How Can You Calculate Jupiter's Mass Using Callisto's Orbital Data?

[BrainMan]

Homework Statement

The planet Jupiter has at least 14 satellites. One of them, Callisto, has a period of 16.75 days and a mean orbital radius of 1.883 x 10⁹ m. From this information, calculate the mass of Jupiter.

Homework Equations

T² = (4∏²/ GM)r³

∏ = pi

The Attempt at a Solution

I attempted to plug the values into the above formula to find the mass

(16.75)² = (4∏²/6.673 x 10^-11M)(1.883 x 10⁹)³

280.5625 = (1.883 x 10⁹)³4∏²/ 6.673 x 10^-11M

280.5625 M = (1.883 x 10⁹)³4∏²/ 6.673 x 10^-11

280.5625 M = 3.95 x 10¹⁷

M = 1.4 x 10¹⁵
The correct answer is 1.89 x 10²⁷ kg

 

[TSny]

What is the SI unit for time?

Also, when you divided by 6.673 x 10^-11, I think you must have plugged in 6.673 x 10⁺¹¹ in your calculator.

 

[BrainMan]

What is the SI unit for time?

Also, when you divided by 6.673 x 10^-11, I think you must have plugged in 6.673 x 10⁺¹¹ in your calculator.

OK I figured it out. Thanks!

 

[D H]

I attempted to plug the values into the above formula to find the mass

This was the source of your difficulties. I realize you have already solved this problem, but don't just "plug the values into the above formula".

Keep the units in your expressions. G is not 6.673×10^-11. It is 6.673×10^-11 m³⋅kg^-1⋅s^-2. Change the units and you'll get a different value for G. If you had carried the units in the expression you would have realized you have a units mismatch between the period in days and the seconds used in G. Other students experience similar difficulties when distances are expressed in kilometers rather than meters. These problems go away (or at least you are alerted to them) if you keep those units in your expressions.