Problem Set 6    ASTR 502    Fall 2015

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 (which have distances as concentric circles, and angles in degrees). (Warning - the jpg of the graph paper is 216K!) 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 10/5/2015