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title: "Three identical satellites orbit a planet of mass \\(M\\).  All three satellites share the same periapsis distance \\(r_p\\): Satellite 1 moves in a circular orbit of radius \\(r_p\\), Satellite 2 moves in a bound elliptical orbit with semi-major axis \\(a > r_p\\), and Satellite 3 moves along a parabolic escape trajectory.  Which row in the table correctly identifies the sign of the total mechanical energy \\(E\\) of each satellite-planet system and the ranking of the speeds of the satellites at periapsis?  | | Satellite 1 (Circular) | Satellite 2 (Elliptical) | Satellite 3 (Parabolic) | Speed at Periapsis | | :— | :— | :— | :— | :— | | Row A | Negative | Negative | Zero | \\(v_1 < v_2 < v_3\\) | | Row B | Negative | Negative | Zero | \\(v_3 < v_2 < v_1\\) | | Row C | Negative | Zero | Positive | \\(v_1 < v_2 < v_3\\) | | Row D | Zero | Negative | Positive | \\(v_1 = v_2 < v_3\\) |"
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url: "https://nerd-notes.com/ubq/124432/"
date_modified: "2026-09-28T14:05:29+00:00"
---

# Three identical satellites orbit a planet of mass \(M\).

All three satellites share the same periapsis distance \(r_p\): Satellite 1 moves in a circular orbit of radius \(r_p\), Satellite 2 moves in a bound elliptical orbit with semi-major axis \(a > r_p\), and Satellite 3 moves along a parabolic escape trajectory.

Which row in the table correctly identifies the sign of the total mechanical energy \(E\) of each satellite-planet system and the ranking of the speeds of the satellites at periapsis?

| | Satellite 1 (Circular) | Satellite 2 (Elliptical) | Satellite 3 (Parabolic) | Speed at Periapsis |
| :— | :— | :— | :— | :— |
| Row A | Negative | Negative | Zero | \(v_1 < v_2 < v_3\) |
| Row B | Negative | Negative | Zero | \(v_3 < v_2 < v_1\) |
| Row C | Negative | Zero | Positive | \(v_1 < v_2 < v_3\) |
| Row D | Zero | Negative | Positive | \(v_1 = v_2 < v_3\) |

Three identical satellites orbit a planet of mass \(M\).

All three satellites share the same periapsis distance \(r_p\): Satellite 1 moves in a circular orbit of radius \(r_p\), Satellite 2 moves in a bound elliptical orbit with semi-major axis \(a > r_p\), and Satellite 3 moves along a parabolic escape trajectory.

Which row in the table correctly identifies the sign of the total mechanical energy \(E\) of each satellite-planet system and the ranking of the speeds of the satellites at periapsis?

| | Satellite 1 (Circular) | Satellite 2 (Elliptical) | Satellite 3 (Parabolic) | Speed at Periapsis |
| :--- | :--- | :--- | :--- | :--- |
| Row A | Negative | Negative | Zero | \(v_1 < v_2 < v_3\) |
| Row B | Negative | Negative | Zero | \(v_3 < v_2 < v_1\) |
| Row C | Negative | Zero | Positive | \(v_1 < v_2 < v_3\) |
| Row D | Zero | Negative | Positive | \(v_1 = v_2 < v_3\) |

![A black-and-white schematic showing three orbital trajectories sharing a common periapsis point labeled P. Near the center is a solid gray circle labeled M representing a central planet. Directly to the right of the center of M, along the horizontal line, is a small filled black dot labeled P. A horizontal line segment connects the center of M to point P, with a label r_p positioned directly below the segment. Three coplanar curves pass through point P with a common vertical tangent: a solid circle centered at M labeled Trajectory 1; a dashed closed ellipse with one focus at M and its rightmost vertex at P, extending further to the left of M, labeled Trajectory 2; and a dot-dashed parabolic curve opening toward the left around M with its vertex at P, labeled Trajectory 3. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1790604329-aURNd3.jpg)

- **A.** Row A
- **B.** Row B
- **C.** Row C
- **D.** Row D

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/124432/*