THE SOLUTION to the Mission 13 Student Challenge: Understanding Weightlessness – You Want Me to Take a Bathroom Scale Where?

To teachers starting Mission 13 to ISS, this challenge was posted on Thursday, September 18, 2018. It is designed to help you get your students immersed in Mission 13 microgravity experiment design by first exploring with them the concept of microgravity (the technical term for the phenomenon of ‘weightlessness’). As promised, here is the solution to the Challenge.  

Note: the science content in this solution to the challenge was covered in detail during the professional development videoconference for your Local Team of educators, which supported the launch of Mission 13 in your community. The videoconferences were conducted by SSEP Program creator and Director Dr. Jeff Goldstein. One core objective of the videoconference was to model best teaching practices for how teachers can introduce the curricular story arc in their classrooms. Dr. Goldstein covered the topics: ‘What is microgravity?’, ‘Why are the astronauts weightless?’, ‘ Why would you want to do science in a microgravity environment?’; and ‘How do you facilitate microgravity experiment design in the classroom?’. The story arc, including this challenge and its solution, are part of the Designing the Flight Experiment page, identified during the videoconference as critically important for all Mission 13 teachers and students. Designing the Flight Experiment is a subpage of the Teacher Resources main page, accessed in the navigation banner above. 

 

Ok, I know you’ve been perplexed, and hanging out on the edge of your seat for the last few days. You’ve been patiently waiting for me to read my bathroom scale on top of my 260 mile high mountain (47 times higher than Mt. Everest) that apparently even the U.S. Geological Survey knows nothing about (I checked at their website.) 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. (Is that Jeopardy music playing in the background?)

And now the answer—

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)! Just 2 seconds ago it was heading right for me but was 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 like there’s no gravity. So then I looked down at my bathroom scale, also expecting to be weightless—after all I’m at the same altitude above Earth’s surface as they are. 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 at sea level, I weigh 135 lbs 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.)

Metric system note: in the metric system, which is the system of units used by researchers and in science classrooms, weight is measured in Newtons (N). 150 lbs is equivalent to 667 Newtons (N). At the top of my mountain I’d weigh 90% of my surface weight, so I’d weigh 600 N.

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 too long to realize that’s a big-time misconception. Gravity is keeping the Earth in orbit around the Sun, the Moon in orbit around the Earth, and the Space Station in orbit around the Earth. The Space Station is like an artificial moon.  If we suddenly turned gravity off, the Earth would fly out of its orbit, off in a straight line, and head out into the cold depths of space – where the oceans would freeze, the gases in the atmosphere would freeze and rain down as ice, and all life on Earth would cease to exist. So … gravity in space … GOOD. No gravity in space … BAD.

First some gravity basics. The force of gravity exists between any two masses, e.g., you and your computer, or your car and the building it’s parked next to. 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 entire planet Earth is what we call YOUR WEIGHT. Let’s think about this for a moment. When you jump up, nobody reaches up, grabs you by the ankle and pulls you back down to Earth. There’s this totally unseen force exerted on you by your planet that pulls you back down. You might have even heard the expression that you’re ‘falling under your own weight”, which is, well, what’s happening.

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.

Why? Because all of the mass of Earth is pulling on you, from the part of Earth just under your feet to the part of Earth found on the other side of the planet. This means half the Earth is farther from you than the center of Earth, and half the Earth is closer to you than the center of Earth. So on average, the distance between you and the Earth is 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 (from 3,963 miles to 3,963+260 miles = 4,223 miles). So my weight only goes down a little bit, and is still 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 my calculation shows more precisely that on the mountain I weigh 88% of what I weigh on the surface of the Earth. I’ll round that to 90% since the Space Station orbit can also be a little lower than 260 miles altitude).

Here’s another thing to ponder. When I’m on top of my mountain, at an altitude of 260 miles, I’m at the same location above Earth’s surface as the International Space Station (ISS). That means it and the astronauts are at the same distance from the Earth as I am. So the force of gravity the Earth exerts on ISS – its weight – is also 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 only APPEAR weightless. Big difference. Again, 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 as if somehow gravity is magically turned off for them, or another way to say it – why are they just floating around inside the Space Station? It has to do with the fact that the only force acting on the Space Station and the astronauts is gravity – the gravity exerted by Earth.

