Kepler’s third law tells us that the ratio you considered in #2 is simply relate
ID: 1439704 • Letter: K
Question
Kepler’s third law tells us that the ratio you considered in #2 is simply related to the mass of the star around which the planets orbit. What is that relationship? (Look for it in your class notes, or the text), and write it here, what is the “??” in this formula?
M = ?? (R3/2)
Now use Newton’s laws (F=ma and F = GmM/r2) and the relation between velocity, radius, and period (v = distance/time. What is the “distance” around one orbit?) to DERIVE the formula above! Show us your work – it’s just a couple steps. Giancoli derives it, but do it yourself so we can follow your reasoning)
Explanation / Answer
From keplers third law
T^2 = (4pi^2R^3)/(GM)
M = (4pi^2/G )(R^3/T^2)
F =GmM/R^2
v =2pi*R/T
Gravitational force =centripetal force
GmM/R^2 =mv^2/R
GM/rR = v^2
GM/r = (2pi*R/T)^2
M = (4pi^2/G) (R^3/T^2)
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