The earth is an approximate sphere. If the interior contained matter which is not of the same density everywhere, then on the surface of the earth, the acceleration due to gravity:
 

As observed from the earth, the sun appears to move in an approximately circular orbit. For the motion of another planet like mercury as observed from the earth, this would:
 

Different points in the earth are at slightly different distances from the sun and hence experience different forces due to gravitation. For a rigid body, we know that if various forces act at various points in it, the resultant motion is as if a net force acts on the centre of mass causing translation and net torque at the centre of mass causing rotation around an axis through the CM. For the earth-sun system (approximating the earth as a uniform density sphere):
 

Satellites orbiting the earth have a finite life and sometimes debris of satellites fall to the earth. This is because:
 

Both the earth and the moon are subject to gravitational force of the sun. As observed from the sun, the orbit of the moon:
 

In our solar system, the interplanetary region has chunks of matter (much smaller in size compared to planets) called asteroids. They:
 

Choose the wrong option.
 

Particles of masses 2M, m and M are respectively at points A, B and C with $AB=\frac{1}{2}\left(BC\right)$. The mass m is much-much smaller than M and at time t = 0, they are all at rest as given in the figure. At subsequent times before any collision takes place,

1. m will remain at rest.

2. m will move towards M.

3. m will move towards 2M.

4. m will have oscillatory motion.

The following are the given statements:
 

Choose the correct alternatives:

1. (b, d)

2. (a, c)

3. (c, d)

4. (a, c, d)

If the law of gravitation, instead of being inverse square law, becomes an inverse cube law:

Choose the correct alternatives:

1. (a, d)

2. (a, c)

3. (c, d)

4. (b, d)