Can anyone help with this problem, I am having a hard time just understanding th
ID: 2060137 • Letter: C
Question
Can anyone help with this problem, I am having a hard time just understanding the concept. It would be a big help if I could get a step by step to understand how to approach a problem like this,Determine Planet's Mass Using Kepler's Law?
The problem:
Data on the Moons of Saturn
Name semimajor axis (m) period (s)
Mimas 185.52 x 10^6 8.14 x 10^4
Enceladus 238.02 x 10^6 11.839 x 10^4
Tethys 294.66 x 10^6 16.311 x 10^4
Dione 377.4 x 10^6 23.647 x 10^4
Rhea 527.04 x 10^6 39.031 x 10^4
slope = _______s^2/m^3
mass = ________ kg
Additional Details
(1) Plot the square of the period against the cube of the radius for these five moons. You can do this by hand with graph paper, or you can use a spreadsheet.
(2) Draw a straight line through the data points. If one or more of the points do not lie very close to the straight line that passes though the other points, check your plotting for errors.
(3) Find, from your graph, the slope of that straight line.
(4) Use the slope of your straight line to calculate the mass of Saturn. Hint: You are looking for a mass that is roughly 100 times the mass of Earth.
(5) When you are confident that your answer is correct, enter your value for the slope (in s^2/m^3) and your value for MSaturn (in kg)
[Enter three sig figs. Format example; 1 million = 1e+6]
Explanation / Answer
Using Kepler's third law P^2 is directly proportional to "a^3" where P is orbital period of the planet and a is semi major axis of the orbit or P^2_planet/a^3_planet = P^2_earth/a^3_earth