Celestia Forums

I am trying to figure out what the gravitational attraction force is between two bodies, but need some additional clarification.

I am familiar with formua
F = (G*m*M)/r^2

F = Magnitude of the Gravitational Force (N)
m = Mass of one body (kg)
M = Mass of a second body (kg)
G = 6.672x10-11 N.m2/kg2 (Universal Gravitational Constant)
r = Distance between the centers of mass of the two objects (m)

But what I am having trouble with is sheer magnitude between two bodies.

Example:

Earth
Mass 5.97E+24 kg
Radius 6,378,000m

Moon
Mass 7.35E+22 kg
Radius 1,738,000m

Distance between Earth and Moon 384,000,000m

Using the equation above
The Earth Surface gravity is 9.79E+00
The Moons Surface gravity is 1.62E+00
The gravity of the Moon at the Earth?€™s surface is 3.32E-05
The gravity of the Earth at the Moon?€™s surface would 2.70E-03
However the combined gravitational force between the two is 1.98E+20.

I guess my question is this correct, and why is there such a huge discrepancy?

The gravitational field is not the gravitational force.
The field is an acceleration, m/s^2

force = mass x acceleration = Newton = kg*m/s^2
force = mass x (gravitational field)

simplify units :

G = 6.672x10-11 N.m2/kg2
N = Newton = force = m*a = kg*m/s^2
G = 6.6E-11 (m^3)/(kg*s^2)

The moon's field in California is called a, for acceleration:

a = (G*mass)/r^2 = 6.6*7.3*E(22-11)/(3.8^2 * E(8+8))
collecting terms : 48/14 * E(11-16) ((m^3)/(kg*s^2))*(kg/m^2)
collecting terms : 3.4 E-5 m/s^2 is the field "a"

The force is M*a = (5.97E+24 kg ) * (3.4 E-5 m/s^2)
M*a = 20.4 E+19 = 2E+20 Newtons force
due to the Moon accelerating the Earth.
This confirms your number has no discrepancy. The units
are important, not just the numbers. Importantly :
the gravitational field is acceleration.

Thanks for the conformation. I just wanted to make sure I was not off my rocker.

Ok question for you scientific people out there.

I am developing a system, and try to do as much upfront work as possible regarding the stability of the system. This is where I seem to be having an issue. Currently I am using the Sol System as model for basing planet stability against my system, and I have notices some interesting things when comparing them. Like at its closest point, Hyperion has about twice the gravitational attraction pressure to Praelos as Earth and Jupiter, and Gigus at its closest point to Praelos has about a third the gravitational attraction pressure as Earth and Jupiter. Now I have used a program to calculate the gravitational effects on all the bodies however the results of the Sol System within the program give me little hope that my system can be calculated accurately. However I did notice one very interesting event if true, the entire orbit of Praelos rotates around Rylix so after 1000yrs where Praelos was originally at its closest point to Rylix on the semi-major access is now the farthest point. It is sort of cool really.

Gigus is just so massive ~8.5 J-mass
And Hyperion is also massive ~5 E-mass
Praelos is ~1.2 E-Mass
Rylix is 1.06 S-mass

Anyway I am trying to tighten up the system and bring the planets closer together. Right now my farthest planet is 72AU from Rylix. This is 33AU father then Pluto, and for a Star that only has 6% additional mass, that orbit seems a bit far flung. I want to know just how close I can get the system together without totally destabilizing the orbits. Looking at Jupiter?€™s moons I am wondering if I can get my planets to oscillate in the 1, 2, 4, 8. This is apparently a very stable orbit for moons.

You can find the Excel File I am using here at take a look at the attraction forces and see if it makes more sense.

One rule-of-thumb to bear in mind is that forming planets close to gas giants can be tricky - this paper suggests that within a factor of three in period you won't form very large planets. Another rule-of-thumb I've come across is that gas giants in eccentric orbits will cause a planet within a factor of eight in period to also end up in an eccentric orbit.

You've therefore got two issues to bear in mind - is the finished system stable (use Gravity Simulator to test this), and is the formation of the planets plausible - there exist configurations which, while stable, are unlikely to occur because of formation problems.

As for the planet being too far out - there is some evidence which suggests some stars do form planets quite a long way out - see here.