I watched director Alfonso Cuarón’s Gravity last night, and if you haven’t seen it, yes, it’s good. It’s suspenseful, it’s got heart, it’s got stunning shots of what the Earth looks like from high orbit, and Sandra Bullock and George Clooney both turn in fine performances.
But beyond being a good movie, it reminded me of something I just read in renowned MIT physics professor Walter Lewin’s For the Love of Physics about why astronauts are weightless in orbit. If you think it’s because they’re far enough away to no longer be affected much by the Earth’s gravity—which is what my intuition was, without having thought about it seriously— think again.
But beyond being a good movie, it reminded me of something I just read in renowned MIT physics professor Walter Lewin’s For the Love of Physics about why astronauts are weightless in orbit. If you think it’s because they’re far enough away to no longer be affected much by the Earth’s gravity—which is what my intuition was, without having thought about it seriously— think again.
Your weight as you stand on the surface of the Earth is a function of your mass, the mass of the Earth (about 6 trillion trillion kg) and the distance between you and the centre of the Earth. This distance is an average of 6,371 km (average because the Earth is not a perfect sphere). As you get farther away from the centre of the Earth, the force of gravity does decrease. But even the Hubble Space Telescope, where our heroes find themselves at the start of the film, is only another 559 km away from the centre of the Earth, which is to say, only about 8% farther. Because the force of gravity is inversely proportional to the square of the distance between two objects, they should still weigh about 85% (92% squared) of what they weigh on the ground.
Now, if they had travelled up a space elevator, for instance, and were standing on the top floor, 559 km up, they would feel only 15% lighter. The reason they feel 100% lighter instead… is that they are in free fall. The Hubble Space Telescope, the International Space Station, and space shuttles and satellites when they’re in orbit, are all in the process of falling back down to Earth. As Professor Lewin explains, “The reason why the astronauts don’t go splat is because the Earth is curved and the astronauts, the spaceship, and everything inside it are moving so fast that as they fall toward Earth, the surface of the planet curves away from them.” And of course, if the force of gravity were really negligible up there, they wouldn’t keep circling the Earth; they would shoot off into space in a straight line.
Even though I have two years of high school physics under my belt, and have tutored high school physics now and again over the years, I still had it wrong. It’s a humbling reminder, for me, of how imperfect human intuition can be.
Now, if they had travelled up a space elevator, for instance, and were standing on the top floor, 559 km up, they would feel only 15% lighter. The reason they feel 100% lighter instead… is that they are in free fall. The Hubble Space Telescope, the International Space Station, and space shuttles and satellites when they’re in orbit, are all in the process of falling back down to Earth. As Professor Lewin explains, “The reason why the astronauts don’t go splat is because the Earth is curved and the astronauts, the spaceship, and everything inside it are moving so fast that as they fall toward Earth, the surface of the planet curves away from them.” And of course, if the force of gravity were really negligible up there, they wouldn’t keep circling the Earth; they would shoot off into space in a straight line.
Even though I have two years of high school physics under my belt, and have tutored high school physics now and again over the years, I still had it wrong. It’s a humbling reminder, for me, of how imperfect human intuition can be.