Alternate assignment for paper 1. Heliocentric model - >Geocentric model conversion


Suppose there are two fictional planets orbiting the sun in circular orbits of radi ( using astronomical units):

Re = 1
Rp = 1.5

The rates of revolution for planet e and p in units of the planet e's period are related by:

We = 2*Wp
Wp = Wp

So the planet e orbits the suns twice before planet p orbits the sun once.

(1) First plot the orbits around the sun. For convenience you can assume that Re = 4cm, Rp = 6cm. If this plot is done on graph paper the next step converting to the geocentric view can be done with a protractor and ruler. Put the sun at the center of the (x,y) coordinate system.

(2A) You want to know what the orbit of planet p looks like from the geocentric view of planet e. For this you will need to obtain the relative distances in the x direction and y direction for planet y with respect to planet e.

OR

(2B) If you know trigonometry you can easily get the steps in 2A using a spread sheet. Then plot the orbit of p as viewed from e.

A table such as this will be helpful. Plot as many angles as you need to connect a smooth curve through the orbit of p as seen from e.

theta_e	thetat_p	xe	xp	ye	yp	(xp-xe)	(yp-ye)
0	0	4	6	0	0	2	0
20	10	etc	etc	etc	etc	etc	etc
40	20
. . .	. . .
680	340
700	350
720	360