# Find mass of Jupiter using Jupiter's moon, Io

1. Mar 25, 2013

### totallyclone

1. The problem statement, all variables and given/known data
Io - mass: 8.9x1022kg
period: 1.77 days
mean distance from Jupiter: 422x103km

Find the mass of Jupiter using the data for Io.

2. Relevant equations
ƩF=ma
Fc=mv2/r
GmM/ro2
v=2∏r/T

3. The attempt at a solution
I am just unsure what should I put the time in?? Seconds, hours, days, months, years?? I'm getting a different answer and as I google the mass of Jupiter, it is about 1.90x1027kg.

I should be getting the same or really close to it. This is how I tackled the question.

Let m=mass of Io, M=mass of Jupiter

ƩF=ma
GmM/ro2=mv2/ro
M=v2ro/G
M=4∏2ro3/GT2
M=4∏2(422x103)3/(6.67x10-11)(1.7x24x3600)2
M=1.90x1018

I'm getting the same answer BUT different exponents. I know I'm missing something out.

Last edited: Mar 25, 2013
2. Mar 25, 2013

### staysys

Your problem is not the time units, but the distance.

Try checking for unit consistency in your equation:
$M=4\pi^{2}r_{0}^{3}/(GT^{2})$

what should the units of $r_{0}$ be in if you want everything to cancel on the right side except for mass?

3. Mar 25, 2013

### rude man

r0 is given in km. What unit should you be using in your (correct) formula?

4. Mar 25, 2013

### totallyclone

If ro is given in km, shouldn't I also use it in km?

I double checked the given for Io and my givens are correct.

Fun=ma
GmM/ro2=mv2/ro
GM/ro2=v2/ro
M=4∏2ro3/GT2

Would T=1.77days be in seconds then if I made the ro to m?

5. Mar 25, 2013

### totallyclone

I realised I made T in terms of seconds, so I think I should make ro in terms of metres.

6. Mar 25, 2013

### totallyclone

M=4∏2ro3/GT2
M=4∏2(4.22x108)3/(6.67x10-11)(1.77x24x60x60)2
M=2.91x1032

Aaaaah! Still not getting it right? Ah, I must be doing something wrong......

7. Mar 25, 2013

### staysys

But it looks right to me.
I just typed in the exact same equation you wrote, with your numbers and I got 1.90x10^27kg as it should be.
Can you double check that you didn't make a mistake in calculating the answer?

8. Mar 25, 2013

### rude man

Me too.

9. Mar 25, 2013

### Sunil Simha

I think you forgot to square the time period. You get 2.91x1032 when you put M=4∏2ro3/GT

10. Mar 26, 2013

### SteamKing

Staff Emeritus
1. By not checking the units of G, you made several mistakes in your initial calculation.
G = 6.67*10^-11 m^3 kg^-1 s^-2 This constant can be easily googled and it shows the proper units. Just because a known datum is given in a certain set of units does not ensure that it can be used without checking to see if those units are compatible with the other elements of an equation.
2. The orbital radius of Io is 422*10^3 km. How many meters is this?

If you correct these errors and redo your calculation, you should get the correct mass of Jupiter.