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Treebeard's Stumper Answer
7 February 2003

Weight Loss

My thoughts are with the space shuttle Columbia this sad week. I stand with grief and respect for the STS-107 science mission and that remarkable crew. They did many microgravity experiments this trip, including three experiments with flames and combustion, one of my very first stumpers. We speak easily of microgravity, zero-g, free fall, and being weightless. But the Earth's gravity does not suddenly stop in space, or else the shuttle (and Moon) would fly away instead of orbiting our planet. How can there be "zero-gravity" so close to home? What can we learn?

This "zero-g" photo is from the collection of STS-107 mission photos at spaceflight.nasa.gov. Don't try this at home! The NASA photo caption reads:

A few of the STS-107 crewmembers pose for a photo in the SPACEHAB Research Double Module aboard the Space Shuttle Columbia. Clockwise from the bottom are astronauts David M. Brown, mission specialist; Michael P. Anderson, payload commander; Kalpana Chawla, mission specialist; and payload specialist Ilan Ramon. The Combustion Module-2 (CM-2) facility is visible in the background. Ramon represents the Israeli Space Agency.

I had this stumper in mind before the Columbia was lost last Saturday. We talked about it in my science classes last week on Tuesday, January 28, the anniversary of the space shuttle Challenger disaster. I remember exactly where I was when I heard the news. Julie woke me with the news on Saturday morning, and I said "No, that was years ago...." I was ready to drop this stumper, but a young DMS student asked something like "I don't get it, what does the space shuttle do?" I think my questions are just right: How can there be "zero-gravity" so close to home? What can we learn from the experiments? Is it worth it?

For more info on the space shuttle Columbia disaster, check out NASA, Space.com, the Columbia Loss FAQ, and all the usual Internet sources.


Gravity always attracts. The space shuttle crews float because they are falling, but they fall around the Earth instead of down. Isaac Newton thought of a cannon on an impossibly tall mountain. Air drag and gravity would bring a normal cannon ball down. But imagine shooting a projectile so fast and high that the curve of its fall matches the curve of the Earth. That's an orbit. It's always falling so an onboard scale would register no weight. We can all experience zero-g for a moment at any amusement park. Only in space can a few fall for weeks and advance our knowledge. Ad astra!

Notes:

Trevor was the first DMS student to figure this out. It was not obvious to my students, and I'm not surprised.

Sir Isaac Newton first explained the idea of an orbit in his 1687 Principia Mathematica. (Though I believe the familiar picture (right) is from his Treatise of the System of the World written in the 1680s?) Imagine a mountain so tall that the summit stands above the Earth's atmosphere. Now fire a cannon straight out from the top. The cannonball falls of course, but with more speed it will go farther around the curve of the planet. With enough speed, it will not hit the Earth at all, but will fall towards the Earth just as fast as the earth curves away from it. With no air resistance above the atmosphere to slow it down, the projectile will travel forever in a circular (or elliptical) orbit around the Earth. It's a brilliant thought experiment that explains everything in an "Aha!" kind of way, and Newton had the math behind it to explain the details. An orbiting body like the Moon or the space shuttle is falling just like an apple from a tree under the force of gravity. Distance and speed make the trajectory different, but they are falling all the time under the same force of gravity.

I don't have to do a physics lesson about gravity here, since it's already been done many times on the Web, eg at The Physics Classroom. I'll try to do this without (much) math, but it's like a burger without the meat.

For one thing, we have the wrong idea of what the space shuttle path around the Earth looks like. I think of the space shuttle as "way up there". In fact the shuttle is in a low orbit of about 300 kilometers or 200 miles above the surface. The Earth's radius is about 6,400 kilometers or 4000 miles. In round numbers, the ratio comes to

    orbit height   300 km    200 miles     1
    ------------ = ------- = ---------- =  --
    earth radius   6000 km   4000 miles    20

That's the radius, so the ratio is about 1/40 for the diameter. If I show the Earth as a 180 pixel diameter (not-quite) circle like Newton's classic picture above, then the space shuttle orbit is not quite 5 pixels above it. Newton's impossible mountain is 17 pixels high, more like 750 miles. Of course gravity is still a factor this close to Earth, about 90% of normal.
            64002
    gs = ----------- = 0.91 g
         (6400+300)2

And yes, a satellite could "in principle" orbit at treetop level if there were no mountains or buildings in the way and no air drag to slow it down. Could a satellite also orbit inside the Earth through an airless tunnel? Would it be faster or slower? Now there's a mass transit system!





