As a moon orbits a planet, its angular position is given by Kepler's equation
where is some constant.
(a) If it takes 50 days for the moon to complete an orbit, what it the value of ?
(b) Find the rate of change when .
Moon orbiting a planet in an elliptical orbit.
| Hint 1
| Remember that 1 revolution is radians.
| Hint 2
| At , the moon has made 1 full revolution so radians and . You can use this to find .
| Hint 3
| To find , consider differentiating both sides of the equation with respect to time, and use the chain rule on the right hand side. Then isolate (solve for) . Only plug in the value at the very end.
When the moon has completed one orbit. This means that :
To solve for when we will derive with respect to time and isolate for :