Respuesta :
Answer:
R = 1.932 x 10⁸ m
Explanation:
given,
gravitational constant = G = 6.67×10⁻¹¹ N.m²/kg²
mass of the earth = 5.98 x 10²⁴ Kg
radius of earth = 6.38 x 10⁶ m
equating gravitational force on the satellite with the centripetal force acting on it.
[tex]\dfrac{GMm}{R^2} = \dfrac{mv^2}{R}[/tex]
[tex]\dfrac{GM}{R^2} = \dfrac{v^2}{R}[/tex]
where v = R ω
[tex]\dfrac{GM}{R^2} = \dfrac{R^2\omega^2}{R}[/tex]
[tex]\dfrac{GM}{\omega^2} =R^3[/tex]
and [tex]\omega = \dfrac{2\pi}{T}[/tex]
T = 84600 sec
[tex]\omega = \dfrac{2\pi}{84600}[/tex]
[tex]\omega =7.43 \times 10^{-6}\ rad/s[/tex]
[tex]R^3 = \dfrac{6.67 \times 10^{-11}\times 5.98 \times 10^{24}}{(7.43 \times 10^{-6})^2}[/tex]
[tex]R^3 =7.22 \times 10^{24}[/tex]
R = 1.932 x 10⁸ m
