Geometry in space

I need help working out this problem

Quote:

---

While a planet P rotates in a circle about its sun, a moon M rotates in a circle about the planet, and both motions are in a plane. Let's call the distance between M and P one {lunar unit}. Suppose the distance of P from the sun is lunar units; the planet makes one revolution about the sun every 3 years, and the moon makes one rotation about the planet every 0.11111111111 years. Choosing coordinates centered at the sun, so that, at time t=0 the planet is at and the moon is at , then the location of the moon at time t, where t is measured in years, is where

---

Hello,

Quote:

---

Originally Posted by viet

I need help working out this problem

---

The planet describes a circle, within period of 3 years, and radius 4.2x10^3 years.

So if we convert it to polar coordinates, we get :

<< period of the motion.
And we know that has a period T, which is something that can be useful.

Since it's a circle,

So if you let and , you'll get the coordinates of the planet P.

Now consider that the moon has a circular motion around P, but the coordinates of P are x(t) and y(t).

Let and be the coordinates of the moon.
It's a period of 0.111...11 year.
The coordinates satisfy this equation :
, where r'=1 (lunar unit)