The physics of energy and Earth's moon as a satellite.

The moon is an Earth satellite of mass 7.35 x 10^22 kg, whose average distance from the centre of Earth is 3.85 x 10^8 m.
a) What is the gravitational potential energy of the moon with respect to Earth?
b) What is the kinetic energy and the velocity of the moon in Earth's orbit?
c) What is the binding energy of the moon to Earth?
d) What is the total mechanical energy of the moon in its orbit?

2.4

To find the answers to these questions, we will need to use the equations related to gravitational potential energy, kinetic energy, velocity, binding energy, and total mechanical energy.

a) Gravitational Potential Energy:
The gravitational potential energy (PE) of an object can be calculated using the equation PE = -GMm/r, where G is the gravitational constant (6.67430 × 10^-11 N(m/kg)^2), M is the mass of the Earth (5.972 × 10^24 kg), m is the mass of the moon (7.35 × 10^22 kg), and r is the distance between the centers of the Earth and the moon (3.85 × 10^8 m).

By substituting the given values into the equation:
PE = -G * M * m / r

b) Kinetic Energy and Velocity:
The kinetic energy (KE) of an object can be calculated using the equation KE = (1/2)mv^2, where m is the mass of the moon (7.35 × 10^22 kg) and v is the velocity of the moon.

Since the moon is in orbit, its velocity can be found using the equation for circular orbit velocity: v = √(GM/r), where G is the gravitational constant (6.67430 × 10^-11 N(m/kg)^2), M is the mass of the Earth (5.972 × 10^24 kg), and r is the distance between the centers of the Earth and the moon (3.85 × 10^8 m).

By substituting the given values into the equation, you can find the velocity of the moon. Once the velocity is known, it can be substituted into the KE equation to calculate the kinetic energy.

c) Binding Energy:
The binding energy (BE) of an object in orbit can be calculated using the equation BE = 2KE, where KE is the kinetic energy of the moon that we calculated in part b.

d) Total Mechanical Energy:
The total mechanical energy (TME) of an object in orbit is the sum of the potential energy and kinetic energy. Therefore, TME = PE + KE, where PE is the gravitational potential energy and KE is the kinetic energy that we calculated.

By substituting the values of PE and KE into the equation, you can calculate the total mechanical energy of the moon in its orbit.

Solve each question by following the steps outlined above, using the given values for the mass of the moon (7.35 × 10^22 kg) and the average distance from the center of the Earth (3.85 × 10^8 m) to get the desired answers.