For elliptical Earth orbits, the near and far points are...

For elliptical Earth orbits, the near and far points are called the perigee and apogee. Find the period of a satellite with perigee and apogee $200 \mathrm{~km}$ and $1600 \mathrm{~km}$ above Earth's surface, respectively.

Key Concepts

Kepler’s Third Law

Kepler’s Third Law states that the square of the orbital period of a satellite is proportional to the cube of the semi-major axis of its orbit. This law provides a way to relate the size of an orbit to the time it takes for the satellite to complete one revolution around the Earth.

Semi-Major Axis

The semi-major axis is half of the longest diameter of an ellipse and is a critical measurement that defines the size of the orbit. It plays a fundamental role in orbital mechanics, as it is directly related to the orbital period according to Kepler's laws.

Orbital Period

The orbital period is the time required for a satellite to make one complete orbit around the Earth. It is calculated using the semi-major axis of the orbit and the gravitational parameters of the Earth, reflecting the balance between gravitational forces and the satellite's inertia.

Elliptical Orbit

An elliptical orbit is the curved, closed path a satellite follows around a central body, such as the Earth, where the distance to the center of the mass varies continuously along the orbit. This type of orbit is characterized by its shape (an ellipse) with the central body located at one of the foci.

Perigee and Apogee

Perigee and apogee are the specific points in an elliptical orbit where the satellite is closest to or furthest away from the Earth, respectively. These points help in determining the shape and parameters of the orbit, as well as influencing the satellite's speed at different positions.

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