Choose the correct alternative:

A. If the zero of potential energy is at infinity, the total energy of an orbiting satellite is negative of its kinetic/potential energy.

B. The energy required to launch an orbiting satellite out of earth’s gravitational influence is more/less than the energy required to project a stationary object at the same height (as the satellite) out of earth’s influence.

A. If the zero of potential energy is at infinity, the total energy of an orbiting satellite is negative of its Kinetic Energy

As total energy of a body is sum of kinetic energy and potential energy, kinetic energy of a body is always positive and depends upon speed of body, potential energy is negative and decreases as we move away from orbiting planet and at infinite distance from planet it becomes 0, the total energy of bound system is negative i.e. if satellite is at finite distance from earth and is under influence of gravitational force of earth its Total energy will be negative and is half of the potential energy, we follow the relation

T = V/2 = -K

Where T is the total energy, V is potential energy and K is kinetic energy

Potential energy and Total energy are negative, the magnitude of total energy is equal to the magnitude of kinetic energy but the sign is opposite as kinetic energy is positive.

B. The energy required to launch an orbiting satellite out of earth’s gravitational influence is less than the energy required to project a stationary object at the same height (as the satellite) out of earth’s influence

As body will be out of earth’s influence when its total energy is Zero or positive and we know the Total energy of a body is the sum of kinetic energy and potential energy

T = K + U

Where T is the total energy, U is potential energy and K is kinetic energy kinetic energy of a body which is always positive and depends upon the speed of the body, potential energy is negative and decreases as we move away from orbiting the planet and at an infinite distance from the planet

Kinetic Energy is given as

Where K is the kinetic energy of a body of mass m, moving with velocity v

The potential energy of a body above the surface of the earth is given as

U = -GMm/r

Where U is the gravitational Potential Energy of body of mass m at a distance r from the centre of the earth and M is the mass of earth G is universal gravitational Constant

If Body have to move out of Earth’s influence its total energy should be positive i.e.

T ≥ 0

Or

so we need to give it energy which will increase its speed and increase its kinetic energy and total energy will be positive , now Both bodies are at same height from earth surface so have same value of negative potential energy Stationary body has zero kinetic energy since its velocity is zero but a body already orbiting earth has some speed i.e. some kinetic energy i.e. its total energy is already less negative than stationary object so consequently less energy is needed to be provided to make its total energy zero consequently i.e. less energy is needed to energy required to launch an orbiting satellite out of earth’s gravitational influence as compared to stationary object at same height