Does a ball fall the same way on every world?

Here are five towers, each 10 metres tall, on five different worlds. The same ball sits at the top of each. Let go of all five at once and watch which lands first.

Every ball in the towers was the same. So what about a heavy thing and a light thing on the same world? On Earth a feather drifts down long after a hammer, which makes it look as if heavy things fall faster.

On 2 August 1971, at the end of the last moonwalk of Apollo 15, astronaut David Scott held a hammer in one hand and a falcon feather in the other, in front of the TV camera. "I'll drop the two of them here and, hopefully, they'll hit the ground at the same time."

They landed together, after 1.41 s. Gravity pulls harder on the hammer, but the hammer also needs a harder pull to get moving, and the two cancel exactly. On Earth it's the air, not gravity, that holds the feather back. The Moon has almost no air, so nothing does.

Everything falls, then. And that means the Moon must be falling too.

Isaac Newton asked this question and answered it with an imaginary cannon on an impossibly tall mountain, with no air anywhere. Fire a ball sideways and it curves down to the ground. Fire it faster and it lands farther away, where the ground has already started to curve away beneath it. Keep going.

Not one speed, as it turns out, but a range: too slow and it lands, a little faster and it circles, faster still and it swings out on an oval. Somewhere above that it never comes back at all. Try it with a planet and the Sun, at Earth's own distance.

Newton could say how strongly gravity pulls, but not how it reaches across empty space. Albert Einstein later gave a different answer: mass bends space and time around it, and things moving nearby follow the straightest path they can through that bent space and time.

The picture everyone uses is a stretched sheet with a heavy ball in the middle. Here the marble's path is worked out from real gravity; the sheet is only a picture of it, with the dent hugely exaggerated. Try to hit a target hidden straight behind the mass.

Where the sheet gets it wrong

• It uses gravity to explain gravity. A real rubber sheet only dents because Earth pulls the ball down. Switch off "Earth's pull under the sheet" and the dent and the bending both vanish.
• It leaves out time. Near Earth, most of what makes things fall is time running slightly slower lower down, and a sheet can't show that.
• It can't get orbits right. No real 2D surface makes marbles roll the way planets move, which is why the paths here come from Newton's gravity instead.
• There is no "down" in space. The dent points into a direction that doesn't exist. A black hole is not a hole or a funnel.

The closer you get to a mass, the stronger its pull. So squeeze a star into a smaller ball, keeping all its mass, and you can stand much closer to its centre. The speed needed to escape from its surface goes up. How small before not even light can get away?

Everything here was falling: the balls, the hammer and the feather, the cannonball, the planet, and the Moon. Earth falls round the Sun at 29.8 km/s, and the Moon falls round Earth at 1.02 km/s.