---
title: "The Schwarzschild Solution: Orbits, Redshift and the Horizon"
description: "The geometry outside a spherical mass has one exact solution, and reading it gives orbital precession, light bending and the way clock rates depend on depth. At one radius the coordinates fail while t"
canonical: https://lightmysky.com/learn/science/the-schwarzschild-solution-orbits-redshift-and-the-horizon-mt_dNZpRDeZUE
source: https://lightmysky.com/learn/science/the-schwarzschild-solution-orbits-redshift-and-the-horizon-mt_dNZpRDeZUE.md
retrieved: 2026-09-12
---

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# The Schwarzschild Solution: Orbits, Redshift and the Horizon

The geometry outside a spherical mass has one exact solution, and reading it gives orbital precession, light bending and the way clock rates depend on depth. At one radius the coordinates fail while the geometry does not, which is what a horizon is.

Subject: Science · Area: Astronomy & Astrophysics · Ages 23 to 24
Page: https://lightmysky.com/learn/science/the-schwarzschild-solution-orbits-redshift-and-the-horizon-mt_dNZpRDeZUE

## Ready when they can

- Reads gravitational time dilation off the metric
- Explains orbital precession as a departure from the inverse-square result
- Separates a coordinate breakdown at the horizon from a genuine singularity

## Lesson: Clocks, orbits, and the edge of a black hole

Outside a spherical mass, geometry has one exact solution: the Schwarzschild metric. Read it and you get how clock rates depend on depth: deeper clocks tick slower as seen from far away.

The same solution corrects orbits. Planets precess because the geometry departs from the inverse-square rule, and light itself bends as it crosses the curved region.

**Example.** Hold one clock high and one clock deep, then compare their ticks from far away. The deeper one lags, and the size of the lag is read straight off the metric.

**Tip.** At one radius the coordinates fail while the geometry stays smooth: that is the horizon, a coordinate breakdown, not a wall. The genuine singularity sits deeper inside, where curvature itself blows up.

**Recap.** One solution gives slow deep clocks, drifting orbits, bending light, and a horizon that is a labelling failure, not a wall.

## Practice

8 questions on this page, each with its working shown.

## Needs first

- [Curvature and the Einstein Field Equation](https://lightmysky.com/learn/science/curvature-and-the-einstein-field-equation-mt_1CxE6kRDt_)
- [Stellar Death: White Dwarfs, Neutron Stars and Black Holes](https://lightmysky.com/learn/science/stellar-death-white-dwarfs-neutron-stars-and-black-holes-mt_k1oUF3mJlu)

## Opens up

- [Linearised Gravity and Gravitational Waves](https://lightmysky.com/learn/science/linearised-gravity-and-gravitational-waves-mt_z0tMZDGMHi)