## THE SOLUTION to the Student Challenge: Understanding Weightlessness – You Want Me to Take a Bathroom Scale Where?

Published on September 21, 2013 by in News

Ok, I know you’ve been perplexed, and hanging out on the edge of your seat for the last week. And to all the students, particularly in North Attleborough, Massachusetts, that left comments, hey they were really great guesses!

You’ve been patiently waiting for me to read my bathroom scale on top of my 260 mile high mountain that apparently even the U.S. Geological Survey knows nothing about (I checked at their web site.) Wait! You say you have no clue what I’m talking about? Hey, you’ve got to read the original challenge FIRST! None of this lazy stuff going right to the answer.

Go read the original challenge, think about it for a while, and come back. I’ll wait right here for you. (What’s that Jeopardy music playing in the background?)

So I go to the top of my 260 mile (420 km) high mountain, and look … here comes the International Space Station … and there it goes! Man, it was moving fast. It was cruising at a whopping 4.7 miles PER SECOND (7.6 km/s)! So 2 seconds ago, it was heading right for me, but still 4.7 miles away. A second ago it flew right by my face, and I looked in the window really really fast. And now it’s 4.7 miles away, heading away from me really fast.

Sure enough, when I looked inside, the astronauts were weightless—just floating around. So then I looked down at my bathroom scale, also expecting to be weightless—after all I’m at the same place they were. BUT WAIT!! My scale says I weigh nearly the same as my weight in my bathroom at home. More precisely, on top of my mountain I weigh 90% of my weight at sea level! So if I weigh 150 lbs (68 kg) at sea level, I weigh 135 lbs (61.2 kg) on my mountain. (Hmmm, wonder if I’ve discovered a new way to diet.) And I bet some of you won’t buy this without seeing the calculations. That’s good. That’s being a great scientist. (Keep reading.)

But this can’t be right!  Why are the astronauts weightless?

Lots of folks assume that a weightless astronaut means that gravity is somehow turned off in space. But you don’t need to think about this long to realize that’s a big-time misconception. Gravity is keeping the Space Station in orbit around the Earth, the Moon in orbit around the Earth, and the Earth in orbit around the Sun. If we suddenly turned gravity off, the Earth would fly out of its orbit, off in a straight line, and head out of the Solar System. Gravity … GOOD. No gravity … BAD.

First some gravity basics. The force of gravity exists between any two masses, e.g., you and your chair, or your car and the fire hydrant it’s parked next to (hey move your vehicle.) But as forces of nature go it’s a really weak force. So for you to easily see it in action, at least one of the masses needs to be really massive. A good example is the force of gravity between YOU and the EARTH. The Earth is pretty massive, and the force exerted on you by the Earth is what we call YOUR WEIGHT. The force between two masses also depends on the distance between them. If you increase the distance between two masses, the force of gravity decreases. This comes together mathematically in the LAW OF UNIVERSAL GRAVITATION, a cool and pretty simple equation courtesy of Mr. Isaac Newton.

Ok, now let’s apply this. In the case of you and Earth, the distance between you and Earth is actually the distance between you and the center of Earth. But that distance is just the radius of Earth, or 3,963 miles (6,378 km.) When I go from sea level to the top of my really tall mountain, 260 miles (420 km) high, I’m increasing the distance between me and the center of Earth only a little bit. So my weight only goes down to 90% of its value at sea level. I actually used Mr. Newton’s equation to calculate my weight on top of my mountain. For those of you that want to see the calculation, I wrote it in my scratchy long-hand HERE. (Note the calculation was actually written for a slightly lower orbit for the Space Shuttle at 210 miles altitude).

Here’s another thing to ponder. The International Space Station (ISS) is pretty massive compared to you, and when it goes into orbit at 260 miles altitude, it also weighs 90% of its weight at sea level. The weight of an astronaut is also therefore 90% of his/her weight at sea level. THEY ARE NOT WEIGHTLESS. The term WEIGHTLESS leads to a deep misconception. They APPEAR weightless. Big difference. Remember that your weight is the force of gravity exerted on you by the Earth. There is NO question that such a force is exerted by Earth on both the Space Station and the astronauts inside.