Newton's Mountain (top) and the
real space shuttle orbit (below).



The space shuttle circles in a near-earth orbit, and the atmosphere is even closer. Consider this sunrise photo by the space shuttle Endeavor STS-47 crew (from APOD, 15 Jan 2000), and the comment by someone who has been there:


"For the first time in my life, I saw the horizon as a curved line. It was accentuated by a thin seam of dark blue light - our atmosphere. Obviously, this was not the "ocean" of air I had been told it was so many times in my life. I was terrified by its fragile appearance." - Ulf Merbold, West German space shuttle astronaut, 1990

The words we use to describe how the shuttle crew can float around in space are also confusing and misleading:

  • Zero Gravity
  • Gravity is a universal force that pervades the universe. It quickly fades away as the inverse square of distance, but it never disappears. Gravity works just fine in a vacuum without an atmosphere. The space shuttle has air, and candles still burn (sort of) and the astronauts can hover without space suits. I suppose there might be places in the Univese where gravity "cancels out" in all directions, but it's still there. "Zero Gravity" is a good name for a carnival ride, but it's not real.
  • Zero-g
  • "Small g" is the acceleration with which a body (any body) falls to Earth by gravity, about 9.8 m/sec2 or 32.2 ft/sec2 at the surface of the Earth. The shuttle astronauts are a bit higher, so their small-g is about 10% less, but still substantial. They are still subject to that acceleration towards the Earth, which is why they orbit instead of flying away on a tangent. They are falling at "one-g" around the Earth, and so is everything else around them.
  • Weightless
  • I wish it was that easy to lose weight! Maybe it's just a matter of words. If you think your weight changes when you ride a roller coaster or jump up and down on your bathroom scale, then so be it. You can also zero-adjust your scale lower without exercising. By physics, your weight is given by the formula w=mg in orbit or not, though your scale might not show it. * sigh *
  • Microgravity
  • Really it's a misnomer, though this is NASA's approved word for what the astronauts study on the space shuttle and ISS missions. "Micro-" means one-millionth, and to get to a place with just one-millionth of the Earth's gravity you would have to travel about 6.4 million kilometers from Earth, almost 17 times farther away than the Moon. NASA studies microgravity another way, by falling...
  • Free Fall
  • This is the right word. Being on the space shuttle really is falling. Everything is falling, so you don't feel the usual counter-force of the floor or chair or bathroom scale pushing back at you. But in orbit you're falling around the Earth, not down like a sky-diver. Of course gravity is still in control - you're falling! I remember doing the Superman free fall ride at Six Flags Magic Mountain for the first time. I was with school kids, so I couldn't chicken out. I held a penny in my hand to see it float and went *upPps* and clenched it when we fell. NASA has an even better ride dedicated to microgravity research at their Glenn Research Center Drop Tower, but it's hard to get a ticket!

    As I write this, the space shuttle Columbia investigation continues. There is endless talk about the future of the space shuttle program by armchair critics:

    The Russian Sputnik 1 was launched on my 10th birthday, October 4, 1957, just the right age to dream great things. Sputnik was the first artificial satellite since Newton got the idea. I saw it pass over Santa Monica, and I heard it warble on my neighbor's ham radio rig. The microgravity research is fascinating and hard to duplicate in a 2.2 second drop tunnel on Earth. I remember Robert A. Heinlein's statement, something like "Earth is too small a basket for mankind to keep all its eggs in." Most of all, space is another chance to get it right. Fix the shuttle, make it better, keep it going, I'll help pay for it. Ad astra!

    Here are some Web links for your own research on this stumper.

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    Copyright © 2003 by Marc Kummel / mkummel@rain.org