Question

The escape velocity from earth is given by
ve​=2gRe​​.....(i)
The orbital velocity of a satellite revolving around earth is given by
v0​=(Re​+h)GMe​​​
where, Me​= mass of earth, Re​= radius of earth, h= height of satellite from surface of earth.
By the relation GMe​=gRe2​
So, v0​=(Re​+h)gRe2​​​.....(ii)
Dividing equation (i) by (ii), we get
v0​ve​​=(Re​)2(Re​+h)​​
Given, v0​=2ve​​
ve​2ve​​=Re​2(Re​+h)​​
Squaring on both side, we get
4=Re​2(Re​+h)​

 or Re​+h=2Re​.

⟹ h=Re​

Answer 1

Answer:

escape velocity ve=GM/R

Orbital velocity vo=GM/2R

so, ve=2vo