Question

Ceres is a large asteroid that orbits the Sun between Mars and Jupiter. Ceres has a mass of 9.4 x 1020 kg and a radius of about 4.7 x 10° m.

If a spacecraft attempts to land on the asteroid, what acceleration due to gravity will it experience near the surface?

Answer 1

The acceleration due to gravity near the surface of Ceres is approximately 0.284 m/s²

Step-by-step explanation:

The given parameters are;

The mass of Ceres = 9.4 × 10²⁰ kg

The radius of Ceres, r = 4.7 × 10⁶ m

By Newton's law of gravitation, we have;

`Gravitational \ force\ on \ the \ spacecraft \ near \ Ceres, \ F =G(m_(1)m_(2))/(r^(2))`

Therefore;

`Acceleration \ due \ to \ gravity \ g =G(m_(1))/(r^(2))`

Where;

m₁ = The mass of Ceres = 9.4 × 10²⁰ kg

m₂ = The mass of the spacecraft

G = 6.6743 × 10⁻¹¹ N·m²/kg²

Substituting the values, we get;

`g \ near \ the \ surface \ of \ Ceres = ( 6.6743 * 10^(-11) * 9.4 * 10 ^(20))/((4.7 * 10^5)^(2)) \approx 0.284 \ m/s^2`

The acceleration due to gravity near the surface of Ceres ≈ 0.284 m/s²