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

Answer:

V' = 4.56Km/s

Explanation:

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

$V = \sqrt{\frac{GM}{r}}$

The relative velocity is given by,

$V' = \sqrt{\frac{GM}{r'}}$

We need to find the relation between the two speeds,

$\frac{V'}{V} = \sqrt{\frac{GM}{r}*\frac{r'}{GM}}$

$\frac{V'}{V} = \sqrt{\frac{r}{r'}}$

$V' = V \sqrt{\frac{r}{r'}}$

Substituting,

$V' = (5)*\sqrt{\frac{5000}{6000}}$

$V' = 4.56Km/s$