---
title: "A space probe of mass \\(m\\) is launched radially outward from the surface of a uniform spherical planet of mass \\(M\\) and radius \\(R\\). The probe is given an initial launch speed equal to the planet’s escape speed, \\(v_{\\text{esc}} = \\sqrt{\\dfrac{2GM}{R}}\\), and no forces other than the planet’s gravity act on the probe. Which of the following graphs best represents the speed \\(v\\) of the probe as a function of radial distance \\(r\\) from the center of the planet for \\(r \\ge R\\)?"
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url: "https://nerd-notes.com/ubq/124374/"
date_modified: "2026-09-28T14:05:00+00:00"
---

# A space probe of mass \(m\) is launched radially outward from the surface of a uniform spherical planet of mass \(M\) and radius \(R\). The probe is given an initial launch speed equal to the planet’s escape speed, \(v_{\text{esc}} = \sqrt{\dfrac{2GM}{R}}\), and no forces other than the planet’s gravity act on the probe. Which of the following graphs best represents the speed \(v\) of the probe as a function of radial distance \(r\) from the center of the planet for \(r \ge R\)?

A space probe of mass \(m\) is launched radially outward from the surface of a uniform spherical planet of mass \(M\) and radius \(R\). The probe is given an initial launch speed equal to the planet's escape speed, \(v_{\text{esc}} = \sqrt{\dfrac{2GM}{R}}\), and no forces other than the planet's gravity act on the probe. Which of the following graphs best represents the speed \(v\) of the probe as a function of radial distance \(r\) from the center of the planet for \(r \ge R\)?

- **A.** Graph A
- **B.** Graph B
- **C.** Graph C
- **D.** Graph D

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/124374/*