The mean radius of earth is R, its angular speed on its own axis is ω and the acceleration due to gravity at earth's surface is g. What will be the radius of the orbit of a geostationary satellite ?

Question

The mean radius of earth is R, its angular speed on its own axis is ω and the acceleration due to gravity at earth's surface is g. What will be the radius of the orbit of a geostationary satellite ? (A) (R2 g / ω2 ) 1/3 (B) (R g / ω2 ) 1/3 (C) (R2 ω2 /g ) 1/3 (D) (R2 g / ω) 1/3

Tardigrade Admin · Accepted Answer

(G M m/r2)=m ω2 r ⇒ r3=(G M/ω2)=(g R2/ω2) ∴ r=(g R2 / ω2)1 / 3

Q. The mean radius of earth is $R$ , its angular speed on its own axis is $ω$ and the acceleration due to gravity at earth's surface is $g$ . What will be the radius of the orbit of a geostationary satellite ?

$(R^{2} g / ω^{2})^{1/3}$

$(R g / ω^{2})^{1/3}$

$(R^{2} ω^{2} / g)^{1/3}$

$(R^{2} g / ω)^{1/3}$

$\frac{GM m}{r ^{2}} = m ω^{2} r$
$\Rightarrow r^{3} = \frac{GM}{ω ^{2}} = \frac{g R ^{2}}{ω ^{2}}$
$∴ r = (g R^{2} / ω^{2})^{1/3}$

Q. The mean radius of earth is R, its angular speed on its own axis is ω and the acceleration due to gravity at earth's surface is g. What will be the radius of the orbit of a geostationary satellite ?

(R2g/ω2)1/3

(Rg/ω2)1/3

(R2ω2/g)1/3

(R2g/ω)1/3