Motion in the Solar System

This applet knows where some things in the Solar System (and beyond) are. You can use it to explore a number of astronomical phenomena.
You can choose where you are from the first pop-up menu, and what you are looking at from the second. If the two are not the same, you can choose the latitude where you are; if they are the same, the latitude scroll bar becomes a "z" scroll bar, allowing you to view the body from above or below. When the "from" and "viewing" targets are different and you are viewing from a planet, you may choose either geocentric or heliocentric views. The applet begins in "heliocentric" mode, meaning you are looking at the sky in flat projection, with the latitude relative to the plane of the Solar System; as you change the date and time, or animate, you will always be at the first object, viewing the second object. In "geocentric" mode, you are viewing from the first object, but seeing the sky in polar projection (as if you were standing on the Earth).

The date and time scroll bars allow you to see the sky at a specific date and time. You can also draw and erase line-of-sight markers using the appropriate buttons, but they are only drawn when the "from" and "viewing" targets are the same.

When the "from" and "viewing" targets are different, the coordinates represent angles and the lattice lines are drawn every 15 degrees. When the "from" and "viewing" targets are the same, the coordinates are distance. All times are Universal Time.

It's a little complicated, but it's a powerful little program. Even the author hasn't fully explored its possibilities...

You need a Java-capable browser to be able to use the applets. If they do not work with your Windows system, download the Java VM (Virtual Machine) for your version of Windows at the download section at java.sun.com.

You can use it to explore the following phenomena:

These GOES 2/26/98 solar eclipse images provide an interesting perspective. (source)

Here is a time-lapse sequence of the Moon through a complete lunar cycle.


Solar System Observation

With careful telescopic observation, we can learn a number of important parameters about some of these bodies in our Solar System:

BodyPerihelionAphelionAng. Diam. @OrbitalOrbitalRotationalAxial Tilt
(AU)(AU)ca. (as)Period (Yrs)InclinationPeriod (Days)
Sun19182.2 * 10825.387.25
Mercury0.30750.466713.030.241758.650
Venus0.7180.72865.440.6153.39-243177.3
Earth0.9831.01715. * 10-50.997323.45
The Moon0.002430.0027119680.0755.14527.326.68
Mars1.3811.66625.731.8811.81.02625.19
Phobos6.175 * 10-56.363 * 10-50.10478.731 * 10-411.026
Deimos1.567 * 10-41.569 * 10-40.058240.0034561.81.026
Ceres2.5492.98531.66584.610.580.379
Eros1.1331.7830.20221.7610.830.2202
Gaspra1.82512.59290.02763.294.10.2942
Ida2.7322.990.063854.841.140.1936
Mathilde1.94223.20820.085414.316.7117.45
Vesta2.15062.57341.25173.637.140.2232
Jupiter4.9525.45550.111.861.3050.41353.12
Io0.002810.0028321.27610.0048440.041.769
Europa0.0044450.0045261.0970.0097230.473.551
Ganymede0.0071380.0071671.8460.019590.217.155
Callisto0.01250.012681.6840.045690.5116.69
Saturn9.02110.0520.7629.42.4840.44426.73
Mimas0.0012150.0012650.067530.002581.530.9424
Enceladus0.0015840.0015980.08510.00375101.37
Tethys0.001970.001970.18260.0051691.861.888
Dione0.0025170.0025280.19290.0074930.022.737
Rhea0.003520.0035270.26320.012370.354.518
Titan0.0079290.0084060.88710.043660.3315.95
Hyperion0.008870.010930.030620.05830.4313(chaotic)
Iaepetus0.023130.024480.24740.217214.7279.33
Uranus18.2920.14.08684.020.77-0.719697.86
Miranda8.658 * 10-48.705 * 10-40.037690.003874.21.413
Ariel0.0012720.0012810.092460.00690.32.52
Titania0.002910.0029230.1260.023840.148.706
Neptune29.8130.332.372164.81.7690.671229.58
Triton0.0023710.0023710.1295-0.01609157.3-5.877

("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 and 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

An ellipse is parametrized by a pair of lengths. In the definition of an ellipse, one is the length between two reference points (called foci), and the other defines the size of the ellipse: for every point on the ellipse, the sum of the distances between that point and the two foci is a constant. We can trade these lengths for two of more physical interest: the perihelion and aphelion. But we often prefer a different pair of values: the length of the semimajor axis (denoted "a") and the eccentricity (denoted "ε"), which is the ratio of the distance between the foci to the semimajor axis length (ε = 0 is a circle):

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

Using the above information and the equations

and

we can compute the following parameters:

Bodya(AU)EccentricityR(m)R(Earth)
Sun1.62 * 1096.955 * 108109
Mercury0.38710.20562.44 * 1060.3825
Venus0.72330.00686.052 * 1060.9488
Earth10.016716.378 * 1061
The Moon0.002570.05491.734 * 1060.2719
Mars1.5240.09343.397 * 1060.5326
Phobos6.269 * 10-50.0151.3816 * 1040.002166
Deimos1.568 * 10-45. * 10-476880.001205
Ceres2.7670.07894.73 * 1050.0742
Eros1.4580.2229110010.001725
Gaspra2.2090.173884280.001321
Ida2.8610.04512.025 * 1040.003175
Mathilde2.6460.2663.265 * 1040.005118
Vesta2.3620.08952.65 * 1050.04155
Jupiter5.2030.048397.149 * 10711.21
Io0.0028210.0041.821 * 1060.2855
Europa0.0044850.0091.565 * 1060.2454
Ganymede0.0071530.0022.634 * 1060.413
Callisto0.012590.0072.403 * 1060.3768
Saturn9.5370.054156.027 * 1079.449
Mimas0.001240.02021.96 * 1050.03073
Enceladus0.0015910.004522.47 * 1050.03873
Tethys0.0019705.3 * 1050.0831
Dione0.0025230.002235.6 * 1050.0878
Rhea0.0035230.0017.64 * 1050.1198
Titan0.0081670.029192.575 * 1060.4037
Hyperion0.00990.1048.878 * 1040.01392
Iaepetus0.023810.028287.18 * 1050.1126
Uranus19.190.047172.559 * 1074.012
Miranda8.681 * 10-40.00272.36 * 1050.037
Ariel0.0012760.00345.79 * 1050.09078
Titania0.0029160.00227.889 * 1050.1237
Neptune30.070.008592.476 * 1073.883
Triton0.0023711.6 * 10-51.352 * 1060.212
Tempel 131034.865 * 10-4
Wild 227504.312 * 10-4

Of course, a and ε are sufficient to describe any one of these orbits, but in order to understand how the planets are oriented with respect to each other we need 4 additional values:

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)

Orbital cycles do not account for the increases in average global temperature since 1880. (source)


Portfolio Exercise: 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.



©2011, 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.