Question

The circular orbit of a stationary Earth's satellite remains motionless with respect to its surface. What is the velocity of the circular orbit in the inertial reference frame fixed at a given moment to the centre of the Earth?

• A. $v=3.1km/s$
• B. $v=7.44km/s$
• C. $v=3.67km/s$
• D. $v=3.9km/s$

Answer 1

The correct option is A $v=3.1km/s$

Let the satellite revolve around the earth in an orbit of radius $R$.

Radius of earth $R_e=6.4\times {10}^6$ $m$

Time period of the satellite $T=2\pi \sqrt{\frac{R^3}{g{R}_e^2}}$

As the satellite is stationary w.r.t earth, so the time period of the satellite must be equal to time period of rotation of earth i.e $24$ hours

$\therefore$ $24\times 3600=2\pi \sqrt{\frac{R^3}{\left(9.8\right)(6.4\times {10}^6{)}^2}}$

$⟹R=4.24\times {10}^7$ $m$

Now velocity of satellite in that orbit $v=Rw=\frac{2\pi R}{T}$

$\therefore v=\frac{4.24\times {10}^7\times 2\times 3.14}{24\times 3600}=3.08$ $km/s$