What linear speed must an Earth satellite have to be in a circular orbit at an altitude of 186 km? What is the period of revolution?

winterWX, Friday, February 16, 2007 at 9:36pm

So GMm/r^2 = mv^2/r and I know that I need to solve for v but what do I use for the mass of the satellite?

Do I just plug in values for G, M, m and r (which equals 6.37e6 + 186e3) and solve for v that way???

You don't need to know the mass of the satellite. Both the left and right sides of the equation are proportional to satellite mass, m. It can be canceled out, leaving
GM/r^2 = v^2/r

To find the linear speed of an Earth satellite in a circular orbit at a certain altitude, you can use the formula: GM/r^2 = v^2/r. In this equation, G is the gravitational constant, M is the mass of the Earth, r is the distance between the center of the Earth and the satellite (which is the sum of the Earth's radius and the altitude of the satellite), and v is the linear speed you're trying to find.

First, you need to plug in the appropriate values for G, M, and r. G is approximately 6.67430 x 10^-11 m^3/kg/s^2, M is the mass of the Earth (which is around 5.972 x 10^24 kg), and r is the distance calculated by adding the Earth's radius (6.37 x 10^6 meters) to the altitude of the satellite (186,000 meters).

Once you have substituted the values, you can solve the equation for v by rearranging it:
GM/r^2 = v^2/r --> GM = v^2r.

Next, isolate v by dividing both sides of the equation by r:
GM/r = v^2.

Now, take the square root of both sides to find v:
v = sqrt(GM/r).

Calculating the values, you should get:
v = sqrt((6.67430 x 10^-11 m^3/kg/s^2) * (5.972 x 10^24 kg) / ((6.37 x 10^6 meters + 186,000 meters)).

After evaluating the expression, you will find the linear speed, v, in meters per second.