Homework Help Forum: Physics

Posted by Amzz on Tuesday, September 22, 2009 at 11:12am.

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.)

• Physics - MathMate, Tuesday, September 22, 2009 at 3:45pm

  radius of orbit of Europa, rm = 671000km rotational period of Europa, T = 3.55 days Rotational velocity of Europa, ω = 2π/(3.55*86400) radians/second Centripetal acceleration, a =rmω² radius of Jupiter, r = to be determined Acceleration due to gravity on Jupiter = GM/r² = 2.36g 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 Check my numbers and my thinking please.

  
  

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