Course:MATH102/Question Challenge/1997 December Q5
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Question
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 .
Hints
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. 
Solutions
Solution 

Part A) When the moon has completed one orbit. This means that :
Part B) To solve for when we will derive with respect to time and isolate for :
