orbital velocity of satellite step by step proof ❤❤❤❤❤❤❤❤❤❤❤❤
Answers
Answer:
Derivation of orbital velocity
Orbital velocity is derived in the following way:
Fg=GMmr2 (gravitational force between the earth and the satellite) (eq.1)
Fc=mV2r (centripetal force acting upon the satellite) (eq.2)
Where,
M: mass of the earth
m: mass of the satellite
r: radius of uniform motion of the satellite around the earth
r=R+h
Where,
R: radius of the earth
h: height of the satellite
V: linear velocity of the satellite
Fc: centripetal force
Fg: gravitational force
Fg=Fc (from eq.1 and eq.2)
GMmr2=mV2r
V=[GMr]12 (eq.3)
Therefore, this is the equation of orbital velocity.
Difference between orbital velocity and escape velocity
Escape velocity is defined as the minimum velocity required by a free object to escape from the gravitational force of a massive body.
It is calculated by the formula given below:
ve=2GMr−−−−√
Where,
G: universal gravitational constant
M: mass of the body to be escaped from
r: distance between the centre of mass of the body and the object
In order to break out from the orbit of the massive body, the object must have escape velocity square root of two times greater than the orbital velocity.
Explanation:
Answer: