Orbital Period vs Radius (Physics)

Lesson notes

Overview

Higher orbits take longer, proportional to r^(3/2). This topic is rated beginner and is number 133 of 227 in Physics. Core ideas and first intuitions. No prior knowledge needed.

What you are seeing

The panel above shows a graph of the function. Each slider changes one parameter, so you can see exactly how the curve bends, shifts or stretches. The animation is drawn live from the model, so everything you see responds to the sliders. Press Space to pause, use Restart to replay from the start, and change the speed to slow down quick events.

In depth

For a circular orbit T = 2π√(r³/GM), so T² is proportional to r³, Kepler’s third law. Higher orbits take much longer: the Moon at 384,000 km takes 27 days, while a geostationary satellite at 42,000 km takes one day, so it stays above the same point on the equator. The relation can be used to weigh a planet by timing its moons.

Reading the relationship

The expression "T = 2π√(r³/GM)" is a compact summary of the idea. It uses the symbols T, π, r, G, M; name what each one stands for before you start. Notice that it contains a square root, so the result grows more slowly than the quantity inside it, and a ratio, so increasing the denominator makes the result smaller. Then use the sliders to see how changing one quantity changes the others.

A guided exploration

1. Set every slider to its middle value and note the shape of the curve. 2. Move one slider at a time and describe whether the curve shifts, stretches or turns. 3. Find the value where the behaviour changes sharply, then connect it to the formula.

Try this

Start by only moving one slider at a time. Say aloud what you expect, then check.

Common pitfalls

Check units and directions first. Many mistakes come from mixing up a scalar with a vector, or from using a formula outside the conditions where it holds.

How it connects

It builds on “Gravitational Potential Energy”, the topic before it in Physics. Once you are comfortable, continue with “Rotational Kinetic Energy”.

Why it matters

Physics explains how the world moves, heats, shines and interacts, and the same principles power technology around you.

Where you might use it

Revising “Orbital Period vs Radius” before a class, exam or certification
Designing vehicles, bridges and devices where motion, forces or waves must be predicted
Understanding how sensors, lasers and communication links actually work
Explaining everyday phenomena such as sound, light, heat and orbits

Frequently asked questions

What is Orbital Period vs Radius?

Higher orbits take longer, proportional to r^(3/2). It is a beginner topic in Physics.

How do I use the Orbital Period vs Radius simulation?

The panel at the top shows a graph of the function. Each slider changes one parameter, so you can see exactly how the curve bends, shifts or stretches. Move the sliders one at a time, then press Space to pause the animation and look closer.

What does the formula mean?

The expression T = 2π√(r³/GM) packs the idea into symbols. Name each symbol first, then change one quantity with the sliders and see which others respond.

Who is this topic for?

Core ideas and first intuitions. No prior knowledge needed. If the quiz feels hard, reread the lesson notes and try the previous topic first.

What should I learn before this?

Start with “Gravitational Potential Energy”, the previous topic in Physics. Each topic in a subject builds on the ones before it.

How do I track my progress?

Press “Mark as learned” on this page. Progress is stored only in this browser and is never sent anywhere. The Browse page can show topics you have learned or still need to learn.