Questions about orbital velocities

[CitizenVeen]

Hey space explorers,

A questions arose when switching between stock ksp and realism overhaul:

In stock we need a speed of arround 3k m/s to maintain a low kerbin Orbit (lko)

In RO we a speed of roughly 8k m/s To maintain a LEO.

According To the ksp wiki, kerbin has the same weight as the earth (from the fact that kerbin has the same gravitational pull, 9.8 m/ss).

Now if i understand my physics correctly, the size of a planet is irrelevant for the speed you need To Orbit arround it.

V=sqrt(GM/r)

Only the distance To the center of mass, and the mass of the planet are relevant here.

If kerbin has the same mass as earth, and it is smaller (which means that being 70km above kerbin surface is alot closer To its center of mass then being 200km above earths surface), why do you need so much less speed To Orbit it? Is there something I misunderstand about orbital physics or is KSP just bending the laws of phisycs To decrease game difficulty a bit?

Thanks!

[Gaarst]

Kerbin doesn't have the same mass as Earth. If it did, then it would have 100 times Earth's gravity at sea level.

Kerbin is about 100 times lighter than Earth because it has a radius 10 times smaller, and gravitation follows an inverse square law for distance (10 times closer = 100 times as much gravity).

Edited February 8, 2016 by Gaarst
Forgetting words :|

[K^2]

Kerbin does not have the same mass. It has the same surface gravity. Since the radius is about 10 times smaller, it means the mass needs to be about 100 times smaller than that of Earth to maintain the same surface gravity. So for LKO vs LEO, the GM/r is about 10 times less, which means that Kerbin's orbital velocity is about a third of Earth's. Which is on par with numbers you see.

[CitizenVeen]

Yay I learned something today

Thanks guys!

[Bill Phil]

Also, look up the vis-viva equation.