Simulated astrophysics equations

[conure]

Simulated "astrophysics" equations

Hi all,

TL;DR - Please tell me what level of mathematics I require for the equations posted at the end

I am a software developer that is eager to improve my knowledge of maths and physics, however the mathematics required for my BSc only went through algebra then onto trigonometry. I don't know any calculus.

I am currently teaching myself from Khan Academy and a few books (both Maths and Physics) because I have 3 months until the next academic year begins for my degree.

In have been playing around with a light simulater called Kerbal Space Program, and in an attempt to improve both my coding, mathematics and physics I would like to build a calculator that runs on my PC (I'll probably get it running on my phone too) for various orbital transfers.

Effectively, I'm going to have to build a program that accepts a number of variables from a user then crunches the equations seen here:

http://forum.kerbalspaceprogram.com/threads/16511-Tutorial-Interplanetary-How-To-Guide

The problem is, my limited knowledge of mathematics/physics means I'm not sure "how advanced" these equations are. Are they calculus, or basic algebra? Is it likely I can tackle them by brushing up on my basic algebra skills?

Please let me know what I need to focus on to understand the maths involved here!

Thanks

 

[almeng]

I'm no mathematician, but there is no differential calculus in the equations you posted. I could assume then that these equations would be easy enough to program. Possibly brush up on indices and I can see an arccos there (cos^-1) which is also basic trigonometry.

Best of luck
Archie

 

[gneill]

Much depends upon what you want to achieve with your project. Basic Hohmann transfers without nit-picky orbital timings and perturbations by nearby bodies can be handled by basic algebra and trig. Crude gravity assist maneuvers likewise, again presuming you don't need precision.

High precision planetary positions are calculated by series-based models, and involve lots of sine and cosine terms. Still manageable with basic algebra/trig if you can fathom the published algorithms.

A good book for astronomy-type calculations is "Astronomical Algorithms" by Jean Meeus. It's essentially a standard text for those who want to implement astronomy related calculations.

Anything beyond simple orbital maneuvers without precise timing requirements will involve vector algebra. I spotted one vector equation, h = r x v. That's a cross product of radius and velocity vectors to yield the specific angular momentum vector, h.

At the basic computer implementation level everything boils down to basic mathematical operations. So if you've got a 'canned' algorithm, no special math is required. If you want to understand where the algorithms come from or solve problems from scratch by concocting your own solutions, you'll need lots of vector math and you'll soon run into calculus. A good (and very inexpensive!) book to have on hand for this is "Fundamentals of Astrodynamics" by Bate, Mueller, and White.