PHYSICS · Multi-part · A Level · Physics · Fields and their consequences · Fields and their consequences
Problem
A deep-space probe passes a small, isolated moon and records the following data for the magnitude of the moon’s gravitational field g at various distances r from the moon’s center.
Distance r (km): 350, 400, 500, 700, 1000
Field magnitude g (m/s2): 1.27, 0.97, 0.62, 0.32, 0.14
Assume the moon is spherically symmetric and has no significant atmosphere.
(a) On graph paper, sketch a plot of g versus r. Clearly label both axes with appropriate scales and units.
(b) Explain how you could transform the given data so that the resulting graph is approximately linear. State which quantities you would plot on the horizontal and vertical axes and why this transformation is useful.
(c) Using the transformed data and an appropriate straight-line fit, determine the mass of the moon. Show your reasoning and explicitly indicate how you extract numerical values from the graph.
(d) Discuss two limitations of using inverse-square modeling with these data points and how each limitation could affect the accuracy of the mass you calculated in part (c).