Question

You want to move a spacecraft that is in 300 km circular orbit around Venus into another circular orbit around Venus of 600 km. Explain how you would accomplish this. Solve for the velocities that need to be applied.

Answer 1

The final velocity will be half of the initial velocity of the spacecraft.

Step-by-step explanation:

Angular momentum is conserved for the circular force motion and central force motion.

Considering

L = MVR = Constant

Where

M = Mass of the object

V = Velocity of the object

r = radius of circle

We know that

V =
`(1)/(R)`

So,

`(V_(2) )/(V_(1) )` =
`(R_(1) )/(R_(2) )`

As per the given data

`R_(1)` = Initial Radius = 300 km

`R_(2)` = Final Radius = 600 km

`V_(1)` = Initial Velocity =

`V_(2)` = Final Velocity =

Placing values in the formula

`(V_(2) )/(V_(1) )` =
`(300 km)/(600 km )`

`(V_(2) )/(V_(1) )` =
`(1)/(2)`

`{V_(2)` =
`(1)/(2) V_(1)`

Hence, The final velocity will half of the initial velocity of the spacecraft.