Here is an analogy to help you understand. You’re in an elevator in a tall building. The elevator is on the top floor with the doors open so it’s not moving, and the elevator has no windows. Inside the elevator you’re standing on your bathroom scale. You note the scale reads the same weight you see in your bathroom on the surface of Earth.

Why? Even the highest floors of the tallest buildings on Earth are essentially at the surface of Earth when compared to a Mountain rising to an altitude of 260 miles (420 km) – 47 times higher than Mt. Everest. The height of the currently tallest building on Earth, the Burj Khalifa in Dubai, is 0.5 miles (0.8 km). My mountain is 520 times taller! So we can think of the highest floor of a tall building still pretty much at the surface of Earth, and you’d weigh virtually the same as in your bathroom on the surface of Earth.

In the elevator, which you’ll recall is not moving, there are two forces acting on you—gravity pulling you down, and thankfully the floor of the elevator pushing you up with an equal and opposite force. Now (sorry) I cut the elevator cable holding the elevator. You feel that in your stomach? You and the elevator are now falling. The force of gravity exerted by planet Earth on you – your weight – is causing you to fall, and the elevator’s floor is no longer there to push back up on you, because the elevator is falling with you. The force of gravity exerted by Earth on the elevator – its weight – is causing it to fall too. The speed of both you and the elevator is increasing, and we therefore say that you are accelerating. Here is another important definition – if the only force acting on you is gravity we say that you are in free fall. But for the elevator you’re not quite in free fall.

Why? If an object is falling inside Earth’s 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 very beginning of the jump, but the drag force from the air you are falling through 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. You are said to reach a ‘terminal velocity’. But that’s far too fast to survive the landing, so you open a parachute to dramatically increase the drag from the air, and you live to jump another day.

There is air in the elevator shaft, and the air below the elevator causes a drag force that increases as the speed of the elevator increases. So for the elevator to truly be in free fall, let’s remove all the air from the elevator shaft. Let’s also make sure the elevator is not rubbing against the walls of the shaft so that there’s no frictional force on the elevator.

Now you and the elevator are in free fall, and are accelerating under the action of gravity. Since there are no other forces acting on you besides gravity, your speed will just keep increasing until something gets in the way of the elevator. This acceleration is in fact called the acceleration due to gravity, and it has a particular value: 9.8 meters per second per second. What does this mean? Well, every second, your speed increases 9.8 meters/second.

Ummm, I know … that’s kind of meaningless to you since ‘meters/second’ is not a unit of speed that is familiar to you. So here is a better way to say it. The acceleration due to gravity causes an object in free fall (in this case, you, your bathroom scale, and the elevator) to increase in speed 20 mph every second. That’s … huge! After one second, you’re moving at 20 mph. After 10 seconds you’re moving 200 mph. After just 100 seconds (a little more than 1.5 minutes) you’re moving 2,000 mph – assuming it’s a really long elevator shaft. But remember that thing I said about no windows in the elevator? Inside the elevator, you look around and see …. well an elevator, and don’t see the world flying by you at an ever increasing speed. Hey, you hear that? There’s even elevator music still playing (it must be a bluetooth speaker with a battery backup.)

OK, READY FOR THE COOL PART?

The elevator and everything inside – you, and your bathroom scale – are all free falling with the exact same acceleration. The floor is 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 appear to be … weightless!

What? Not convinced? Oh, ok, here’s another way to think about the elevator. Imagine you’re back at the top floor of the building, and inside the motionless 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’re accelerating toward the surface of the Earth in the direction of the elevator’s floor BUT the elevator’s floor is also accelerating toward the surface of the Earth, which is away from you. Every time you move down a certain distance, the floor moves down the exact same distance. You’ve stepped off the chair, but you never get any closer to the floor! What do you see as a passenger inside the windowless elevator? You’re not aware of anything moving. Inside the elevator, you are floating a foot above the floor – you are weightless, and in that elevator it APPEARS as if gravity is turned completely off. The obvious irony is that it is the force of gravity exerted by planet Earth on the elevator, you, the bathroom scale, and the chair that is causing everything to accelerate downward together, yet inside this freely falling environment – inside this freely falling laboratory,  it’s as if gravity has been turned completely off.

