Question

A spacecraft is in orbit around Mars. Suppose that it was previously observed to have speed 5 km/sec while at a distance r = 5000 km from planet center. Suppose it is now at a distance r = 6000 km from planet center. What speed would you expect it to be traveling at now? Note that for Mars we have GmMars = µMars ' 42, 828 km3 /sec2

Answer 1

V' = 4.56Km/s

Step-by-step explanation:

We can use the formula of Orbital Speed, who say,

`V = \sqrt{(GM)/(r)}`

The relative velocity is given by,

`V' = \sqrt{(GM)/(r')}`

We need to find the relation between the two speeds,

`(V')/(V) = \sqrt{(GM)/(r)*(r')/(GM)}`

`(V')/(V) = \sqrt{(r)/(r')}`

`V' = V \sqrt{(r)/(r')}`

Substituting,

`V' = (5)*\sqrt{(5000)/(6000)}`

`V' = 4.56Km/s`