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

The radius of orbit=
`2.49* 10^7 m`

Step-by-step explanation:

We are given that

Orbital speed=
`4.00* 10^3`m/s

We have to find the radius of orbit of spacecraft.

We know that

Gravitational constant=
`6.67* 10^(-11)m^3/kgs^2`

Mass of earth=
`5.972* 10^(24) kg`

Orbital speed=
`\sqrt{(GM)/(r)}`

Where G= Gravitational constant

M=Mass of earth

r=Radius of orbit

Substitute the values in the formula

`4* 10^3=\sqrt{(6.67* 10^(-11)* 5.972* 10^(24))/(r)`

Squaring on both sides

`16* 10^6=(6.67* 10^(-11)* 5.972* 10^(24))/(r)`

`r=(6.67* 10^(-11)* 5.972* 10^(24))/(16* 10^6)`

`r=2.49* 10^7 m`

Hence, the radius of orbit=
`2.49* 10^7 m`