Newton’s Law of Gravitation
Lesson notes
Overview
Gravity weakens with the square of the distance between masses. This topic is rated beginner and is number 36 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
Every two masses attract each other with a force F = Gm₁m₂/r², proportional to the product of the masses and inversely proportional to the square of their separation. The constant G is very small, 6.67 × 10⁻¹¹ N·m²/kg², so gravity is only noticeable when one body is astronomically large. The same law explains falling apples, tides and the orbits of planets, which was Newton’s great unification.
Reading the relationship
The expression "F = Gm₁m₂/r²" is a compact summary of the idea. It uses the symbols F, G, m₁m, r; name what each one stands for before you start. Notice that it contains a squared term, so doubling that quantity changes the result by a factor of four, 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 “Escape Velocity”, the topic before it in Physics. Once you are comfortable, continue with “Travelling Waves”.
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 “Newton’s Law of Gravitation” 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 Newton’s Law of Gravitation?
Gravity weakens with the square of the distance between masses. It is a beginner topic in Physics.
How do I use the Newton’s Law of Gravitation 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 F = Gm₁m₂/r² 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 “Escape Velocity”, 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.