Question

Help please...its a sudden assignment

Answer 1

Let an object is revolving around a planet of Radius 'R' at a distance 'h' from its centre.

Let mass of planet be 'M' and that orbital velocity of the object is 'v'.

Now, for the object to continue it's state of motion, centripetal force must act upon it. This centripetal force is provided by the Gravitational Force of Attraction(g) acting radially inwards.

Thus,

Centripetal Force = Gravitational Force

$\frac{ \cancel{m} {v}^{2} }{ \cancel{h}} = \frac{GM \cancel{m}}{ {h}^{ \cancel2} } \\ {v}^{2} = \frac{GM}{h} \\ v = \sqrt{ \frac{GM}{h} }$

Thus, orbital velocity = v = √GM/h