A geophysics research team is planning three distinct investigations involving motions of Earth and the Moon. For each investigation, the team must decide whether to model the body (or system of bodies) as a single object located at its center of mass or as a rigid system whose internal rotation must be tracked in detail.
Investigation 1 – Measuring the length of an Earth day with high-precision atomic clocks placed at the equator.
Investigation 2 – Computing the orbital angular momentum of Earth about the Sun to compare with that of other planets.
Investigation 3 – Determining the trajectory of the Earth–Moon barycenter during a lunar fly-by maneuver of a future spacecraft.
Assume that Earth maintains essentially constant size and shape during all three investigations and that tidal distortions can be neglected over the time intervals considered.
(a) For Investigation 1, state whether Earth should be treated as a single object or as a rigid system. Explain how the motion being measured guides your modeling choice.
(b) For Investigation 2, state whether Earth should be treated as a single object or as a rigid system. Justify your answer with specific reference to the quantity being calculated.
(c) For Investigation 3, decide how the Earth–Moon combination should be modeled. Describe the reasoning that leads to your choice and identify which internal motions, if any, are irrelevant for the stated task.
(d) Some beginning students model Earth as a single object when trying to measure the length of a day. Predict one observable consequence of this incorrect choice and explain why it occurs.