- #1
emadtheman
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Homework Statement
Given that Jupiter has a mass of 1.9*10^27kg, and the sun has a mass of 1.99*10^30kg:
a)Calculate the value of Kepler's constant for Jupiter
Homework Equations
k = r^3/T^2
K = G(M+m)/4pi^2
The Attempt at a Solution
Well since the question only gave me the mass of Jupiter and the Sun I'm assuming that I should use Gm/4pi^2 instead even though this formula should only be used when the masses of the two objects (Jupiter and Sun) are close to each other...right?
Let G = Universal gravitational constant
Let M = mass of the Sun
Let m = mass of Jupiter
K = G(M+m)/4pi^2
k = (6.67*10^-11)(1.99*10^30 + 1.9*10^27)/4pi^2
=3.365*10^18, I'm not sure about the units for this formula
I'm pretty sure I can't use k = r^3/T^2 because the question didn't provide me with enough information to do so, but out of curiosity I googled the radius of Jupiter along with its period and plugged it in the formula:
radius (r) is in meters and period (T) is in days (should it be in days or years?)
k = r^3/T^2
= 71492000^3/4331.57^2
= 1.9475*10^16 m/d
If T was in years (11.89):
k = r^3/T^2
= 71492000^3/11.89^2
= 2.584*10^21 m/y
Ok, so clearly these numbers aren't close to the one above. Can you guys point out what I'm doing wrong?
also another confusion that I have, according to other sources(Wikipedia) Kepler's constant should be k = T^2/r^3 rather than(my textbook) k = r^3/T^2.
and if I use K = T^2/r^3 (for T is in days)
K = 5.134*10^-17 d/m
for T in years:
k = 3.868*10^-22 y/m
Please help me out on this