mass of Jupiter is 319 times more than that of the earth but it is acceleration due to gravity is only 25 times more than earth.why?
Answers
g=-GM/(r^2),
where :
g is the acceleration of Gravity at a particular point. On the surface of the Earth (planet), g is approximately 9.81 m/s², and for Jupiter (planet), as we'll calculate will come out to be 24.79 m/s²
G is the universal gravitational constant = 6.67x10^-11 Nm^2/kg^2
M is the mass of the object. For earth M = 5.98x10^24 kg, For Jupiter M = 1.898E27 kg (317.8 Earth mass)
r is the distance from the center of the gravitating body. For the surface of the Earth, r is approximately 6,371 km, For Jupiter, its 69,911 km.
So the calculation for earth is : -6.67E-11 * 5.98E24/((6.38E6)^2). The negative sign is used to reflect the fact that the pull of gravity is toward the center, which usually a negative point on an Earth-based coordinate system.
This works for any point outside the planet, and is based on the assumption that the gravitational pull of other objects is negligible. If you want to calculate the gravitational pull on a point inside the planet, the calculation gets messy because you have to take into consideration how the mass is distributed inside.
Thus we get gravity in Jupiter = 24.79 m/s² ≃ 2.52 times of Earth's.