Problem Set 6 ASTR 502
Points: 6
(3 pts) 1. Draw a "God's eye" view of the solar system as
of the evening of Dec 21, 2012. Use two sheets of polar
graph paper, inner
and outer solar
system, (which have distances as concentric circles, and angles in
degrees). Label 0 degrees as 0 hours RA; 90 degrees as 6 hours; 180 as 12
hours; etc. Put the Earth's orbit as a circle of radius 1 (AU) and the Sun at
the center. Place the Earth's position on that circle so that the position of
the Sun as seen from the Earth is correct for Dec 21 (RA 18 hr
2 min). Use the table below to place all of the planets in their proper
locations, using their distances from the Earth and their angles as seen from
Earth. (You can get these data for any specified day from Fourmilab.ch/cgi-bin/Solar).
First, fill out the "polar angle" column by
multiplying the Right Ascension Hour number by 15 and adding the Minute number
divided by 4. For example, if the RA is 08:16, then the polar angle = 124 =
8*15 + (16/4). Make two plots: one for the inner planets (maximum distance 4 AU
- put Mars in the inner planet plot) and one for the outer planets (maximum
distance 35 AU on the bottom). Do the outer planet plot first - you may assume
that the Earth is essentially at the Sun, so the polar angles can be measured from
the center directly. You still want to place the Earth on that plot, though...
so that you can get a more accurate measure of the distance from the Sun.
2. (3 pts) For the inner planet plot, you must allow for
parallax: If Venus (for example) is at 0 H Right Ascension, then the line from
the Earth to Venus should be parallel to the line from the Sun to 0
Right Ascension. You then place Venus on its correct place given its DISTANCE
FROM THE EARTH. You can check your results by logging into Solar System LIVE: http://fourmilab.ch/cgi-bin/Solar/(but
don't just copy their figure - you don't know where their zero is!) After you
draw your figure, estimate the distance from the Sun for each of the planets
(measure on the graph and fill in the last column). (You may put the Moon at .1
AU, but it's really at 62 RE
= .002 AU).
|
Object |
distance from Earth (AU) |
Right Ascension (H:M) |
polar angle (degrees) |
distance from sun (AU) |
|
Sun |
0.984 |
18:02 |
|
|
|
Mercury |
1.311 |
16:57 |
|
|
|
Venus |
1.512 |
16:22 |
|
|
|
Moon |
62.3 Earth Radii |
01:10 |
|
|
|
Mars |
2.2 |
19:56 |
|
|
|
Jupiter |
4.13 |
04:29 |
|
|
|
Saturn |
10.37 |
14:28 |
|
|
|
Uranus |
19.96 |
00:18 |
|
|
|
Neptune |
30.47 |
22:12 |
|
|
last update 10/27/2025
