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