Suppose the space shuttle is in orbit 390 km from the Earth's surface, and circles the Earth about once every 92.4 minutes. Find the centripetal acceleration of the space shuttle in its orbit. Express your answer in terms of g, the gravitational acceleration at the Earth's surface.

See my answer to your repost of the same question.

To find the centripetal acceleration of the space shuttle in its orbit, we can use the formula:

a = (v^2) / r

Where:
a = centripetal acceleration
v = orbital velocity
r = radius of orbit

First, we need to find the orbital velocity. We can use the equation:

v = 2πr / t

where:
v = orbital velocity
r = radius of orbit
t = time for one complete orbit

In this case,
r = 390 km = 390,000 m
t = 92.4 minutes = 92.4 * 60 seconds = 5544 seconds

Substituting these values into the equation, we get:

v = 2π * 390,000 / 5544

Calculating this, we find that v ≈ 11199.1 m/s.

Now that we have the orbital velocity, we can substitute it along with the radius of the orbit into the formula for centripetal acceleration:

a = (v^2) / r

Substituting the values, we get:

a = (11199.1^2) / 390,000

Calculating this, we find that a ≈ 320.98 m/s^2.

Since we expressed the gravitational acceleration (g) at the Earth's surface, we can relate the centripetal acceleration to it:

a = 320.98 m/s^2 = (320.98 m/s^2) / (9.8 m/s^2) * g

Therefore, the centripetal acceleration of the space shuttle in its orbit is approximately 32.78 g, where g is the gravitational acceleration at the Earth's surface.