What is the formulae for finding my orbital speed at a specific point in my orbit? ie perapsis.

[leocrumb]

Im getting a bit confused because there seem to be several and I dont understand the notation. Surely if I know my mass and semi-major axis. I should be able to work out/predict my orbital speed when I hit perapsis.

For example knowing how fast i'll be going on my return to Kerbin when I hit a specific altitude, and estimate what my altitude should be for aerobraking

Edited July 4, 2015 by leocrumb

[Gaarst]

V² = GM ( 2/r - 1/a ) with:

V your speed

G the gravitational constant

M the mass of the object you're orbiting

a the semi-major axis of your orbit

r your distance to the orbit focus (the body you're orbiting), (centre of gravity not altitude !)

It is called the vis-viva equation.

Edited July 4, 2015 by Gaarst

[leocrumb]

Thankyou

V² = GM ( 2/r - 1/a ) with:

V your speed

G the gravitational constant

M the mass of the object you're orbiting

a the semi-major axis of your orbit

r your distance to the orbit focus (the body you're orbiting), (centre of gravity not altitude !)

It is called the vis-viva equation.

[Kryxal]

As for how it all works, energy is energy ... potential energy is defined as zero at an infinite distance, and negative as you get closer (U = -GMm/(r^2)). Kinetic energy is .5*mv^2. Given GM, and any three of initial r, initial v, final r, and final v, it's easy enough to find the final term. Note that your mass doesn't matter unless you're approaching the size of the other body in the equations.

[leocrumb]

Thankyou

Is there some online calculator for the Kerbal system so you dont always have to enter 6.674 x 10 to the -11 every time you want G, or masses set up for the different p[lanets?

[Gaarst]

Is there some online calculator for the Kerbal system so you dont always have to enter 6.674 x 10 to the -11 every time you want G, or masses set up for the different p[lanets?

There are mods adding calculators to KSP: this one (Kalculator) for example; and another one (SOC) helping you with orbital elements calculation. I don't know if KER actually displays speed at apo or peri but have a look, it is extremely useful anyway.

[leocrumb]

There are mods adding calculators to KSP: this one (Kalculator) for example; and another one (SOC) helping you with orbital elements calculation. I don't know if KER actually displays speed at apo or peri but have a look, it is extremely useful anyway.

Thanks thats very useful. I use KER it doesnt have speed at peri which is why I want an easy way to have it in game

[Padishar]

Thanks thats very useful. I use KER it doesnt have speed at peri which is why I want an easy way to have it in game

If you ask nicely in the KER thread then cybutek (or that other bloke that helps develop it) might add a new readout for it...

[tomf]

I'll just point out that normally rather that using G and M as seperate constants people normally use the standard graviational parameter for a body, μ. This =GM and is listed on the wiki for each body.

[AlexinTokyo]

I'll just point out that normally rather that using G and M as seperate constants people normally use the standard graviational parameter for a body, μ. This =GM and is listed on the wiki for each body.

And, somewhat surprisingly (to me anyway) is known for real world bodies with more precision than either M or G!

[Padishar]

And, somewhat surprisingly (to me anyway) is known for real world bodies with more precision than either M or G!

This shouldn't be that surprising, there is no way of directly measuring either G (you need to measure the effect on a mass) or M (certainly not on your average bathroom scales ) but you can effectively measure GM by careful timing and altitude measuring of a satellite.

[Sharpy]

You can accurately estimate M by force required to accelerate/decelerate it. Which you can't really do with planets, but which you can do with a several ton lead ball, as Henry Cavendish did. If you can then measure the gravitational pull between two such lead balls, you can get the G. And since G is global (as far as we know it), knowing the orbital parameters of a satellite of a planet, you can calculate its M.