A small research probe of negligible mass takes off vertically from the surface of the dwarf planet Ceres. At four marked positions during the ascent, the probe’s onboard accelerometer records the following magnitudes of the local gravitational field:
Position P: at the surface (distance r0 from Ceres’s center)
Position Q: 1.5r0 from the center
Position R: 2.0r0 from the center
Position S: 3.0r0 from the center
Assume Ceres is spherically symmetric and has no atmosphere.
(a) Rank the magnitudes of the gravitational field at positions P, Q, R, and S from greatest to least. If any are equal, state so explicitly.
(b) Describe, in words, the physical reasoning that supports your ranking. Your explanation should refer to the underlying relationship between distance from the planet’s center and the gravitational field strength.