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5  DYNAMICS

P50 003.m

From nearest to furthest, the four satellite moons of Jupiter first observed by Galileo in the year 1610 are called Io, Europa, Ganymede and Callisto. For the first three moons, the orbital period T of each is exactly twice the period of the one orbiting immediately inside it.

            

The mass of Jupiter is 1.90x1027 kg, and the orbital radius of Io is 421 600 km.

             (a)   Use Kepler’s Law of Periods to calculate Ganymede’s orbital radius.

             (b)   Calculate Ganymede’s orbital speed.  

 

View solution below only after you have completed the answering the question.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Solution

            mass of Jupiter            M = 1.90´1027 kg

            orbital radius of Io      R = 421 600 km = 4.216´108  m

            G = 6.67´10-11  N.m2.kg-2

           

(a)       Ganymede’s orbital radius

            Io                          

            Ganymede         

                                         

alternatively

                                        

 

(b)      Ganymede’s orbital speed

                              

Alternatively

            centripetal force = gravitational force