Engineers designing a scientific lander for an asteroid wish to include a simple device for measuring the asteroid’s surface gravity. The lander carries a lightweight rigid rod and bob that can pivot freely to form a simple pendulum. After deployment, an onboard sensor measures the length of the pendulum to be 0.650m±0.003m. The lander then records the time required for 15 full oscillations as T15=23.4s±0.1s while the amplitude remains below 4∘.
(a) Derive an algebraic expression for the gravitational field strength g on the asteroid in terms of the measured length l and the average period T.
(b) Calculate the asteroid’s surface gravity using the measured values. Show all work, include units, and report your answer to an appropriate number of significant figures.
(c) Determine the absolute uncertainty in the calculated value of g by propagating the provided measurement uncertainties.
(d) Suppose the asteroid has a radius of 350m and is approximately spherical with uniform density. Using your value of g, estimate the asteroid’s mass. State any additional assumptions clearly.
(e) Comment on one limitation of using a simple pendulum for gravity measurements in the low-gravity environment of a small asteroid.