Modelling Gravitational Motion

[microguy]

Modelling "Gravitational" Motion

Hi All,

I am new here and this is not a homework question... I'm turning 40 this year and my retention of physics is low to say the least. I am trying to rekindle some knowledge... Just for fun!

I am trying to use a spreadsheet to model the motion of a system of two particles under gravitational-type forces where one particle has a fixed position and the other is given an initial position and velocity vector. Both particles also have a known mass, e.g.,

P1(m1,x1,y1) [fixed position]
P2(m2,x2,y2,v2)

The way I'm approaching this, P2 should move predictably in a time-slice dt. P2 is influenced by its momentum as well as the "gravitational" attraction to P1.

I can figure the "gravitational" force vector with no problem.

The thing I am hung up on is how to figure the contribution of P2's momentum. I'm not even sure I'm using the correct term here. Once I know how to calculate this vector correctly, I think I can do the math.

Please let me know if anything is unclear.

Thanks!

 

[atyy]

Maybe something along these lines

F=Gm1m2/(distance between the masses)² [Newton's law of gravitation]

F=m2(change in velocity)/(change in time) [Newton's 2nd law of motion]

Combining the two laws

Gm1m2(change in time)/(distance between the masses)²=m2(change in velocity)

You can cancel m2 out, and start with 1D motion to see if it makes sense. There's a minus sign somewhere you have to take care of, but I don't remember - just choose it so that gravity attracts, not repels the masses.

Edit: Actually, you can start out with a calculation in which gravity is constant (ie. not dependent on the distance between the masses), just to see if it makes sense. Of course, that result will only be correct over short distances, but it sometimes helps to start with a simple situation.

 

[microguy]

Thanks for that! This makes sense and you helped me notice something I was not doing quite right.