Question

A particular satellite was placed in a circular orbit about 247 mi above Earth.

(a) Determine the orbital speed of the satellite.

m/s

(b) Determine the time required for one complete revolution.

min

Answer 1

The orbital speed is

$v=\sqrt{GM/r}$

where G is the gravitational constant, M is the mass of earth and r is the distance from satellite to the center of the earth

Note that

$r=(6371+(247\times 1.6))\times 10^3\,\,m$

$v=\sqrt{6.67\times 10^{-11}\times 5.972 \times 10^{24}/(6,371 +(247\times 1.6)\times 10^3}$

this gives

$v=7671.4\,\,m/s$

b) The time period is

$T=\frac{2\pi r}{v}=\frac{((6371 + (247\times 1.6 )) 10^3)}{7671.4}=5543.66\,\,s$

Answer is min is

$T=5543.66/60=92.4\,\,min$