Gravitation

Since, orbital speed depends upon mass of earth and the separation. Hence, is same for both satellites.

Potential energy
and Total energy
Potential energy (Total energy)

The acceleration due to gravity

According to the questions,So, the curves represents the variation of total energy with radius r for a satellite in a circular orbit.

Radius of earth
According to the question,

The correct answer is D:
The formula for acceleration due to gravity is , where is the gravitational constant, is the planet's mass, and is the planet's radius. According to the question, the acceleration due to gravity is the same on both planets. Therefore, we can set up the equation:
Simplifying this equation leads to: . Further simplification gives:
Given the information that the density of planet is twice the density of planet , i.e., , we can substitute this into the previous equation: . This leads to the conclusion: .

For configuration (i), gravitational force on due to and

For configuration , gravitational force on due to and

For configuration (iii), gravitational force on

angle between F'and F'' is )

For configuration , gravitational force on , where ,




( for
From Eqs. , , and , we get
\) F_{2}

By Kepler's law, when a satellite is moving around the earth on elliptical path, then its angular momentum remains constant
i.e.

But,


Here,

From E ,


or