Determine the time it takes for a satellite to orbit the earth in a circular "near-earth" orbit. a "near-earth" orbit is at a height above the surface of the earth that is very small compared to the radius of the earth. [hint: you may take the acceleration due to gravity as essentially the same as that on the surface.]

Explanation:

The gravitational force a satellite of mass m orbiting the Earth of mass at a radius equal to the radius of the Earth is:

Where is the gravitational constant.

Newton's 2nd Law tells us that this satellite of mass m under the mentioned force F will experiment an acceleration given by F=ma.

This acceleration is a centripetal acceleration, so we can use the formula:

The velocity will be given by the relation between the circumference of the orbit and the time taken, that is, v=C/t, and we know that the circumference is .

We can put everything together now:

Substituting our values we have:

Which are more than 84 minutes. For reference, the ISS has a period of almost 93 minutes, so we know the result makes sense (and the equation will give us this result considering it orbits 408Km above Earth's surface).

the answer would be c

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