A Bit of Orbital Mechanics

[ODSTalex]

Hello, ODSTalex here. I have just recently joined the KSP forums, and I was hoping to get some constructive criticism on a bit of orbital mechanics I have been learning. I plan to post here semi regularly with new pieces of orbital mechanics as I learn them; so please feel free to criticize and otherwise give me tips on orbital mechanics as you see fit.

Thank you.

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Finding Your Semi Major Axis:

Finding your semi major access is very easy but quite important. To find the semi major axis of any orbit your simply find the average of your Apoapsis and Periapsis like so:

a = ((R1 + R2) / 2)

Where “a†is your semi major axis, and R1 and R2 are your Apoapsis and Periapsis respectively. As such, if you wanted to find the semi major access of an eccentric orbit with an Apoapsis of 200km, and a Periapsis of 100km. Then you would set up the equation like this:

a = ((200 + 100) / 2)

From which you would end up with:

a = 150

leaving you with a semi major axis of 150.

Or if for example, you had a circular orbit with both an Apoapsis and a Periapsis of 100km. Then your semi major axis would (unsurprisingly) be 100km.

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Thank you for reading, and as stated above; please feel free to criticize and otherwise give me tips on orbital mechanics as you see fit.

-ODSTalex

Edited February 14, 2014 by ODSTalex

[K^2]

R1 and R2 include radius of the parent body. So if your apoapsis is 200km, and periapsis is 100km, but you are around Kerbin, your R1 and R2 are 600km + 200km and 600km + 100km respectively. Giving you semi-major axis of 750km.

Things get a bit more complicated with a real body, like Earth, since it's not exactly a sphere. But if you don't know the actual orbital parameters, and you just know the altitude of apses, you can use Earth's mean radius for a decent enough estimate.

[ODSTalex]

ah, I see, that clears up some confusion I had while learning this.

thank you

[FanaticalFighter]

If you're learning orbital mechanics, I'd also recommend learning a bit about conic sections, as all orbits in KSP are conic sections, or for trajectories leaving SOI, composed of multiple conic sections.

[SpaceGremlin]

Axis, not access.

[ODSTalex]

If you're learning orbital mechanics, I'd also recommend learning a bit about conic sections, as all orbits in KSP are conic sections, or for trajectories leaving SOI, composed of multiple conic sections.

ok, I will look into them. Thanks

[ODSTalex]

Axis, not access.

yeah, I tend to make mistakes like that a lot. thanks for the correction

[ODSTalex]

I'm having some difficulty with finding my orbital velocity using the following equation:

V² = GM((2/r)-(1/a))

Where “V†is the orbital velocity. “G†is the universal gravitational constant, which should be 6.67*10^-11. “M†equals the mass of the object that you are orbiting (for Kerbin it should be 5.2915793×1022kg). “r†is the current distance from the center of gravity of what you are orbiting. And “a†is your orbits semi major axis.

The problem I'm running in to is that when I plug these numbers in to the equation, along with the parameters for a 100km circular orbit I run in to problems.

V² = (6.67*10^-11)(5.2915793×1022)((2/700000)-(1/700000))

V² = 5.153045754*10^-13

V = 0.000000718

I don't think that the orbital velocity of a 100km circular orbit around Kerbin is 718 nanometers per second.

help would be much appreciated.

thanks,

-ODSTalex

[Kerbart]

As a slightly unrelated tip you can write 10^15 as 10¹⁵ making everything a lot more readable. Use the tags [noparse] ^and [/noparse] to enclose what you want in superscript (the exponent, obviously). This will make it a lot easier to read what you're writing.

Even better, use an online equation editor to get the bbCode embed code for a proper equation like this:

(Without daring to suggest anything to Squad, it would be nice if the forum software had some kind of latex plugin to do that stuff directly. Given the audience and subject, it would make sense)

Edited February 14, 2014 by Kerbart

[Kerbart]

V² = (6.67*10^-11)(5.2915793×1022)((2/700000)-(1/700000))

It's 10²², not 1022. That's where you're going wrong.

[ODSTalex]

As a slightly unrelated tip you can write 10^15 as 10¹⁵ making everything a lot more readable. Use the tags [noparse] ^and [/noparse] to enclose what you want in superscript (the exponent, obviously). This will make it a lot easier to read what you're writing.

Even better, use an online equation editor to get the bbCode embed code for a proper equation like this:

http://latex.codecogs.com/gif.latex?v_{orbit}&space;=&space;\sqrt{\frac{GM}{R}}

(Without daring to suggest anything to Squad, it would be nice if the forum software had some kind of latex plugin to do that stuff directly. Given the audience and subject, it would make sense)

thanks for the tip, I will look in to it.

[ODSTalex]

It's 10²², not 1022. That's where you're going wrong.

thanks a ton! although now I feel like a bit of an idiot....

but whatever the case thanks for the response, it helps a lot.

[Kerbart]

No worries. We've all been there! I've been yelling half the week at our data warehouse team that the screwed up my contract database dump. Only to find out that I'd been using an old file from my archive.

[K^2]

(Without daring to suggest anything to Squad, it would be nice if the forum software had some kind of latex plugin to do that stuff directly. Given the audience and subject, it would make sense)

We really need a Latex parser on this board. Something like what they have on Physics Forums would do nicely.

[Camacha]

No worries. We've all been there!

Somehow the complicated stuff seems to always work out, while misplacing commas or orders of magnitude is the stuff that screws you over.

[FanaticalFighter]

Somehow the complicated stuff seems to always work out, while misplacing commas or orders of magnitude is the stuff that screws you over.

Yeah. I made this all purpose KSP calculator, for propogating orbits and stuff to learn the math, and the thing just won't work. Then I realized that I'd put a '+' sign instead of a '*' between G and M. I do crazy stuff like that sometimes

[ODSTalex]

Hello!

Sorry for lack of updates, I have been a deadly combination of lazy and busy. I hope to have an update in the next few days.

Also I have made a post in the "General Add-on Affairs" section if you want to take a look at it here is a link: http://forum.kerbalspaceprogram.com/threads/72454-Mech-Jeb-Guide?p=1020700#post1020700