Expert: Ed - 9/6/2007

Question

Hi,
I am a computer engineering student and am working on a simulation program. I am stuck.
Could u tell me the relation between the following things?
1.   elliptical orbit of the heavenly bodies around the sun (ie how exactly the distance between the sun and the body changes
2.   The forces involved (in the orbit) and variation in the forces involved with respect 2 time and position
3.   The change in velocity of planets as the approaches perihelion and aphelion?  
Preferably relation between all the three or between them (some how).
Guide me with the equations or direct me to a website or book (commonly available) that will help me with the same.

Thanking u and hoping for a positive and quick reply


Answer
Shrutesh,

I am sorry to be late. I was busy this weekend.  Also, this is a very complicated question.

Here are some webpages with relatively basic equations:
http://en.wikipedia.org/wiki/Perihelion
http://en.wikipedia.org/wiki/Kepler%27s_laws_of_planetary_motion

You should pay especially close attention to Kepler's Second Law of planetary motion.

For your second question, basically this is all about gravity.  Here is the basic equation.
http://en.wikipedia.org/wiki/Newton%E2%80%99s_law_of_gravitation

Here is a very good NASA website, which should give you the most important statistics for each individual planet.  You should pay especially close attention to the second category of statistics on the webpage for each planet, which is entitled "Orbital Parameters."  Look for max. orbital velocity and min. orbital velocity.  Velocity is at a max at  perihelion, and at a minimum at aphelion.
http://nssdc.gsfc.nasa.gov/planetary/planetfact.html

I think this should get you started.  Please e-mail me again if you need more help, as you probably will.  I will have more time to be helpful tomorrow.
--Ed