- A uniform, spherical planet P has mass M and radius R.
(a) A projectile of mass m is launched with kinetic energy (2/3)(GMm/R) from the surface of P.
Determine whether the projectile will escape the gravitational field of P. [2]
(b) The surface of P is an equipotential surface E₀. The dotted circle labeled E₁ is an equipotential line at a distance 3/2 R from the centre of P. The potential difference between E₁ and E₀ is 2.2 × 10⁶ J kg⁻¹.
equipotential lines E₀ and E₁ around planet P
(i) The radius R of P is 8.5 × 10⁶ m. Estimate the magnitude of the gravitational field strength between E₁ and E₀. [2]
(ii) E₂ is an equipotential line such that the potential difference between E₂ and E₁ is also 2.2 × 10⁶ J kg⁻¹. Draw the equipotential line E₂ on the diagram. [1]