Let g be the acceleration due to gravity on the surface of the star. By Newton's second law, the gravitational force felt by the object has a magnitude of
F = GMm/r ² = mg
where
• G = 6.67 × 10⁻¹¹ Nm²/kg² is the gravitational constant,
• M = 2.08 × 10³⁰ kg is the mass of the star,
• m is the unknown mass of the object, and
• r = 6.73 × 10³ m is the radius of the star
Solving for g gives
g = GM/r ²
g = (6.67 × 10⁻¹¹ Nm²/kg²) (2.08 × 10³⁰ kg) / (6.73 × 10³ m)²
g ≈ 3.06 × 10¹² m/s²
The object is in free fall with uniform acceleration and starting from rest, so its speed after falling 0.0093 m is v such that
v ² = 2g (0.0093 m)
v = √(2g (0.0093 m))
v ≈ 240,000 m/s ≈ 240 km/s
