The radius of the satellite's motion is 2.49 × 10⁷ m
Since the centripetal force, F = mv²/r equals the gravitational force, F' = GMm/r² on the satellite,
F = F'
mv²/r = GMm/r²
v² = GM/r
Making r subject of the formula, we have
r = GM/v² where r = radius of satellite's motion, G = universal gravitational constant = 6.67 × 10⁻¹¹ Nm²/kg², M = mass of earth = 5.972 × 10²⁴ kg and v = speed of satellite = 4,000 m/s.
Substituting the values of the variables into the equation, we have
r = GM/v²
r = 6.67 × 10⁻¹¹ Nm²/kg² × 5.972 × 10²⁴ kg/(4,000 m/s)²
r = 39.83324 × 10¹³ Nm²/kg ÷ 16 × 10⁶ m²/s²
r = 2.4895775 × 10⁷ m
r ≅ 2.49 × 10⁷ m
So, the radius of the satellite's motion is 2.49 × 10⁷ m.
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