Review point-mass gravitational fields in Edexcel A-Level Physics through g = GM/r² calculations, inverse-square reasoning and planet data comparisons.
The dwarf planet Ceres is the largest object in the asteroid belt.
Ceres has a mass of 9.38×1020 kg. Ceres has a circular orbit of radius 4.14×1011 m around the Sun.
Mercury is the smallest planet in our solar system. The gravitational field strength gm at the surface of Mercury is 3.7Nkg−1.
It is claimed that the gravitational field strength at the surface of Ceres is less than 5% of gm.
Evaluate whether this claim is accurate.
radius of Ceres =470 km
Use g = GM/r² to calculate the gravitational field strength at the surface of Ceres.
Calculate the ratio of the field strengths, or calculate 5% of the field strength at Mercury.
g_C is 7.7% of g_m, so the claim is inaccurate. Alternatively, g_C = 0.283 N kg⁻¹ and 5% of g_m = 0.185 N kg⁻¹, so the claim is inaccurate.
Example: g_C = (6.67 × 10⁻¹¹ N m² kg⁻² × 9.38 × 10²⁰ kg)/(4.7 × 10⁵ m)² = 0.283 N kg⁻¹; g_C/g_m = 0.283/3.7 = 0.0765.