How Can You Calculate Jupiter's Radius Using Europa's Orbital Data?

[brookbj]

The moon Europa, of the planet Jupiter, has an orbital period of 3.55 days and an average distance from the centre of the planet equal to 671,000 Km. If the magnitude of the gravitational acceleration at the surface of Jupiter is 2.36 times greater than that on the surface of the Earth, what is the radius of Jupiter? (hint: begin by calculating the rotation speed.

So I calculated the velocity and acceleration of the moon, but I am confused on how to calculate the radius without having the mass of Jupiter, is this where the 2.36 x g comes into play, do I use this to calculate the mass of Jupiter, which will then give me the radius.

thanks,

 

[Doc Al]

Hint: What force produces the moon's acceleration?

 

[baba89]

I understand your confusion and I am happy to help clarify. In order to calculate the radius of Jupiter, you will need to use the formula for gravitational acceleration, which is G (gravitational constant) multiplied by the mass of the planet divided by the square of its radius. Since you already have the value for the gravitational acceleration on the surface of Jupiter, you can use that to solve for the mass of Jupiter. Once you have the mass of Jupiter, you can use the given distance of Europa from the center of Jupiter to calculate the radius using the same formula. I hope this helps.