The radius of its orbit, measured from Earth's center is 1.44 x 10⁷ m.
What is gravity?
The force of attraction felt by a person at the center of a planet or Earth is called as the gravity.
The gravitational force, Fg is the attractive force exerted by the Earth on the object that is equal to the mass of the object times the gravitational acceleration.
Force of gravitation is also given by
F = GMm/R² .......................(1)
where G = gravitational constant = 6.67 x 10⁻¹¹ N.m²/kg² and R is the distance between two masses.
Satellite A revolves around Earth 5 times a day. Assume that Earth generates the only significant gravitation attraction on the satellite.
The Mass of Earth M= 5.98 × 10²⁴ kg
The centrifugal force Fc = mv²/r ......................(2)
Linear speed v = r ω
ω = 5 x 2π / 86400s
ω = 3.63 x 10⁻⁴ rad/s
Equating both the equations, we get
r = GM/v²
Using linear speed relation, we have
r = ∛(GM/ω²)
Substituting the values, we get
r= ∛ [ (6.67 x 10⁻¹¹ N.m²/kg²x 5.98 × 10²⁴ kg)/ ( 3.63 x 10⁻⁴ )² ]
r = 1.44 x 10⁷ m.
Thus, the radius of its orbit, measured from Earth's center is 1.44 x 10⁷ m.
Learn more about gravity.
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