orbital velocity formula (1 Viewer)

[oompaman]

How is orbital velocity related to radius
Do v=2πr/t. And v=√Gm/r. Contradict?

 

[Fizzy_Cyst]

How is orbital velocity related to radius
Do v=2πr/t. And v=√Gm/r. Contradict?

No, they do not contradict. In the second equation, GM is constant, therefore v proportional to 1/√r

First equation, T is also variable, so we cannot say that v is directly proportional to r, but you could say v is directly proportional to r/T

 

[oompaman]

No, they do not contradict. In theout when it's velocity increases? second equation, GM is constant, therefore v proportional to 1/√r

First equation, T is also variable, so we cannot say that v is directly proportional to r, but you could say v is directly proportional to r/T

How do we explain why an object in orbit will move further out when the velocity increases?

 

[hit patel]

well are these 2 good ways fizzycyst? a = gm2/r^2 therefore as lim r -> infinity , the gravitational acceleration approaches zero. This means the acceleration due to gravity towards centre decreases therefore the velocity away from the centre would increase and again supporting that as acceleration towards earth approaches 0, the gravitational force decreases. Now from fc= mv^2/r we know that m stays constant and we proved radius of orbit to approach infinity when gravitation acceleration approaches 0 ( this is enough to prove the statement however lets continue),but from gm1m1/d^2 the force due to gravity must approach zero also when d approaches infinity therefore again gravitation force must approach zero. since fc=fg in orbit, and v^2= rfc/m the velocity must increase.
Well i showed two ways, but i am in a hurry so please correct any mistakes oompaman. Hope that is useful.

Good luck