The ratio of kinetic energy to potential energy for a satellite moving in an orbit around Earth is 1/2.

Explanation:

Understanding the Concept:
When a satellite moves in an orbit around Earth, it experiences two types of energy: kinetic energy and potential energy.

Kinetic Energy:
Kinetic energy is the energy possessed by an object due to its motion. In the case of a satellite, it is moving in its orbit with a certain velocity. The formula for kinetic energy is given by:

Kinetic Energy = (1/2) * mass * velocity^2

As the satellite is moving, it possesses kinetic energy.

Potential Energy:
Potential energy is the energy possessed by an object due to its position or height above a reference point. In the case of a satellite, its potential energy is due to its height above the Earth's surface. The formula for potential energy is given by:

Potential Energy = gravitational potential energy = mass * gravitational field strength * height

As the satellite is at a certain height above the Earth's surface, it possesses potential energy.

The Ratio of Kinetic Energy to Potential Energy:
To find the ratio of kinetic energy to potential energy, we need to divide the kinetic energy of the satellite by its potential energy.

Kinetic Energy / Potential Energy = [(1/2) * mass * velocity^2] / [mass * gravitational field strength * height]

Simplifying the equation, we get:

Kinetic Energy / Potential Energy = (1/2) * velocity^2 / (gravitational field strength * height)

Now, let's consider the case of a satellite in a circular orbit around Earth. In a circular orbit, the gravitational force provides the necessary centripetal force for the satellite to maintain its circular path. The gravitational force is given by:

Gravitational Force = (mass * velocity^2) / radius of orbit

Since the satellite is in equilibrium, the gravitational force is equal to the centripetal force:

(mass * velocity^2) / radius of orbit = mass * gravitational field strength

Simplifying the equation, we get:

velocity^2 = gravitational field strength * radius of orbit

Substituting this value back into the equation for the ratio of kinetic energy to potential energy, we have:

Kinetic Energy / Potential Energy = (1/2) * (gravitational field strength * radius of orbit) / (gravitational field strength * height)

The gravitational field strength cancels out, and we are left with:

Kinetic Energy / Potential Energy = (1/2) * radius of orbit / height

In a circular orbit, the radius of the orbit is equal to the height above the Earth's surface. Therefore:

Kinetic Energy / Potential Energy = (1/2) * 1 = 1/2

Hence, the correct answer is option 'B', which states that the ratio of kinetic energy to potential energy for a satellite moving in an orbit around Earth is 1/2.

Key idea: Kinetic energy of satellite is half of its potential energy.