Question

Two identical satellites orbit the earth in stable orbits. One satellite orbits with a speed v at a distance r from the center of the earth. The second satellite travels at a speed that is less than v. At what distance from the center of the earth does the second satellite orbit?

Answer 1

Answer:

The second satellite will orbit at a larger distance

Explanation:

A satellite orbits the Earth due to its gravitational attraction to the Earth, which is equal to the centripetal force, so we can write

$G\frac{Mm}{r^2}=m\frac{v^2}{r}$

where

G is the gravitational constant

M is the Earth's mass

m is the satellite's mass

r is the distance of the satellite from Earth's center

v is the speed of the satellite

We can rewrite the formula as

$r=\frac{GM}{v^2}$

so we see that the distance of the satellite from the center of the Earth is inversely proportional to the square of the distance. This means that the second satellite, which travels at a lower speed, will have a larger distance from the centre of the Earth.