Ok, just stopped you with the emergency brakes. Were you worried?

So here is the deal. If you are inside something freely falling (in free fall) like our elevator in an airless shaft, 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.

Now back to the idea of weightlessness as experienced by the astronauts. The Space Station is not resting on a mountain or anything else. The Space Station and everything inside – including the astronauts –  are ONLY experiencing the force of gravity.

Why? 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, so air resistance is pretty negligible.

The Space Station and the astronauts are therefore in free fall, just like you in the elevator, and inside Station everything therefore appears to be weightless.

The International Space Station is falling! This seems contrary to the way most of us think about falling objects, where an object that is falling is getting closer to the Earth. But that too is a misconception. The Space Station is only experiencing the force of gravity, it is therefore in free fall – 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.

The Connection to Microgravity Experiment Design

So what does all this have to do with you designing a real microgravity experiment? The freely falling International Space Station serves as a laboratory for microgravity research. It is one of the main reasons it was built. What that means is that if we bring your experiment in your mini-laboratory to Space Station (say a physical, chemical, or biological system you’d like to study), it will behave as if gravity is turned off. If you conduct the same experiment at the same time on Earth in gravity – called your ‘control’ or ‘ground truth’ experiment – then once your flight experiment is returned to you, a formal comparison of both will allow you to assess the role of gravity in the system you are studying, by seeing if the experiment behaved differently in microgravity when compared to the experiment operated in gravity on the ground. And what you’d like to study … is up to you! You and your team are the microgravity researchers here, so find a system to study that you find interesting. And there are lots of disciplines you can explore, like seed germination, crystal growth, micro-encapsulation, chemical processes, physiology and life cycles of microorganisms (e.g. bacteria), cell biology and growth, food studies, and studies of micro-aquatic life. Your teacher will provide you an understanding of these science disciplines over the next few weeks, which is all covered in the curriculum in the Document Library. So the essential question driving experiment design is …

What physical, chemical, or biological system would I like to explore with gravity seemingly turned off for a period of time, as a means of assessing the role of gravity in that system?

For your next stop on this journey in real science and real spaceflight, go check out the Designing the Flight Experiment page.

Good luck to all SSEP Mission 13 to ISS student microgravity researchers!


To Community Leaders and Teachers

We developed a great grade 5-8 lesson which easily demonstrates that astronauts inside a free falling soda bottle space shuttle appear weightless. The lesson is part of the Building a Permanent Human Presence in Space compendium of lessons for the Center’s Journey through the Universe program. The lesson is titled Grade 5-8 Unit, Lesson 1: Weightlessness, which can be downloaded as a PDF from the Building a Permanent Human Presence in Space page. You can also read an overview of the lesson conducted as part of one of the many Journey through the Universe Educator Workshops, this one in Muncie Indiana.

Photo credit: NASA (there was no mountain in their photo — promise. I’m getting good at photoshop.)

 


The Student Spaceflight Experiments Program (SSEP) is a program of the National Center for Earth and Space Science Education (NCESSE) in the U.S., and the Arthur C. Clarke Institute for Space Education internationally. It is enabled through a strategic partnership with DreamUp PBC and NanoRacks LLC, which are working with NASA under a Space Act Agreement as part of the utilization of the International Space Station as a National Laboratory. SSEP is the first pre-college STEM education program that is both a U.S. national initiative and implemented as an on-orbit commercial space venture.

The Smithsonian National Air and Space MuseumCenter for the Advancement of Science in Space (CASIS), and Subaru of America, Inc., are U.S. National Partners on the Student Spaceflight Experiments Program. Magellan Aerospace is a Canadian National Partner on the Student Spaceflight Experiments Program.

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The Student Spaceflight Experiments Program (SSEP) is a program of the National Center for Earth and Space Science Education (NCESSE) in the U.S., and the Arthur C. Clarke Institute for Space Education internationally. It is enabled through a strategic partnership with DreamUp PBC and NanoRacks LLC, which are working with NASA under a Space Act Agreement as part of the utilization of the International Space Station as a National Laboratory. SSEP is the first pre-college STEM education program that is both a U.S. national initiative and implemented as an on-orbit commercial space venture.