But why do they APPEAR weightless? Well in my case, I’m standing on top of my mountain, where the mountain is holding me up and keeping me from falling under the action of gravity. Gravity is pulling me down with a force defined as my weight, and the mountain is reacting under the ‘load’ with an equal and opposite force up. So for me, I feel two forces: gravity pulling me down, and the mountain pushing me up. The forces cancel each other, so my body isn’t literally forced to go somewhere else, and I just stand there at 90% of my sea level weight. I know my weight because the spring in my bathroom scale is being compressed between the two forces, which causes the scale to show my weight. My bones also feel the resulting compression, which lets my body know that my bones are doing a good thing and are useful to keep (not the case in orbit where my body senses no bone compression, therefore thinks bones serve no useful purpose, and bone calcium is excreted.)

But the Space Station is not resting on a mountain or anything else. The Space Station is ONLY experiencing the force of gravity. When that happens we call the situation free fall. The International Space Station is falling!! (I know!) This seems contrary to the way most of us think about falling objects, where an object that is falling is headed toward the Earth. But that too is a misconception. The Space Station is only experiencing the force of gravity, it is therefore falling – and it is moving around the EarthHere’s something I wrote for a grade 5-8 lesson on free fall (See the “To Community Leaders and Teachers” section below), and it explains how you can be falling around the Earth.

Now back to the idea of weightlessness. Here is an analogy to help you understand. You’re in an elevator in a tall building. The elevator is on the top floor. Inside the elevator you’re standing on your bathroom scale. You note the scale reads your correct weight plus a couple of pounds ’cause you just finished lunch at the spiffy top floor restaurant. Two forces are acting on you—gravity pulling you down, and thankfully the floor of the elevator pushing you up. Now (sorry) I cut the elevator cable. You feel that in your stomach? You’re now in free fall. You’re falling because I removed the ability of the elevator’s floor to push you back. The floor of the elevator is now falling WITH you. And the bathroom scale between your feet and the floor? Well, it’s also falling WITH you! There is now no way for the spring in the scale to be compressed between your feet and the floor … because the floor isn’t going to be pushing back. Look at the scale … it reads ZERO. You are weightless! What …. that’s not convincing you?? Hmmmm……

Oooh oooh! Got it! Here’s another way to think about the elevator!  Ok, imagine you’re back at the top floor and inside the elevator you are standing on a small chair, which puts you 1 foot above the floor. You decide to walk off the edge of the chair. But at the moment you walk off the chair you hit a button on the wall that detaches the cable holding the elevator, and the elevator and you plummet downward together, accelerating under the action of gravity. Now you are accelerating in the direction of the elevator’s floor BUT the elevator’s floor is accelerating in the same direction, which is away from you. You’ve stepped off the chair, but you never get any closer to the floor! What do you see as a passenger inside the elevator? You’re not aware of anything moving. Inside the elevator, you are floating a foot above the floor, as if weightless!

Ok, just stopped you with the emergency brakes.

So here is the deal. If you are inside something falling (in free fall) like an elevator or Space Station, you appear weightless. That’s because everything inside is falling with you, including the floor, walls, and ceiling—though calling them floor, walls, and ceiling is now rather meaningless.

A note to the deep thinkers (those that want to say “but Dr. Jeff you’re wrong.”) Yes, if the object is falling inside the atmosphere (like our elevator), it is technically not in free fall very long since the drag caused by the air soon becomes a force that needs to be considered. For instance, if you jump out of a plane, you’re in free fall in the beginning of the jump, but the drag force increases as your speed increases. Soon you get up to about 100 mph (160 km/hr) and you won’t go any faster because the force of gravity down is balanced by the drag force up due to the air. But that’s still a bit too fast for a landing, so you open a parachute to dramatically increase the drag from the air, and you live to jump another day.

So what I said above would definitely be the case if the air in the elevator shaft were removed. And for the Space Station, well it’s in OUTER SPACE (say it with an echo for effect), and above the atmosphere, at least 99.999% of the atmosphere, and it is truly falling around the Earth. That’s how I can read 90% of my weight standing on the mountain, and still see “weightless” astronauts inside the Station as it flies by the top of my mountain.