Solve Satellite Problem: Speed & Orbit Time

[africanmasks]

Homework Statement

The astronaut orbiting the Earth in Figure P4.32 is preparing to dock with a Westar VI satellite. The satellite is in a circular orbit 600 km above the Earth's surface, where the free-fall acceleration is 8.18 m/s2. Take the radius of the Earth as 6400 km.

a.) Determine the speed of the satellite.

b.) Determine the time interval required to complete one orbit around the Earth.

Homework Equations

centripetal(radial) acceleration= v^(2) / r

v= 2(pi)r/ T

The Attempt at a Solution

8.18 m/s^(2) * 600,000m= v^(2)

v= 2215.401 m/s

Is that right?

 

[jbsteele]

For b) I am assuming that you mean for the satellite to complete one orbit around the Earth?2(pi)*6400,000m/2215.401 m/s= TT= 2.45x 10^(4) s

 

[tomcue]

Yes, your solution for the speed of the satellite is correct. To determine the time interval required for one orbit, you can use the formula v = 2πr/T, where v is the speed of the satellite, r is the radius of the orbit, and T is the time interval. Rearranging the formula to solve for T, we get T = 2πr/v. Plugging in the values, we get T = 2π(6400 km + 600 km) / 2215.401 m/s = 5569.8 seconds. Therefore, it takes approximately 5569.8 seconds or 92.83 minutes for the satellite to complete one orbit around the Earth.