Introduction:
The kinetic energy required for a satellite to escape from the Earth's surface is different from the kinetic energy required for it to revolve around the Earth in orbit just above the Earth's surface. This difference is related to the gravitational potential energy of the satellite in each scenario.

Escape Velocity:
To escape the Earth's gravitational pull, a satellite must reach the escape velocity. The escape velocity is the minimum velocity required for an object to escape from the gravitational field of a celestial body. For Earth, the escape velocity is approximately 11.2 kilometers per second.

Kinetic Energy for Escape:
The kinetic energy required for a satellite to escape from the Earth's surface can be calculated using the formula: KE = 1/2 * m * v^2, where KE is the kinetic energy, m is the mass of the satellite, and v is the velocity.

Orbital Velocity:
To revolve around the Earth in orbit, a satellite must maintain a specific velocity known as the orbital velocity. The orbital velocity depends on the altitude of the satellite above the Earth's surface. For a satellite in a low Earth orbit just above the surface, the orbital velocity is approximately 7.9 kilometers per second.

Kinetic Energy for Orbit:
The kinetic energy required for a satellite to revolve around the Earth in orbit can also be calculated using the same formula: KE = 1/2 * m * v^2, where KE is the kinetic energy, m is the mass of the satellite, and v is the velocity.

The Ratio:
To find the ratio of the kinetic energy required for escape to the kinetic energy required for orbit, we can divide the two equations:

KE_escape / KE_orbit = (1/2 * m * v_escape^2) / (1/2 * m * v_orbit^2)

The mass of the satellite cancels out, leaving us with:

KE_escape / KE_orbit = (v_escape^2) / (v_orbit^2)

Substituting the values for escape velocity and orbital velocity:

KE_escape / KE_orbit = (11.2^2) / (7.9^2)

Simplifying the equation:

KE_escape / KE_orbit ≈ 1.82

Therefore, the ratio of the kinetic energy required for escape to the kinetic energy required for orbit is approximately 1.82. This means that the kinetic energy required for escape from the Earth's surface is 1.82 times greater than the kinetic energy required for a satellite to revolve around the Earth in orbit just above the Earth's surface.

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