Problem: The earth has a radius of 6380 km and turns around once on its axis in 24 h.a) What is the radial acceleration of an object at the earth's equator? Give your answer in m/sec2b) What is the radial acceleration of an object at the earth's equator? Give your answer as a fraction of g.c) If arad at the equator is greater than g, objects would fly off the earth's surface and into space. What would the period of the earth's rotation have to be for this to occur?

FREE Expert Solution

Angular frequency,

ω=2πT

Linear velocity,

v=rω

Centripetal acceleration,

ac=v2r=rω2

Velocity in circular orbits,

v=gr

(a) 

T = 24 h (3600 s / h) = 86400 s

R = 6380 Km (1000 m/ 1 Km) = 6380000 m

View Complete Written Solution
Problem Details

The earth has a radius of 6380 km and turns around once on its axis in 24 h.

a) What is the radial acceleration of an object at the earth's equator? Give your answer in m/sec2

b) What is the radial acceleration of an object at the earth's equator? Give your answer as a fraction of g.

c) If arad at the equator is greater than g, objects would fly off the earth's surface and into space. What would the period of the earth's rotation have to be for this to occur?

Frequently Asked Questions

What scientific concept do you need to know in order to solve this problem?

Our tutors have indicated that to solve this problem you will need to apply the Satellite Motion: Speed & Period concept. You can view video lessons to learn Satellite Motion: Speed & Period. Or if you need more Satellite Motion: Speed & Period practice, you can also practice Satellite Motion: Speed & Period practice problems.