Question

As observed from earth, the sun appears to move in an approximate circular orbit. For the motion of another planet like mercury as observed from earth, this would,
A. be similarly true
B. not be true because the force between earth and the mercury is not inverse square law
C. Not be true because the major gravitational force on mercury is due to sun
D. not be true because mercury is influenced by forces other than gravitational forces.

Answer 1

Hint: The gravitational force is a central force which acts along the line of joining the center of masses. When a body is moving in a circular path with uniform velocity then the gravitational force balances the outward centrifugal force on the body.

Formula used:
\[{F_g} = \dfrac{{G{m_1}{m_2}}}{{{r^2}}}\]
Here G is the universal gravitational constant, \[{m_1}\] and \[{m_2}\] are the masses of the bodies separated at the distance of r and \[{F_g}\] is the magnitude of the gravitational force between the given bodies.

Complete step by step solution:
As observed from the earth, the sun appears to move around the earth in a path which is circular. This is the relative motion of the sun with respect to earth. When we define the relative motion of one body with respect to the other body then we assume the second body at rest and then the first body appears to have relative motion.

In reality, the sun is fixed and the planets in the solar system revolve around the sun under the influence of gravitational force of attraction. The sun is a very massive star which attracts the planet with huge gravitational force. Hence, in actuality the earth is revolving around the sun due to gravitational force between the sun and the earth.

According to Newton’s universal law of gravitational force, the magnitude of the gravitational force between two bodies separated at distance follows inverse square law,
\[{F_g} = \dfrac{{G{m_1}{m_2}}}{{{r^2}}}\]
As the gravitational force between two bodies is proportional to the product of the masses of the body and the mass of earth is very small as compared to the sun.

Hence the gravitational force of attraction between the sun and mercury is much larger than that acting between the mercury and the earth. So, the mercury revolves in a circular orbit around the sun and not around the earth. Hence, for the motion of another planet like mercury as observed from earth, this would not be true because the major gravitational force on mercury is due to sun

Therefore, the correct option is C.

Note: The planets revolve around the sun in an elliptical path and not in a perfect circular path. For the purpose of mathematical calculations we assume the path to be circular with the sun at the centre.