---
title: "Planet X and Planet Y are two spherical planets composed of the same uniform mass density. The radius of Planet Y is exactly twice the radius of Planet X (​\\(R_Y = 2R_X\\)). A research probe measures the gravitational field strength \\(g_X\\) at a height \\(H\\) above the surface of Planet X. The probe is then moved to a height \\(H\\) above the surface of Planet Y, where it measures the gravitational field strength \\(g_Y\\). What is the ratio \\(g_Y / g_X\\) in terms of \\(R_X\\) and \\(H\\)?"
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url: "https://nerd-notes.com/ubq/113106/"
date_modified: "2026-05-05T04:25:12+00:00"
---

# Planet X and Planet Y are two spherical planets composed of the same uniform mass density. The radius of Planet Y is exactly twice the radius of Planet X (​\(R_Y = 2R_X\)). A research probe measures the gravitational field strength \(g_X\) at a height \(H\) above the surface of Planet X. The probe is then moved to a height \(H\) above the surface of Planet Y, where it measures the gravitational field strength \(g_Y\). What is the ratio \(g_Y / g_X\) in terms of \(R_X\) and \(H\)?

Planet X and Planet Y are two spherical planets composed of the same uniform mass density. The radius of Planet Y is exactly twice the radius of Planet X (​\(R_Y = 2R_X\)). A research probe measures the gravitational field strength \(g_X\) at a height \(H\) above the surface of Planet X. The probe is then moved to a height \(H\) above the surface of Planet Y, where it measures the gravitational field strength \(g_Y\). What is the ratio \(g_Y / g_X\) in terms of \(R_X\) and \(H\)?

![Two spheres labeled Planet X and Planet Y. Planet Y is twice as large as Planet X. For Planet X, a dotted line indicates the radius R_X, and a point P_X is shown at a height H above the surface. For Planet Y, a dotted line indicates the radius R_Y = 2R_X, and a point P_Y is shown at the same height H above its surface.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1777955112-urKwkk.jpg)

- **A.** \(2 \left( \dfrac{R_X + H}{2R_X + H} \right)^2\)
- **B.** \(4 \left( \dfrac{R_X + H}{2R_X + H} \right)^2\)
- **C.** \(8 \left( \dfrac{R_X + H}{2R_X + H} \right)^2\)
- **D.** \(8 \left( \dfrac{2R_X + H}{R_X + H} \right)^2\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/113106/*