Figure below shows two orbits make a circular mo+on. These orbits has a radii r1 and r2, and connected by an ellip+cal orbit as shown as transfer ellipse. Point 1 and 2 are at the ends of the semimajor axis of ellipse.
a) Using two conserva+on laws prove that veloci+es at points 1 and 2 are as given below if the satellite moving along the ellip+cal orbit:
##$%&!"' ##$% (!#) " = !# and " = !"
! ()( # ()( #" #"
The prime indicates that these are the veloci+es on the ellip+cal orbit.