The astronaut orbiting the Earth in Figure P 4.30 is...

The astronaut orbiting the Earth in Figure $\mathrm{P} 4.30$ is preparing to dock with a Westar VI satellite. The satellite is in a circular orbit $600 \mathrm{~km}$ above the Earth's surface. where the free-fall acceleration is $8.21 \mathrm{~m} / \mathrm{s}^{2}$. The radius of the Earth is $6400 \mathrm{~km}$. Determine the speed of the satellite and the time required to complete one orbit around the Earth.

Key Concepts

Orbital Period

The orbital period is the time an object takes to complete one full orbit around the central body. It is calculated by dividing the circumference of the circular orbit by the orbital velocity, illustrating how the size of the orbit and the speed of the object determine the period of revolution.

Orbital Velocity

Orbital velocity is the speed an object must have to maintain a stable orbit around a central body. It is derived from setting the gravitational force equal to the centripetal force, leading to the formulation where velocity is proportional to the square root of the gravitational acceleration times the orbital radius or, alternatively, to the square root of (GM/r) where G is the gravitational constant and M is the mass of the central body.

Circular Orbits

A circular orbit is the path taken by an object moving around a central body in a circle, where the gravitational force acts as the centripetal force needed to keep the object in orbit. This concept is fundamental in orbital mechanics, as it simplifies the analysis to constant speed and a fixed orbital radius.

Centripetal Force

Centripetal force is the net force required to keep an object moving in a circular path. In the context of orbital mechanics, this force is provided by gravity. The balance of gravitational force and centripetal force ensures the object remains in a stable circular orbit.

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