Let be the speed of a planet at perihelion in an elliptical orbit of semi-major axis…

PHYSICS · Single correct · A Level · Physics · Fields and their consequences · Fields and their consequences

Problem

Let

v_{p}

be the speed of a planet at perihelion in an elliptical orbit of semi-major axis

a

and eccentricity

e

. Let

v_{c}

be the speed of a satellite moving in a circular orbit of radius

a

around the Sun. Which expression gives the ratio

v_{p}/v_{c}

in terms of

e

? (a)

\displaystyle \frac{1+e}{1-e}

(b)

\displaystyle \sqrt{\frac{1-e}{1+e}}

(c)

\displaystyle \sqrt{\frac{1+e}{1-e}}

(d)

\displaystyle \sqrt{\frac{1+e^{2}}{1-e^{2}}}