Introduction to Classical Mechanics · Problem 11.2
Relativity (Kinematics) — Morin
Physics — Mechanics · explaining-time-dilation
Problem
Two planets, A and B, are at rest with respect to each other, a distance L apart, with synchronized clocks. A spaceship flies at speed v past planet A toward planet B and synchronizes its clock with A's right when it passes A (they both set their clocks to zero). The spaceship eventually flies past planet B and compares its clock with B's. We know, from working in the planets' frame, that when the spaceship reaches B, B's clock reads L/v. And the spaceship's clock reads L/γv, because it runs slow by a factor of γ when viewed in the planets' frame.
How would someone on the spaceship quantitatively explain to you why B's clock reads L/v (which is more than its own L/γv), considering that the spaceship sees B's clock running slow?