AP Physics 1
6.6 Motion of Orbiting Satellites
2.9 Circular Motion
2.6 Gravitational Force
Multi-Unit
The orbital period \(T\) and average orbital radius \(r\) are measured for four small moons in circular orbits around a newly discovered gas giant of mass \(M\), as shown in the table. Gravitational interactions between the moons are negligible compared to the gravitational force exerted by the gas giant.
To determine \(M\), a researcher wants to construct a linear graph such that the slope \(k\) of the best-fit line is directly proportional to \(M\). Which of the following correctly identifies the quantities that should be plotted on the vertical and horizontal axes, along with the correct expression for \(M\) in terms of \(k\) and the universal gravitational constant \(G\)?
| Moon | Orbital Radius \(r\) (\(10^8\text{ m}\)) | Orbital Period \(T\) (\(10^5\text{ s}\)) |
|---|---|---|
| 1 | \(2.0\) | \(1.4\) |
| 2 | \(4.0\) | \(4.0\) |
| 3 | \(6.0\) | \(7.3\) |
| 4 | \(8.0\) | \(11.3\) |
To determine \(M\), a researcher wants to construct a linear graph such that the slope \(k\) of the best-fit line is directly proportional to \(M\). Which of the following correctly identifies the quantities that should be plotted on the vertical and horizontal axes, along with the correct expression for \(M\) in terms of \(k\) and the universal gravitational constant \(G\)?
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