a spacecraft is orbiting the earth..question.1.which path shows the spacecraft moving at constanst speed? why?

Question

the next question is 2.) Suppose the engines are fired to make the spacecraft go faster. Which path illustrate it? please help me..this is all about curvilinear motion

Answer 1

1. Assuming a circular orbit of radius R. If it moves with a constant speed V it must have a centripetal acceleration ac.

ac=V^2/R
The the the centripetal force must balance out the gravitational force and thus allowing the spacecraft to maintain the orbit.
Fc=Fg

m ac = G mM/R*2 where

m- mass of the spacecraft
G -universal gravitational constant
M - mass of the Earth

2. Evidentially if it will go faster it will clime to the next higher orbit as ac will increase