: How gravitation force for planets like Jupiter, Saturn, Neptune etc. is calculated? Is it accurate or rough estimate?

In: Physics

Since at least one satellite orbits or has orbited most planets, we can calculate the gravitational pull of a planet from the speed of the satellite in orbit and the distance of the satellite from the planet.

Or, we can measure the affect of the planet on satellites as they approach and leave the vicinity of a planet. We know the speed of the satellite, the mass of the satellite, and the trajectory. So, the amount the satellite deflects from its original trajectory allows the calculation of the planet’s mass.

Alternatively, since most planets have moons, the centripetal force of a moon has to equal the gravitational force of the planet. We know how long it takes a moon to orbit a planet and the distance of the moon from the planet.

The force holding the satellite in orbit is gravitational force. (preventing it from flying off)

G M m

F(gravity) = ——-

R^2

– M = mass of planet (unknown)

– m = mass of satellite (unknown)

– R = distance (measurable)

– G = a gravitational constant experimentally determined

The force pulling the satellite away. (preventing it from falling down)

m V^2

F(Centrifugal) = ———

R

– m = mass of satellite (unknown)

– R = distance (measurable)

– V = tangential speed of satellite (measurable)

since the satellite doesn’t fly off neither it falls down it means the forces must be equal. F(gravity) = F(Centrifugal)

G M m m V^2

——- = ———

R^2 R

After a bit of algebra you get

V^2 R

M = ——-

G

The only unknown is the mass of the planet and once you know the mass of the planet you can calculate the gravitational force using

G M

F(gravity) = ——-

R^2

There is a thing called the gravitational constant that lets you calculate an objects gravitational pull.. which is directly proportional to the mass and inversely proportional to the distance between the bodies.. it’s expressed as F=G.m1.m2/r^2

So what you would need to calculate Jupiter’s gravitational pull on an object, would first be Jupiter’s mass (1.898×10^27kg) then the relative distance to whichever object you’d like to calculate it (say the sun and that’s roughly 7785000000000m) and then multiply both objects masses by the gravitational constant (6.67408×10^-11 N.m^2/km^2) and then divide it by the distance between the two objects multiplied by itself.