The average speed of an orbiting space shuttle is 20100 mi/h. The shuttle is orbiting about 196 mi above the Earth’s surface. Assume the Earth’s radius is 3963 mi.

How long does it take to circle the Earth? Answer in units of h ( hours)

I am not providing further assistance unless you show work. Start by calculating the circumference of the orbit.

Time = orbit circumference divided by speed.

It might be of some interest to you is the fact that a spacecraft's orbital speed at 196 miles altitude is
V = sqrt[1.407974x10^16/(3963+196)(5280)] = 25,321fps = 17,265mph.

So would I take the answer from the formula for a circumference of a circle(24900.26337) and divide it by 17,265 to get 1.442239408(~1.44h)?

How I got the circumference: 2 x pi x 3963=24900.26337

Yes, that is correct, but I would verify the units. radius is in miles, so circumference is in miles, speed is in miles per hour, so time is in hours.

I tried 1.44 h, but I got the answer wrong. Can you please tell me what I may be doing incorrectly with the significant figures? thanks

78

To find the time it takes for the space shuttle to circle the Earth, we need to calculate the circumference of the orbit and divide it by the average speed of the shuttle.

First, let's find the radius of the orbit. The Earth's radius is given as 3963 mi, and the shuttle is orbiting 196 mi above the Earth's surface. So the radius of the orbit would be:

Radius of orbit = Earth's radius + altitude of the shuttle
= 3963 mi + 196 mi
= 4159 mi

Now, let's calculate the circumference of the orbit using the formula:

Circumference = 2 * π * Radius

Circumference = 2 * π * 4159 mi
≈ 2 * 3.14159 * 4159 mi
≈ 26127 mi

Now, we can divide the circumference of the orbit by the average speed of the shuttle to find the time it takes to circle the Earth:

Time = Circumference / Average speed

Time = 26127 mi / 20100 mi/h
≈ 1.299 hours

So, it takes approximately 1.299 hours for the space shuttle to circle the Earth.