In its orbit each day, the International Space Station makes 15.65 revolutions around the earth. Assuming a circular orbit, how high is this satellite above the surface of the earth?

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First, understand that the International Space Station (ISS) completes 15.65 revolutions around the Earth in one day. This information can be used to find the orbital period (T) of the ISS.

Calculate the orbital period (T) by dividing the total time in one day (24 hours) by the number of revolutions (15.65). Convert the time into seconds for consistency in units.

Use Kepler's Third Law, which relates the orbital period (T) to the radius of the orbit (r). The formula is:

T^{2} = \frac{4 π^{2}}{G M} r^{3}

, where G is the gravitational constant and M is the mass of the Earth.

Rearrange the formula to solve for the radius (r) of the orbit:

r = {\frac{G M T^{2}}{4 π^{2}}}^{\frac{1}{3}}

Finally, subtract the Earth's radius from the calculated orbital radius to find the height of the ISS above the Earth's surface. The Earth's average radius is approximately 6,371 kilometers.

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Orbital Mechanics

Orbital mechanics involves the study of the motion of objects in space under the influence of gravitational forces. For a satellite like the International Space Station (ISS), understanding its orbit requires knowledge of how gravitational forces from Earth dictate its path and speed, ensuring it remains in a stable orbit.

Circular Orbit

A circular orbit is a type of orbit where the satellite maintains a constant distance from the center of the Earth, resulting in a circular path. This simplifies calculations as the radius of the orbit remains constant, allowing for easier determination of orbital parameters such as altitude and velocity.

Gravitational Force

Gravitational force is the attractive force between two masses, such as the Earth and the ISS. It is crucial for maintaining the satellite's orbit, as it provides the necessary centripetal force to keep the ISS moving in its circular path. The strength of this force depends on the mass of the Earth and the distance between the Earth and the satellite.