called orbital elements. From them we can predict the past and future positions of any of the planets, to reasonable accuracy, within about 20 years of the time mentioned above. Beyond those dates, gravitational interactions between the planets must be taken into account.

There are subtle variations in eccentricity and tilt which cause long term cycles in the amount of sunlight received in the northern hemisphere, and which drive cyclic climate change:

These cycles were discovered by Milutin Milankovitch, a Serbian mathematician, and account for the ice ages which occur in 100000 and 41000 year cycles, as well as the smaller variations that occur in 19000 to 23000 year cycles (source).

They do not account for the increases in average global temperature since 1880.

Portfolio Exercise 5: Compute the following characteristics for each body in the table above: volume (in units of Earth's volume), surface area (in units of Earth's surface area) and average orbital velocity (in km/hour). Include details on the formulas used to compute the radius of each body.

Mass and Motion

orbital period = 2 * p * (semimajor axis³ / (G * mass))^1/2

force due to gravity = G * mass₁ * mass₂ / distance²

The relationship between Newton's Law of Gravity and Kepler's Laws of Motion is discussed in a Mathematica Notebook. You need Mathematica or Mathematica Player to view Mathematica Notebooks.

Gauss' Law tells us that the gravitational force due to a spherically symmetric mass is equivalent to the force due to a point particle of the same mass, located at the center. Therefore we will usually treat planets (and stars!) as if all their mass was located at a point at their center.

Using these masses, we can compute a number of interesting parameters: their average densities, their surface gravities (by setting "mass₂" to 1 and "distance" to the radius), their orbital angular momenta ("L", using the equation

angular momentum = 2 * p * mass * rotation rate * orbital radius²)

and the escape velocity (obtained from equating the kinetic energy mv²/2 to the gravitational energy Gm/r):

escape velocity = (2 * G * mass / distance)^1/2

In both of these equations, the mass is the mass of the body we are orbiting or escaping from; the results are independent of the mass of our spacecraft. The distance in each equation is the distance from the center of the body (its radius in the case of the escape velocity).

Planetary magnetic fields are believed to be the product of rotation and liquid metallic cores. We have been able to measure the magnetic fields of some of these bodies using space probes:

Body	Magnetic Field (Earth)
Sun	2
Mercury	0.011
Venus	0.001
Earth	1
Mars	0.001
Jupiter	13.89
Saturn	0.67
Uranus	0.74
Neptune	0.43

Here are images of auroras on Earth in optical wavelengths:

(source), Jupiter in x-ray wavelengths:

(source) and Saturn in ultraviolet wavelengths:

(source). There is also a good movie of terrestrial auroras from the POLAR mission (source).

Portfolio Exercise 6: Use the relation between the orbital period, the semimajor axis length and the total mass, to compute the masses of the Sun and those planets with moons.

Recall from our derivation of Kepler's Laws from Newton's that the mass in this relation is the combined mass of the parent and the satellite. For this reason, you will get the best results if you choose the satellite with the lowest mass (ie., use Mercury's orbital parameters to compute the mass of the Sun, Deimos' to compute Mars' mass, etc.).

Compare these values to the measured values quoted above: in terms of a percentage, how far off are your values from those in the table above?

For each body in the table above, compute the orbital velocity at a distance of 400 km from the surface, and the escape velocity from the surface. Compute each value in both km/hr and in multiples of the Earth's value.

Here are some time lapse photos of tidal phenomena caused by the Moon.

