Course:MATH102/Question Challenge/1997 December Q5

Question

As a moon orbits a planet, its angular position is given by Kepler's equation

${\displaystyle kt=\theta -{\frac {1}{2}}\sin(\theta )}$

where ${\displaystyle k}$ is some constant.

(a) If it takes 50 days for the moon to complete an orbit, what it the value of ${\displaystyle k}$?

(b) Find the rate of change ${\displaystyle {\frac {d\theta }{dt}}}$ when ${\displaystyle \theta ={\frac {\pi }{3}}}$.

Moon orbiting a planet in an elliptical orbit.