# Determine the mass of Jupiter using keplers 3rd law and properties of its satelites

1. Dec 6, 2008

### bemc

my problem involves creating a graph of log10(a) vs log10(P) of the Galilean satellites and 3 others, then calculate the mass of jupiter from the graph. P= period of the satelite, a is the semi-major axis

I have created the graph and it seems to be right since the of the trend line is 3/2. My problem is that I am unsure how to go about calculating the mass from the graph.

to get the equation y = 1.5012x - 8.1973

I have tried using m1+m2= (4*P^2*a^3)/(G*P^2)G being the universal gravitational constant 6.67206 x 10-11 m3/kg s2. I used P and A values of Io. Unfortunatly that produced a rather large value and doesn't utilize the graph at all.

Any help or nudges in the right direction would be greatly appreciated, Thanks!

2. Dec 6, 2008

### Confundo

Re: determine the mass of Jupiter using keplers 3rd law and properties of its satelit

You can neglect the masses of the satellites I think, since Jupiter is so much more massive than its satellites. Remember that the gradient is just effectively$$log_{10}(a) / log_{10}(p)$$.
Start by rearranging the kepler equation so you can the gradient part on one side, then take the log remembering $$log_b(x^y) = ylog_b(x)$$

,

3. Dec 6, 2008

### marcus

Re: determine the mass of Jupiter using keplers 3rd law and properties of its satelit

You have miscopied the equation. That is not the Kepler law equation. You should have written
m1+m2= (4*PI^2*a^3)/(G*P^2)

where PI stands for the number 3.14....