Question

Jupiter is at an average distance from the Sun of 778,000,000 kilometers. It has a radius of 71,492 kilometers and a mass of 1.898 x 1027 kilograms. The Sun has a mass of 1.989 x 1030 kilograms. Answer the following:

*What is the acceleration due to gravity on Jupiter?

*How long does it take to revolve around the Sun in Earth-years?

*How fast is it moving in its orbit around the Sun?

*What is the magnitude of the force of gravity between Jupiter and the Sun?

Answer 1

Average distance of Jupiter from the Sun ,

Radius oh Jupiter,

Mass of Jupiter,     

Universal Gravitational Constant,

1)

Acceleration due to gravity,

Substituting

2)

According to Kepler's third law ( Law of periods ), the square of the period ( ) of any planet is proportional to the cube of the semimajor axis ( or the average distance ) of its orbit.

    

OR   

Time period of jupiter,     

where ,  Time period of Earth,

Average distance to Sun to Jupiter,  

   Average distance to Sun to Jupiter, ( standard value)

Subsituting,   

3)

Velocity = Average Distance/Time taken

Average Distance =

time taken =

Velocity =  

4)

Gravitational Force between two masses and separated by a distance is given by,

here, = Mass of Sun ,

=  Mass of Jupiter,        

= Distance between Sun and Jupiter

Universal Gravitational Constant

Substituting,