) Newton's law emits elliptic orbits. If the Sun is taken to be at the origin, the radius rr of an orbit as a function of the angle from the Su\thetaθ is given by

r = \frac{b}{1+e\cos(\theta)},r=1+ecos(θ)b,

where ee is known as the eccentricity of the orbit and bb is a constant with units of length. For elliptic orbits 0 \lt e \lt 10

For the modified potential, if aa is large enough, the orbits are very nearly elliptica and a similar formula holds with only the eccentricity modified:

r = \frac{b}{1 + e'\cos(\theta)}r=1+e′cos(θ)b

What are the eccentricities ee and e'e′ of the orbits for the two cases considered in the previous part?

Give your answer to three significant figures