Question

A satellite is rotating around Earth at 0.25 radians per hour at an altitude of 242 km above Earth. If the radius of Earth is 6378 kilometers, find the linear speed of the satellite in kilometers per hour.

Answer 1

Answer:

The linear speed is 1655 kilometer per hour

Explanation:

For an object that is describing circular movement, the relation between radial speed (ω) and linear speed (v) is:

$v=\omega r$

With r the radius of the circumference the satellite “draws”  with respect the center of gyration, in our case the satellite is rotating in almost a circumference centered on earth, that implies $r=r_{earth}+altitude=6378+242$

$r=6620km$

So:

$v=(0.25\frac{rad}{h})*6620km$

$v=1655\frac{km}{h}$