Calculating Jupiter's Mass from Log10(a) vs Log10(P) Graph

[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!

 

[Confundo]

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 $$log_b(x^y) = ylog_b(x)$$

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[marcus]

I have tried using m1+m2= (4*P^2*a^3)/(G*P^2)

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...