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------------------------------------------------ What is the speed of a satellite orbiting 6.00 km above the surface? Express your answer with the appropriate units.

A satellite 6km above the Earth's surface moves at an approximate speed of 7.91 kilometers per second. The calculation involves the use of the formula for orbital velocity and relies on the gravitational constant, Earth's mass, and the distance from the center of the Earth to the satellite.

Explanation:

The orbital speed of a satellite orbiting 6.00 km above the surface of the Earth can be calculated using the laws of planetary motion. Firstly, the radius of the orbit is the radius of the Earth plus the height above the surface, which is 6370 km (radius of the Earth) + 6.00 km = 6376 km. To find the velocity, we use the formula for circular orbital velocity: v = √(G*M/R), where G represents the gravitational constant, M refers to the mass of the Earth, and R is the distance from the center of the Earth to the object.

Substituting values into the equation, v = √((6.674 * 10^-11 m³kg⁻¹s⁻² * 5.972 * 10^24 kg) / 6376000 m) gives an approximate speed of 7.91 km/s. So, a satellite 6 km above the Earth moves at a speed of approximately 7.91 kilometers per second.

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