Question

Suppose the rocket in the Example was initially on a circular orbit around Earth with a period of 1.8 days

(a) What is its orbital speed (in m/s)?

(b) If we want to propel a portion of the rocket to infinity (in the direction tangential to the circular orbit), what's the escape speed from there (in m/s)?

Answer 1

a)
let r is the radius of the orbit pf the rocket.

we know, T = 2*pi*r^(3/2)/sqrt(G*Me)

T^2 = 4*pi^2*r^3/(G*Me)

r^3 = G*Me*T^2/(4*pi^2)

r = (G*Me*T^2/(4*pi^2) )^(1/3)

= (6.67*10^-11*5.98*10^24*155520^2/(4*pi^2))^(1/3)

= 6.25*10^7 m

orbital speed, vo = 2*pi*r/T

= 2*pi*6.25*10^7/155520

= 2525 m/s <<<<<<<<<<-------------Answer

b) escape speed, ve = sqrt(2)*vo

= sqrt(2)*2525

= 3571 m/s <<<<<<<<<<-------------Answer