# Kepler's Law of Periods and Jupter's Mass

1. Feb 16, 2010

1. The problem statement, all variables and given/known data

I just finished an experiment asking us to experimentally find Jupiter's mass by using Kepler's Law of Periods T2=((4π2)/GM) * r3. An important property of the law is that period squared is proportional to the radius (circular orbit) or semi-major axis (elliptical orbit) squared.

Our main objective in this part was to determine the mass of Jupiter using a rewritten form of Kepler’s Law of Periods along with some astronomical data (provided at the time of the lab). To satisfy our quest of finding Jupiter’s mass, we rearranged Kepler’s Law as Ln(r)=1/3 Ln[GM/(4π2)]+2/3 Ln(T). We plugged the gravitational constant G into the aforementioned formula to find Jupiter’s mass M.

Using data (mean distance from center of moon to center of Jupiter, orbital period, and mass) for the 4 Galilean moons, we found Jupiter’s mass to be between 1.727x1027kg and 2.068x1027kg, an error of between -9.11% and +8.84%.

When factoring in all 16 of Jupiter's moons, we found Jupiter’s mass to be between 1.8923x1027kg and 2.089x1027kg, an error of between -0.37% and +9.95%.

My question is "Where is the error coming from?" Is it that we're using old astronomical data? Could it be coming from relativity? By this, I mean, is the experimental data obtained for things like orbital periods, mean distances from Jupiter, and mass of the moons of Jupiter somehow flawed due to Einstein's relativity? Perhaps it is flawed due to imprecise observational equipment?

2. Relevant equations

Kepler's Law of Periods T2=((4π2)/GM) * r3

rewritten as:

LN(r) = 1/3 Ln[GM/(4π2)]+2/3 Ln(T).

3. The attempt at a solution

N/A... See part 1 above.