# Determine the mass of Jupiter using data about a moon

1. Mar 25, 2015

### Calpalned

1. The problem statement, all variables and given/known data
Determine the mass of Jupiter using the data for the moon Io.
Mass of Io: $8.9*10^{22}$
Period: $1.77$ Earth days
Mean distance from Jupiter in km: $422*10^3$

2. Relevant equations
Centripetal acceleration $a = \frac{v^2}{R}$
Universal law: $\frac{GMm}{R^2}$

3. The attempt at a solution
$\frac{m_Iv^2}{R} = \frac{m_IM_JG}{R^2}$
$v^2 = \frac{M_JG}{R}$
$M_J = \frac{v^2R}{G}$
$\frac{(2\pi R)^2R}{G} = 1.419*10^{37}$ kg. My answer = wrong
Just like in the post about binary star systems, I see no error in my calculations, yet I am ten magnitudes too great...
Correct answer is $1.9*10^{27}$

Last edited: Mar 25, 2015
2. Mar 25, 2015

### Staff: Mentor

$2 \pi R$ is not a velocity.

3. Mar 25, 2015

### Calpalned

Thanks Gniell. Once again I forgot to divide $2\pi R$ by T. I solved the problem again, corrected my mistake, and got the right answer.

4. Mar 25, 2015

### tms

Just a little $\LaTeX$ note: you can say $8.9 \times 10^{22}$ (8.9 \times 10^{22}) instead of using an asterisk.