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

  • #1
BrainMan
279
2

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
 
Physics news on Phys.org
  • #2
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.
 
  • Like
Likes 1 person
  • #3
TSny said:
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!
 
  • #4
BrainMan said:
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.
 
Back
Top