Body 1	Body 2	atidal (Moon on Earth)	atidal / g
Sun	Mercury	2.955	9.008 * 10-7
Sun	Venus	1.123	1.429 * 10-7
Sun	Earth	0.4481	5.161 * 10-8
Sun	The Moon	0.1218	8.43 * 10-8
Earth	The Moon	21.7	1.502 * 10-5
The Moon	Earth	1	1.152 * 10-7
Mars	Phobos	1274	0.387
Mars	Deimos	45.22	0.01899
Jupiter	Io	5476	0.003438
Jupiter	Europa	1167	0.001007
Jupiter	Ganymede	484.5	3.837 * 10-4
Jupiter	Callisto	80.96	7.349 * 10-5
Io	Jupiter	13.33	6.069 * 10-7
Io	Europa	1.081	9.327 * 10-7
Io	Ganymede	0.1029	8.146 * 10-8
Europa	Jupiter	1.593	7.252 * 10-8
Europa	Io	0.6768	4.25 * 10-7
Europa	Ganymede	0.2377	1.882 * 10-7
Ganymede	Jupiter	1.135	5.168 * 10-8
Ganymede	Io	0.1178	7.395 * 10-8
Ganymede	Europa	0.4343	3.748 * 10-7
Callisto	Jupiter	0.1444	6.574 * 10-9
Saturn	Mimas	2067	0.03581
Saturn	Enceladus	1233	0.01818
Saturn	Tethys	1396	0.01058
Saturn	Dione	701.9	0.003384
Saturn	Rhea	351.6	0.001503
Saturn	Titan	95.2	7.935 * 10-5
Saturn	Hyperion	1.837	3.062 * 10-4
Saturn	Iaepetus	1.069	5.825 * 10-6
Tethys	Saturn	0.2478	2.677 * 10-8
Tethys	Enceladus	0.1015	1.496 * 10-6
Dione	Saturn	0.19	2.053 * 10-8
Dione	Tethys	0.1229	9.31 * 10-7
Rhea	Saturn	0.1352	1.461 * 10-8
Titan	Saturn	0.5673	6.13 * 10-8
Titan	Hyperion	0.08113	1.352 * 10-5
Uranus	Miranda	1109	0.01583
Uranus	Ariel	858	0.003604
Uranus	Titania	97.81	2.917 * 10-4
Miranda	Uranus	0.1275	1.626 * 10-8
Ariel	Uranus	0.73	9.309 * 10-8
Ariel	Miranda	0.1663	2.374 * 10-6
Titania	Uranus	0.1409	1.797 * 10-8
Neptune	Triton	368.9	5.33 * 10-4
Triton	Neptune	1.565	1.585 * 10-7

In addition, it is interesting to compare the tidal accelerations to that of Europa on Io, which is thought to account for much of Io's internal heating, and subsequent active volcanism. Note that values in the final column are all less than 1. If the tidal acceleration were equal to or greater than the surface gravity, the body would be gravitationally unstable and would break up. This happens to bodies lying withing the Roche Limit. Saturn's Rings lie within Saturn's Roche Limit:

(source)

Atom or Molecule	Molecular Weight
H2	2
He	4
C H4 (methane)	16
N H3 (ammonia)	17
H2 O	18
C O	28
N2	28
C2 H6 (ethane)	30
O2	32
Ar	40
C O2	44
C3 H8 (propane)	44

(View GOES Isabel mov (source); Saturn mov (source), Cosmos DVD 4, episode 6, on Jupiter, the Red Spot and Neptune.)

(View Martian Dust Devils as photographed by Spirit (source))

Dust is responsible for heat transport on Mars much as water is here on Earth.

Gravity Waves are seldom noticed in action because of their long periods; this movie is a time lapse over 40 minutes:

(View movie of gravity wave (source))

Solar System Formation

Material	Melting Point (K)
Iron	1808
Silicon	1684
Ice	273
Ammonia	195
Methane	91

(source)

HD 107146 is a yellow star much like our Sun but between 30 and 250 million years old. The radius of the cleared central region is approximately 40 AU:

(source)

In comparison, the Kuiper Belt (home to short period comets) extends to about 50 AU from the Sun. The Oort Cloud (home to long period comets) has a radius of approximately 100000 AU.

The mass of Comet Halley is about 10¹⁴ kg. It is about 40% water and about 20% organic compounds. Assuming that it is an average comet, and that comets were responsible for the presence of water on the Earth, we can compute the frequency of cometary impact in the Earth's early history. These impacts occurred mainly during a period of about 200 million years, approximately 4 billion years ago. If the total amount of water on the Earth is 1.65 * 10²¹ kg, it would have taken 41.25 million cometary impacts, or an average of about 5 impacts a year. These impacts would have deposited a further 8.25 * 10²⁰ kg of organic material.

(View Animations of Solar System Formation (source) (source))

• Introduction
• Astronomical Observation
• The Solar System
• Stars
• Galaxies
• Cosmology
• Postscript: Extraterrestrial Life
• References
• Useful Equations and Constants
• Glossary

©2008, Kenneth R. Koehler. All Rights Reserved. This document may be freely reproduced provided that this copyright notice is included.

Please send comments or suggestions to the author.