2015

Mass from an escape speed

Round: Theory
Points: 10
Level: Silver
Taught in: Section 3.11

Adapted from IOAA 2015 (Magelang), theory problem 11. We have restated it in our own words and kept the original data. The solution was last checked on 21 October 2026.

The density of a body falls in inverse proportion to the distance from its centre, $ρ = α / r$ , with $α = 5.0 \times 10^{13}$ kg/m². The escape speed at its surface is $v_{0} = 1.5 \times 10^{4}$ m/s. Find the total mass of the body.

I solved it without the solution

AnswerThe mass is $9.04 \times 10^{21}$ kg.

This problem also appears among the olympiad problems of Section 3.11, Problems for Chapter 3, which teaches the ideas it uses. Equation and figure numbers refer to the course.