A space probe of mass 95 kg is designed to land on the surface of an asteroid. The gravitational field strength g of the asteroid at its surface is 2.7×10−3 m s−2.
(a) The radius r of the asteroid is 230 km. Calculate the mass of the asteroid.
(b) The probe is carried to the asteroid on board a spacecraft.
Calculate the weight of the probe when close to the surface of the asteroid.
(c.i) As the probe approaches the surface of the asteroid, a rocket engine is fired to slow its descent. Explain how the engine changes the speed of the probe.
(c.ii) A constant force of 12.0 N is exerted by the rocket engine. Determine the time for which the rocket must fire to reduce the speed of the probe from 0.64 m s−1 to zero. State your answer to an appropriate number of significant figures.
(d) As the probe lands, a small stone resting on a rock on the asteroid's surface is projected horizontally from the top of the rock. The horizontal speed of the stone is 34 m s−1 from a height of 1.9 m above the surface of the asteroid.
diagram not to scale
Estimate the horizontal distance from the stone's point of projection along the line AB at which the stone lands. Ignore the curvature of the asteroid.