Question

a satellite moves in a elliptical Orbit with the earth at one focus. At the perigee its speed is v and its distance from the centre of the Earth is R. if the eccentricity of its orbit is 0.5, calculate the speed at the apogee.​

Answer 1

A satellite moves in a elliptical Orbit with the earth at one focus. At the perigee its speed is v and its distance from the centre of the Earth is R. if the eccentricity of its orbit is 0.5, calculate the speed at the apogee

Perigee = R

Apogee = X

eccentricity =( X -R)/2a

0.5 = (X -R)/2a

X - R = a

X = R + a

a = (X+R)/2

a = (R+a+R)/2

2a = 2R + a

a = 2R

X = 3R

velocity^2 proprional to 2/r - 1/a

v^2 = k * (2/R - 1/2R)

v^2 = k * (3/2R)

speed at apogee = s

s^2 = k * (2/3R - 1/2R)

s^2 = k * (1/6R)

s^2/v^2 = 2/18

s^2/v^2 = 1/9

s/v = 1/3

s = v/3

speed at apogee = 1/3rd of of speed at perigee