Gravity and Orbits
Gravity
Everything falls at the same rate; weight is not mass
Drop your phone and a coin from the same height and they hit the floor together, though one weighs many times the other. Watch footage of astronauts and they drift weightless around a station that is, in fact, deep inside Earth's gravity. Two things everyone half-remembers, both backwards. Gravity is simpler and stranger than the school-yard version.
Predict first: the two-object drop
Play with it: drop them in a vacuum
The widget below drops a hammer and a feather side by side. Leave the air on first and watch the feather dawdle behind, exactly as you predicted. Then press the vacuum button and drop again. Read the two landing times underneath.
In air the feather's drag holds it back - the mass is a red herring, the air is the difference.
With the air gone, the hammer and the feather land at the same instant. The weight difference, which felt like the whole story, made no difference at all once the air was removed. Whatever gravity does to falling objects, it does it the same way to a heavy one and a light one. That is the first big idea, and the widget just showed it to you: in air the feather is held back by drag; in vacuum its lightness buys it nothing.
Why heavy and light fall together
This looks like it should be impossible. Gravity pulls harder on the heavy hammer, so why does it not win? Because the same heaviness that gives it a bigger pull also gives it more , and more mass is harder to accelerate. The two effects are in a tug of war, and it is a perfect tie. From the straight-line law that acceleration equals force over mass (the exchange rate between push, heft, and motion), if the gravitational pull is itself proportional to mass, the mass cancels:
The acceleration that is left over does not mention mass at all. Near Earth's surface it is about for every falling object, feather or cannonball. This is a derived result: the equal-fall fact is a direct consequence of gravity's pull being proportional to mass, which is the deep and initially surprising thing that had to be true.
Weight is not mass
These two words get used interchangeably in daily life, and the drop makes it worth separating them. Mass is the amount of stuff, unchanging wherever you go. is the force gravity exerts on that mass right now, and it depends on where you are.
Your mass is the same on Earth and on the Moon, but your weight on the Moon is about a sixth, because the Moon's is smaller. You feel this split every time a lift starts down: for a second you feel lighter, not because your mass changed but because the floor briefly pushes up on you with less force. Push that idea all the way and you get weightlessness, which we will need in a moment.
The inverse-square law: gravity thins with distance
Gravity does not stop at the ceiling or the sky. Every mass pulls every other mass, and the strength of that pull follows one clean rule: multiply the two masses, and divide by the distance between their centers squared.
The in the bottom is the part to feel in your hands, so switch the widget to its second tab. Drag the small mass around the central one and watch the pull arrow. Move out to twice the distance and the force does not drop to a half, it drops to a quarter. Three times as far, a ninth. The pull spreads out over the surface of an ever-bigger sphere, and a sphere's area grows with the square of its radius, which is exactly where the squaring comes from. This same inverse-square shape will come back for electric charge and for light.
Gravity never quite reaches zero
Astronauts are not beyond gravity
Here is the second trap. Astronauts on the space station float, so it is natural to assume they have escaped gravity. But the station orbits only a few hundred kilometers up, barely farther from Earth's center than the ground is. Plug that distance into the inverse-square law and gravity there is still about ninety percent of its surface strength.[3] They are drenched in gravity. So why do they float?
Because they, and the station, and everything inside it, are all together. Recall the lift: you feel lighter when the floor pushes up less. In a station that is falling around the Earth, the floor is falling at exactly the same rate you are, so it pushes up on you not at all. Nothing presses on you, so you feel no weight, even though gravity is very much still pulling. Weightlessness is not the absence of gravity, it is the absence of anything holding you up against it. How that endless fall becomes a stable orbit rather than a crash is the whole story of the next lesson.
Lock it in
- In a vacuum, all objects fall with the same acceleration g, because gravity's pull grows with mass exactly as fast as resistance to acceleration does.
- Mass is how much stuff there is and never changes; weight is the force m times g and depends on where you are.
- Newton's law F = G m1 m2 over r squared: double the distance and the pull falls to a quarter.
- Gravity fades with distance but never reaches zero, so orbiting satellites are still firmly held.
- Astronauts float because they are in continuous free fall, not because gravity is gone.
Check yourself
Move a satellite from one Earth-radius away to two Earth-radii away. The gravitational force on it becomes:
Astronauts on the space station float weightlessly mainly because they are:
On the airless Moon, an astronaut drops a hammer and a feather from the same height at the same moment. Which lands first, and why?
Connect equal fall to the mass cancelling. Try to state it, then check.
Match each term to what it means.
how much stuff there is, and its resistance to acceleration
the gravitational force on you, mass times g
the acceleration of free fall, about 9.8 on Earth
moving under gravity alone, which feels weightless
Primary source
The Feynman Lectures on Physics, Vol I, Ch 7 (The Theory of Gravitation)Feynman tells the story of how the inverse-square law was found and why it governs everything from a dropped stone to the orbit of the planets. Free to read online.
Sources