Gravity Calculation

[Granpafishy]

With the new stuff being done for 2300AD, and me trying to get a game going using the old rules, I was wondering if anybody has or could write up a program or spreadsheet that figures the gravity at variable distances from celestial bodies (stars, planets, etc.)? The reason for this is the stutterwarp drive. Since it has changes in it's efficiency at .0001g and at .1g, being able to figure out where those are is kind of important. Can someone out there help me?

 

[tjoneslo]

Gravitational force is inversely proportial to distance from the body squared. If you know the gravity at the surface (say 1G), divide that by the square of the distance from the surface of the body.

So Gravity (felt) = Gravity(Surface) / (Distance * Distance)

Reversing this you get the following:

for 0.1G: Distance = square root (Gravity (Surface) / 0.1). Note this is in units of planetary radius. If your planet is 7000 miles in diameter, the 0.1G marker is 3.16 radius or about 11,060 miles away.

for 0.0001G: Distance = sqrt (Gs/0.0001). Again in planetary radii. From example above, 100 radi or 350,000 miles.

 

[Granpafishy]

GREAT!!!! Since I use H&E, it gives the planets radius and gravity. Now, how can I figure out the surface gravity and radius of stars?

 

[tjoneslo]

I'd go back to the basic equation at this point.

F = G Mm/r^2 (divide by 9.98 to get Gravity in Gs).
G = 6.672e-11 m3 /(kg sec2)
M is the mass of the body in question
M = 1.989e30 kg (1 solar mass)
r = distance between the two bodies.

GM = 1.32e20
Diameter of the sun is 1,390,000 km, gives a force of about 27G

As above, reverse the equation to get distance for force: F (0.1G = 1) = G M / r^2 or r = sqrt (GM)
or 1.151e20m or 1.151e7 km or 0.07AU
F = (0.0001G) r = sqrt(GM * 100000) = 3.633e12m or 24AU

If you have a star's mass (in stellar masses) (which you should), multiply the distances by the square root of the stellar mass.