Mass of Jupiter
Calculation of the mass of Jupiter
|Updated June 01, 2013
We suggest determining the mass of Jupiter by studying the movement of its main satellites: Io, Europe, Ganymede and Callisto.
The movement of a satellite, a mass m is studied in repository one considered as Galilean, having his origin in the center of Jupiter and its axes steered towards distant stars, considered as fixed .On will suppose that Jupiter and its satellites have a distribution of mass in a spherical symmetry. The satellite moves on a circular orbit, at the distance R of the center of Jupiter:
The periods of revolution and beams of the orbits of four main satellites of Jupiter were determined and have the following values:
- Represent on graduated paper the graph giving the variations of T² According to R3. Conclude.
data: G = 6,67 times 10-11N.m2.kg-2.
The satellite is subjected to the only strength of centripetal gravitation
In the base of Frenet: according to the axis n = GMm /R² = mv²/ (R+h) where from the speed: v² =GM / R
T² According to (R+h) in the cube give a right the guiding coefficient of which is 4pi²/GM
Mass of Jupiter: T² / R3 = 4p²/(GM) (3rd law of Kepler).
|M = 4p² / ( 3,15 10-16 *6,67 10-11) = 1,87 1027 kg.