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

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To calculate Jupiter's radius using Europa's orbital data, the gravitational acceleration at Jupiter's surface, which is 2.36 times that of Earth's, is crucial. The orbital period of Europa is 3.55 days, and its average distance from Jupiter is 671,000 km. The discussion emphasizes the need to first determine the velocity and acceleration of Europa to find Jupiter's mass. Once the mass is established using the gravitational acceleration, the radius of Jupiter can be calculated. Understanding the forces that produce the moon's acceleration is essential for this calculation.
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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,
 
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Hint: What force produces the moon's acceleration?
 

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