Astr 345 Assignment 2: equatorial and ecliptic coordinates
Due before midnight Fri, Sep 5, 2008 (full credit), before midnight Fri Sep 12, 2008 (half credit)
1. Derive the transform from Cartesian (x, y, z)to spherical polar (r, ψ,φ) coordinates:
x=Rcos ψcos φ
y=Rcos ψsin φ
z=Rsin ψ
NOTE the non-standard definition: rrepresents the distance from the origin, ψrepresents the latitude,
i.e., the angle from the xy plane, and φrepresents the azimuthal angle, i.e., the angle in the xy plane
from the xaxis measured counterclockwise.
2. Complete the derivation, started in class, to transform back-and-forth between equatorial (RA/dec or α/δ)
and ecliptic (lat/long or β/λ) coordinates. The angle represents the obliquity of the ecliptic, i.e., the
angle between the zand z0axes.
cos δsin α= cos βsin λcos −sin βsin
sin δ= sin βcos + cos βsin λsin
cos βsin λ= cos δsin αcos + sin δsin
sin β= sin δcos −cos δsin αsin
cos δcos α= cos βcos λ
3. The locations of the planets at 1200h 27/08/2008 UTC in the equatorial system are given. Transform
them to the ecliptic system using the equations in question 2, above. Be sure to calculate both the sine
and cosine of the positions so you can determine which quadrant the longitude angle resides in. I will give
you one answer so you can check your algorithm: for Jupiter, the ecliptic longitude is 282.62◦, and ecliptic
latitude is 0.2863◦. In all cases, note that ecliptic latitude will be close to zero.
Planet RA Dec
Mercury 177.63◦+0.5443◦
Venus 176.86 +2.6641
Mars 184.85 −1.5064
Jupiter 283.75 −23.1251
Saturn 162.93 +9.0418
Uranus 352.23 −4.2313
Neptune 324.87 −14.3789
Pluto 268.35 −17.2684
Grading:
•You can share concepts, but all work must be completely original
•Write neatly and legibly
•Line up equal signs in a straight vertical column, and never have more than one equal sign on a line
•Define all non-standard variables
•Do not skip essential lines of algebra
•Develop ideas logically from start to finish
•Include a statement at the end of each problem interpreting the result
•Label your diagrams; all plots must be computer plots
•Take pride in your work
•All assignments are out of 30 points