Aspacecraft of mass 1.00×103kg orbits the sun (mass 1.99×1030kg) in a circular orbit of radius 1.50×1011m (equal to the average distance from the sun to the earth). you wish to move the spacecraft into a smaller circular orbit around the sun of radius 1.08×1011m (equal to the average distance from the sun to venus). in doing this, what will be the change in the spacecraft's kinetic energy? neglect the gravitational pulls of the planets on the spacecraft. express your answer with the appropriate units.

Change in Kinetic Energy is

Solution:

As per the question:

Mass of space craft,

Mass of the sun, M =

Radius of the orbit, R =

Radius of smaller orbit around the sun, r =

Now,

We know that the Gravitational Potential Energy is given by:

where

G = Gravitational constant

r = distance of the space craft from the center of the sun

Now,

Initial Gravitational Potential Energy is:

Now,

Final Gravitational Potential Energy is:

Change in the Gravitational Potential Energy equals the change in the kinetic energy of the space craft.

Thus