---
title: "Two spherical planets, Planet 1 and Planet 2, are separated by a center-to-center distance of \\(L\\). Planet 1 has mass \\(M_1\\) and Planet 2 has mass \\(M_2\\). A small satellite is positioned at a point along the line connecting the centers of the two planets such that the net gravitational field at that point due to the two planets is zero. If the distance from the center of Planet 1 to this point is \\(r_1\\), which of the following is a correct expression for \\(r_1\\)?"
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url: "https://nerd-notes.com/ubq/109922/"
date_modified: "2026-03-26T06:56:39+00:00"
---

# Two spherical planets, Planet 1 and Planet 2, are separated by a center-to-center distance of \(L\). Planet 1 has mass \(M_1\) and Planet 2 has mass \(M_2\). A small satellite is positioned at a point along the line connecting the centers of the two planets such that the net gravitational field at that point due to the two planets is zero. If the distance from the center of Planet 1 to this point is \(r_1\), which of the following is a correct expression for \(r_1\)?

Two spherical planets, Planet 1 and Planet 2, are separated by a center-to-center distance of \(L\). Planet 1 has mass \(M_1\) and Planet 2 has mass \(M_2\). A small satellite is positioned at a point along the line connecting the centers of the two planets such that the net gravitational field at that point due to the two planets is zero. If the distance from the center of Planet 1 to this point is \(r_1\), which of the following is a correct expression for \(r_1\)?

![Two spheres represent planets. Planet 1 on the left is smaller than Planet 2 on the right. A dashed horizontal line connects their centers. The total distance between the centers is labeled L. A point P is marked on the line between the planets. The distance from the center of Planet 1 to point P is labeled r1.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1774508199-mgxMyU.jpg)

- **A.** \( r_1 = \dfrac{L \sqrt{M_1}}{\sqrt{M_1} + \sqrt{M_2}} \)
- **B.** \( r_1 = \dfrac{L M_1}{M_1 + M_2} \)
- **C.** \( r_1 = \dfrac{L \sqrt{M_2}}{\sqrt{M_1} + \sqrt{M_2}} \)
- **D.** \( r_1 = L \sqrt{\dfrac{M_1}{M_2}} \)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/109922/*