Show that the Galilean satellites obey a form of Kepler's 3rd Law as they orbit Jupiter (Io, Europa, Ganymede, Callisto). Be sure to include a Statement that explains why what you did shows this result?
Please help me with all the numbers and with the reasoning
2007-03-22 07:02:05 · 2 answers · asked by Whale 1 in Science & Mathematics ➔ Astronomy & Space
Don't expect someone else to do your homework!
Step I: Find the periods of those satellites.
Step II: Find the distances of those satellites from Jupiter.
Step III: Draw a graph of the distance cubed versus the period squared. Show that it is close to a straight line through the origin.
2007-03-22 07:10:51 · answer #1 · answered by mathematician 7 · 5⤊ 0⤋
Adding to Mathmatician's suggestion, you may also show that when you apply Kepler's 3rd Law directly that you will find that there is an error in the computation. eg: if you square the periods, then take the cube root, the result will not be the semi-major axis. There will be an error that is constant.
This is because Kepler's law only works for the sun and a planet. To compensate, you have to re-derive for any two bodies. Isaac Newton did this. So to get the correct answer, you have to use Newton's version of Kepler's 3rd law.
2007-03-26 09:46:03 · answer #2 · answered by sparc77 7 · 0⤊ 0⤋