Kepler's constant and average radius of orbit

AI Thread Summary
The discussion focuses on calculating Kepler's constant for Jupiter and determining the average radius of its orbit based on its mass and orbital period. The calculations yield Kepler's constant as approximately 3.21x10^15 m^3/s^2 for Jupiter and 3.36x10^18 m^3/s^2 for the Sun. The average radius of Jupiter's orbit is calculated to be around 7.8x10^11 meters. Participants express uncertainty about the accuracy of their results but confirm they align with Kepler's third law. Overall, the calculations are deemed correct, and the methodology is validated by peers.
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Homework Statement


Given that Jupiter has a mass of 1.9x10^27 kg, and the sun has a mass of 1.99x10^30 kg:

a) Calculate the value of Kepler's constant for Jupiter.

b) If Jupiter's orbital period is 11.89 Earth years, calculate the average radius of its orbit.


Homework Equations



K = Gmp/4pi^2 = r^3/T^2
11.89x365x24x3600 = 374963040

The Attempt at a Solution



For a) Kjupiter = Gmp/4pi^2
(6.6x10^-11)(1.9x10^27)/4pi^2

= 3.21x10^15 m^3/s^2

b) Ksun = Gmp/4pi^2
ksun = (6.67x10^-11)(1.99x10^30)/4pi^2

3.36x10^18 m^3/s^2

Ksun=r^3/T^2
Therefore: r^3 = Ksun*T^2
r = cubed rt. of Ksun*T^2
r = cubed rt. of (3.36x10^18)(374963040)^2
r = cubed rt. of 4.724068653x10^35
r = 7.8x10^11m

I am really unconfident about these answers, can someone tell me if I am one the right track or should give up on Physics?
Thank you in advance.
 
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I obtained similar results. Wondering if anyone can verify if they are correct.
 
well for (b) i guess its pretty correct

i even confirmed it using kepler's 3rd law in its pure form

I don't know what's kepler's constant but if you are given a straight formula so it has to be correct
 
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