Question

You wish to place a spacecraft in a circular orbit around the earth so that its orbital speed will be 4.00×103m/s. What is this orbit's radius?

Answer 1

Answer:

The radius of orbit=$2.49\times 10^7 m$

Explanation:

We are given that

Orbital speed=$4.00\times 10^3$m/s

We have to find the radius of orbit of spacecraft.

We know that

Gravitational constant=$6.67\times 10^{-11}m^3/kgs^2$

Mass of earth=$5.972\times 10^{24} kg$

Orbital speed=$\sqrt{\frac{GM}{r}}$

Where G= Gravitational constant

M=Mass of earth

r=Radius of orbit

Substitute the values in the formula

$4\times 10^3=\sqrt{\frac{6.67\times 10^{-11}\times 5.972\times 10^{24}}{r}$

Squaring on both sides

$16\times 10^6=\frac{6.67\times 10^{-11}\times 5.972\times 10^{24}}{r}$

$r=\frac{6.67\times 10^{-11}\times 5.972\times 10^{24}}{16\times 10^6}$

$r=2.49\times 10^7 m$

Hence, the radius of orbit=$2.49\times 10^7 m$