Question

Question #f0549

Answer 1

`7427.18ms^(-1)`

Explanation:

The centripetal force is given by:

`F=(m_2v^2)/r`

and the force of gravity by:

`F=(Gm_1m_2)/r^2`

As the centripetal force is provided solely by the force of gravity in orbital mechanics then set these equal to each other:

`(Gm_1m_2)/r^2=(m_2v^2)/r`

Rearrange for `v`:

`->(Gm_1)/r=v^2->v=sqrt((Gm_1)/r)`

The values are:

`G=6.67times10^(-11)Nkg^-2m^2` (The universal gravitational constant)
`r=(850+6371)km=7221times10^(3)m` (Radius of the earth plus the height of the satellite)
`m_1=5.972times10^24kg`

Sub into formula for `v`.

`v=sqrt(((6.67times10^(-11))(5.972times10^(24)))/(7221times10^3))=7427.18ms^(-1)`