A question on centripetal acceleration

[hubexcube]

Estimate the time it takes a satellite in “near-earth” orbit to go once around the earth. To do this, assume that it is close enough to the earth’s surface that the gravitational force acting on it is about equal to its weight on earth, mg. Proceed as follows:

a. Find the centripetal acceleration the satellite must experience in its circular orbit.

a=v^2/r
Since we're talking about the earth, I'm assuming that we use the Earth's radius, 6400km. However, I have no idea where to get the velocity of this satellite from.

 

[e(ho0n3]

What is the centripetal force acting on the satellite? Can you use this to find the velocity of the satellite?

 

[m2003]

Hello! I would first like to clarify that the formula you provided, a = v^2/r, is the correct formula for calculating centripetal acceleration. Now, in order to estimate the time it takes for a satellite in near-earth orbit to go once around the earth, we need to know the velocity of the satellite. This velocity can be calculated using the formula v = √(GM/r), where G is the universal gravitational constant (6.67 x 10^-11 Nm^2/kg^2), M is the mass of the earth (5.97 x 10^24 kg), and r is the distance between the satellite and the center of the earth (assuming a circular orbit, this would be the radius of the earth + the altitude of the satellite).

Using this formula, we can calculate the velocity of the satellite and then use it to find the centripetal acceleration. Once we have the centripetal acceleration, we can use the formula a = v^2/r to find the time it takes for the satellite to go once around the earth. Keep in mind that this calculation assumes that the satellite is in a circular orbit and that there are no other external forces acting on it.

I hope this helps answer your question on centripetal acceleration and estimating the time it takes for a satellite in near-earth orbit to go once around the earth.