Is there a astronomer who can explain this to me?

[willow]

Hey,

KSP got me interested in how orbits work. And so I tried to figure it out. I\'ve written a small program that simulates a gravity well and a planet moving inside it. This actually works. So far so good.

It occurs to me though that there should be another way using keplers planetary laws. Using the web I figured out how to determine period from semi-major axis and I understand the basics of the angular momentum and how this is a constant for every orbit..

I can\'t figure out though how to calculate the actual position of the planet at a certain time when I know the semi-major axis eccentricity and inclination. It\'d be easy if the orbit was perfectly circular. Only it usually isn\'t.

I\'m good with math when used in computer science, but to my shame I am very rusty on the formal math notations. I know we\'ve got some experts on the forum. Is there anyone who is willing to point me to the proper resources to help me figure this out? And who I could inconvenience with some questions? I promise I\'ll try not to be too dense

Kind regards

Willow

[Ydoow]

The only things I\'ve ever found on this were 'It involves very complex calculus'

So I don\'t know how to help :l I\'m guessing your going to have to do real research, beyond anything google will give you.

I\'m thinking (dun dun dun) actual books (gasp) dealing with this specific mattter

[willow]

I refuse to believe there is anything the internet can\'t solve for me

This guy gives what seems to be an elaborate explanation. I should be working now, so I\'m going to study it some more tonight...

He\'s a bit sparse on some details however, he uses the constant 57.2957796 and I could not figure out what it was. Untill it dawned it\'s a conversion factor between radians and degrees. That number would probably be obvious to any experienced mathemagician.

Oh well... slowly but surely right? I studied calculus as part of a university course but that\'s almost 20 years ago and I had very little practice to keep my skills sharp.. I\'m rusty, but hopefull. If someone with the relevant expertise would want to give me a hand I\'d be very grateful.

[maltesh]

Some references that helped me out when writing my orbital calculator:

http://www.nature1st.net/bogan/orbits/kepler/orbteqtn.html

http://www.braeunig.us/space/orbmech.htm.

What you want, basically, is True Anomaly as a function of time. The problem is that there isn\'t a simple equation that you can plug time values into and get True Anomaly out of, unless your orbit is circular or parabolic.

The equations at the first link relate Mean Anomaly (which is easily expressible a a function of time), Eccentric Anomaly, and True Anomaly. You\'re going to need to use a root-finding algorithm to get from Mean anomaly to true anomaly.

[willow]

Thanks Maltesh. If you\'re looking for me I\'ll be studying these pages tonight. 8)

[Agamemnon]

iirc:

'I can\'t figure out though how to calculate the actual position of the planet at a certain time when I know the semi-major axis eccentricity and inclination.'

this is not enough to identify the position... as far as i remember, you need 6 things to uniquely identify the position (iirc, these 6 things are called 'orbital elements')...

and just from the top of my head:

if you know the orbit, then you would need at least one known position - a known position in any time... then you can calculate where the planet (satellite) is at any other time...

of course, i could be wrong, it\'s been some time... and i guess i did not write everything and forgot something important...

[willow]

As far as I understand you need

• [li]time of measurement since periapsis[/li]
  [li]the length of the major axis (center of ellipse to periapsis)[/li]
  [li]the orbital eccentricity[/li]
  [li]the inclination of the plane[/li]

The orbital period, mean anomaly eccentric anomaly, true anomaly and vector to the planet are derived from the first 4 variables.

Thanks to the sites you gave Maltesh and the guy I found earlier I\'ve gotten ahead quite a bit. I\'ve got a spread sheet in which I fill out the first 3 variables and it produces the other variables including true anomaly and radius which together are location of the planet at time t. I haven\'t worked in the inclination of the plane yet. I\'ll get to that later on. Once you understand what all the bits in the formulas do it\'s really not that complicated in the end. It\'s been very educational.

Thanks guys!