Question

A satellite revolves from east to west in a circular equatorial orbit of radius $R=1.00\times {10}^{4}km$ around the Earth. What is the acceleration of the circular orbit in the inertial reference frame fixed at a given moment to the centre of the Earth?

• A. $2.2m/s^2$
• B. $0.22m/s^2$
• C. $22m/s^2$
• D. $220m/s^2$

Answer 1

The correct option is B $0.22m/s^2$

Time period of stationary orbit $T=24hrs=24\times 60\times 60s$

Angular velocity $\omega =\frac{2\pi }{T}=\frac{2\pi }{24\times 60\times 60}$
Acceleration $={\omega }^2{R}_e={\left(\frac{2\pi }{24\times 60\times 60}\right)}^2\times 6.4\times {10}^6=0.22m{s}^{-2}$