(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

The moon Europa, of the planet Jupiter, has an orbital period of 3.55 days and

an average distance from the center 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.)

radius of orbit of Europa, rm = 671000km

rotational period of Europa, T = 3.55 days

Acceleration due to gravity on Jupiter = GM/r² = 2.36g

radius of Jupiter, r = ?

2. Relevant equations

Rotational velocity of Europa, ω = 2π/(3.55*86400) radians/second

Centripetal acceleration, a =rmω²

3. The attempt at a solution

Gravitational acceleration on Europa

=GM/(rm)²

=(GM/r²)*r²/(rm)²

=(2.36g)(r/rm)²

Equating gravitational acceleration with centripetal acceleration,

(2.36g)(r/rm)² = rmω²

r=(rm)³ω²/(2.36g)

=74,038 km

According to Google, r(Jupiter) = 71,492 km. Did I miss something?

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# Homework Help: Gravitational Acceleration to calculate radius of Jupiter

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