Question

The planet mercury travels around the sun in an elliptical orbit given approximately by r=(3.44x10^7)/(1-0.206cos theta) where r is the distance from mercury to the sun in miles. Find the smallest positive theta (in degrees) such that mercury is 3.09x10^7 miles from the sun

Answer 1

\[r=a/(1-b \dot\space cos \theta)\]
a=3.44x10^7
b=0.206
r=3.09x10^7

rearranging the equation gives
\[1-b \dot\space cos \theta=a/r \rightarrow cos \theta =\frac{1-a/r}{b}\]
Use arccosine function to solve for the angle.