Kepler's constant and average radius of orbit

In summary, the conversation discussed the calculation of Kepler's constant for Jupiter, given its mass and orbital period. It also explored the calculation of the average radius of Jupiter's orbit using Kepler's third law. The calculated results were confirmed to be correct using a different method. Overall, the conversation showed that the individual was on the right track in their understanding of physics.
  • #1
Tyyoung
7
0

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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  • #2
I obtained similar results. Wondering if anyone can verify if they are correct.
 
  • #3
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
 

1. What is Kepler's constant?

Kepler's constant, also known as the gravitational constant, is a numerical value that describes the strength of the force of gravity between two objects. It is denoted by the letter G and has a value of approximately 6.67 x 10^-11 Nm^2/kg^2.

2. How is Kepler's constant related to the average radius of orbit?

Kepler's constant is used in Kepler's third law of planetary motion, which states that the square of a planet's orbital period is proportional to the cube of its average distance from the sun. This means that the average radius of orbit is directly related to Kepler's constant.

3. What are the units of Kepler's constant?

Kepler's constant has units of Newton-meter squared per kilogram squared (Nm^2/kg^2). This unit is used to measure the strength of the force of gravity between two objects.

4. How is Kepler's constant calculated?

Kepler's constant can be calculated using the formula G = (4π^2*r^3)/(T^2*m), where r is the average radius of orbit, T is the orbital period, and m is the mass of the larger object.

5. Why is Kepler's constant important?

Kepler's constant is important because it helps us understand the motion of celestial objects, such as planets, moons, and satellites, in our solar system. It also allows us to make predictions about the orbits of these objects and calculate their masses. Additionally, Kepler's constant is a fundamental constant in physics and plays a role in many other scientific calculations and equations.

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