Satellite Motion: Speed & Period Video Lessons

Concept

# 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,

$\overline{){\mathbf{\omega }}{\mathbf{=}}\frac{\mathbf{2}\mathbf{\pi }}{\mathbf{T}}}$

Linear velocity,

$\overline{){\mathbf{v}}{\mathbf{=}}{\mathbf{r}}{\mathbf{\omega }}}$

Centripetal acceleration,

$\overline{){{\mathbf{a}}}_{{\mathbf{c}}}{\mathbf{=}}\frac{{\mathbf{v}}^{\mathbf{2}}}{\mathbf{r}}{\mathbf{=}}{\mathbf{r}}{{\mathbf{\omega }}}^{{\mathbf{2}}}}$

Velocity in circular orbits,

$\overline{){\mathbf{v}}{\mathbf{=}}\sqrt{\mathbf{g}\mathbf{r}}}$

(a)

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

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

###### 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?