Introduction:
The kinetic energy required for a satellite to escape Earth's surface and the kinetic energy required for it to revolve around the Earth in an orbit just above the Earth's surface are related to the concept of gravitational potential energy.

Gravitational Potential Energy:
Gravitational potential energy is the energy possessed by an object due to its position in a gravitational field. It is given by the equation:
PE = mgh

Where:
PE is the gravitational potential energy
m is the mass of the object
g is the acceleration due to gravity
h is the height or distance from the reference point

Escape Velocity:
The escape velocity is the minimum velocity required for an object to escape the gravitational pull of a planet or celestial body. It is given by the equation:
v = sqrt(2gh)

Where:
v is the escape velocity

Kinetic Energy and Escape from Earth's Surface:
To calculate the kinetic energy required for a satellite to escape Earth's surface, we need to consider the gravitational potential energy. The kinetic energy required to escape Earth's surface is equal to the gravitational potential energy at the surface.

Kinetic Energy and Orbiting the Earth:
To calculate the kinetic energy required for a satellite to revolve around the Earth in an orbit just above the Earth's surface, we need to consider the gravitational potential energy at that height. The kinetic energy required for the satellite to revolve around the Earth is equal to the difference in gravitational potential energy between the surface and the orbit height.

Ratio of Kinetic Energies:
The ratio of the kinetic energy required to escape Earth's surface to the kinetic energy required to revolve around the Earth in an orbit just above the Earth's surface can be calculated by dividing the gravitational potential energy at the surface by the difference in gravitational potential energy between the surface and the orbit height.

Conclusion:
The ratio of kinetic energy required to escape Earth's surface to the kinetic energy required to revolve around the Earth in an orbit just above the Earth's surface is determined by the gravitational potential energy. Understanding this ratio is important in space exploration and satellite missions as it helps in determining the energy requirements for different orbital maneuvers.

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