On May/18/2016 at 6:58 AM, Joe Pfeiffer wrote :
Alain Fournier writes:

On May/16/2016 at 6:50 AM, Joe Pfeiffer wrote :
Robert Heller writes:

I am writing a program that simulates a planetary system (a star and a group
of planets in orbit about it). I am writing the program in Tcl and I have
ported a C program, Stargen
(http://www.eldacur.com/~brons/NerdCo.../StarGen.html), to generate
the planetary system and part of the ORSA (http://orsa.sourceforge.net/), to
perform orbital calculations.

At this point I can generate a planetary system and compute the orbits of the
planets. I want to add in spacecraft, but I am not sure how to determine a
spacecraft's orbit -- for a given position and velocity, which planet (if any)
would the spacecraft be in orbit about? I don't know if I should create a
'body' (an ORSA data type/class), with a given mass, position, and velocity
for the spacecraft and then compute this body's orbit with each planet and the
star (the ORSA library has a method which computes the orbital parameters
given a pair of bodies). How do I tell which is the most likely orbit?

I'm not familiar with the software you're using, but the trajectory of
every body in the system is dependant on every other body. If ORSA
simplifies this to your spacecraft being in orbit around one other body,
it isn't going to be accurate enough to be of any use in most
circumstances. But, if you must assume you're only in orbit around one,
it'll be the one exerting the most force, ie the one for which M/r^2
(the mass of the body divided by the distance from your spacecraft to
that body squared) is greatest.

No that wouldn't be the best choice. Here on Earth, the gravitational
force of the Sun is stronger than the gravitational force of the Moon.
The Sun has about 27 million lunar mass and the distance from the
Earth to the Sun is about 389 times the distance from the Earth to the
Moon.
So the gravitational force of the Sun is about 27,000,000/(389^2)
≈ 323 times the gravitational pull of the Moon. Yet, when we look at
tides, clearly the Moon has a greater effect.

But what's relevant to his question isn't tides, it's the earth's
orbit -- and the sun clearly has a greater effect than the moon on that!
If I were calculating forces on me, the planet would dwarf the forces of
either the sun or the moon.

It does turn out my answer was wrong anyway -- if I didn't miss a
decimal somewhere, the sun exerts roughly twice as much force on earth's
moon as the earth does, but you'll get a more accurate model of the
moon's orbit calculating it as orbiting the earth (of course). Though,
of course, the orbit around the earth is a pretty minor perturbation
compared to the orbit around the sun!

Yes exactly. I was about to write something around those lines. I myself
thought that my tide example was poor and using the Moon's orbit around
the Earth is a much better image of why you don't necessarily want to
use the body exerting the biggest force.


Alain Fournier