The Physics of Artificial Gravity
AbstractHow can we make space stations with artificial gravity a reality? In this science project, you will explore the physics of creating artificial gravity with circular motion.
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Determine how circular motion can be used to generate artificial gravity similar to Earth's.
Movies about space travel frequently feature circular or doughnut-shaped ships and space stations that rotate to generate artificial gravity (Figure 1). Artificial gravity could help reduce the negative health effects of prolonged space travel, like loss of bone and muscle mass. It could also make other tasks that are difficult in space, like going to the bathroom, much easier! However, despite their frequent appearance in movies, rotating spaceships with artificial gravity do not yet exist (as of 2020). To understand some of the challenges behind building such a spaceship, first you need to understand the physics of artificial gravity. That is what you will explore in this project.
Figure 1. Concept art for the Nautilus-X space station, including a spinning, doughnut-shaped section to generate artificial gravity.
Real gravity occurs because of the gravitational attraction between two objects with mass. Earth is very massive, so there is a strong gravitational attraction between Earth and our bodies. That is what keeps us from floating off into space! The downward acceleration due to gravity of an object in free-fall at Earth's surface is 9.8 meters per second squared (m/s²). When you stand on the surface of Earth, your weight due to gravity pulls you down. According to Newton's third law of motion, for every reaction there is an equal and opposite reaction, so the surface of Earth pushes back up on your feet. This reaction force is called the normal force. "Normal" means "perpendicular"—the force is perpendicular to Earth's surface (Figure 2).
Figure 2. A person standing on the surface of Earth with arrows representing the person's weight (W) and the normal force on the person's feet (N). Image not to scale!
There is no way we could build a spaceship massive enough to have its own gravity similar to Earth's. However, we can use a trick—make the spaceship spin instead. Any object moving in a circle experiences a centripetal acceleration. The classic example of this is a ball being twirled on a string in a horizontal plane (Figure 3). The centripetal force on the ball is the tension T from the string. If the ball moves in a circle with radius r with linear velocity v, then the centripetal acceleration is
Figure 3. Top view of a ball being twirled on a string with radius r and velocity v. The tension T in the string is the only force acting on the ball (neglecting air resistance).
You feel a centripetal force when you ride in a car that goes around a sharp turn. For example, if you are sitting on the right-hand side of a car that turns sharply to the left, you will feel the door of the car push on you. This force points inward, toward the center of the car's circular path. We can use the same effect to make a space station with artificial gravity. If an astronaut stands on the inner wall of a rotating circle, the inner wall of the circle will exert a normal force on his or her feet. This allows the astronaut to stand on the inside of the circle (Figure 4) without floating away, as if it were on the ground. The centripetal acceleration felt by the astronaut can be calculated using Equation 1.
Figure 4. An astronaut standing on the inner wall of a rotating circle with radius r. The astronaut's feet move with linear velocity v, and the normal force on the astronaut's feet is N.
So, at this point, you might be thinking: "Ok, this is easy! Just build a space station with a radius and velocity such that the centripetal acceleration is 9.8 m/s2. Done!" Unfortunately, it is not that simple; there are some important design tradeoffs to make. For example, if the radius of the station is too small, there could be a significant difference between the acceleration felt by the astronaut's head and the astronaut's feet (see the reference by C. Scharf in the Bibliography). You could get around this problem by making the station very large, so the radius difference between the astronaut's head and feet is negligible, but such a huge station would be very difficult and expensive to build. If the station spins too fast, the astronauts could get disoriented when they look out the window and see all the stars spinning. If the station spins too slowly, astronauts could even negate the effects of artificial gravity by running "backwards" inside the circle!
In this science project, you will do your own experiment to determine how changing radius or rotational speed affects centripetal acceleration. Can you come up with your own design for a space station?
Some students get confused when they see the formula for centripetal acceleration. If you have taken high school physics, you probably learned that linear acceleration is change in velocity per change in time, or
But in Equation 1, there is only one value for velocity, v. How can there be acceleration if there is no change in velocity? It is important to remember that velocity is a vector—it has both a magnitude and a direction. Even if the magnitude of the velocity does not change, its direction can still change. That is what happens with an object moving in a circle at constant speed; its direction changes, so the object still experiences acceleration. See the "Geometric Proof of Inward Acceleration" paragraph under the "Acceleration" section in the Physics Classroom link in the Bibliography for a more-detailed explanation.
Sometimes people get the words "centripetal" and "centrifugal" mixed up or use them interchangeably. Be careful! The words have very different meanings. Centripetal force is the real, physical force exerted on an object that makes it move in a circle, such as the tension on the string in Figure 3, or the normal force on the astronaut's feet in Figure 4. It points toward the center of the circle. Centrifugal force is an "imaginary force" that only exists in the reference frame of an observer rotating along with the ball on a string (or with the astronaut). Rotating reference frames are an advanced topic in physics. You do not need to worry about them in this project, but the Physics Classroom reference in the Bibliography has more information if you are curious.
Terms and Concepts
- Artificial gravity
- Normal force
- Centripetal acceleration
- Centripetal force
- How is artificial gravity different from "real" gravity?
- How does centripetal acceleration change if you increase the radius?
- How does centripetal acceleration change if you increase the velocity?
- What are some practical concerns with artificial gravity?
- Scientific American. (2005, August 15). How does spending prolonged time in microgravity affect the bodies of astronauts?. Retrieved September 4, 2020.
- Scharf, C. (2015, April 6). Watch the First Artificial Gravity Experiment. Retrieved September 4, 2020.
- Bisceglio, P. (2013, March 13). How Do Astronauts Go to the Bathroom in Space?. Smithsonian Magazine. Retrieved September 4, 2020.
- Henderson, T. (n.d.). Mathematics of Circular Motion. The Physics Classroom. Retrieved September 4, 2020.
- Hall, T. (2018, September 9). Comfort Criteria. SpinCalc. Retrieved September 4, 2020.
Materials and Equipment
- Smartphone, with permission to download an accelerometer app that can record data
- Sturdy string or small-diameter rope
- Small cardboard box
- Foam padding
- Masking tape
- Optional: Duct tape
- Permanent marker
- Tape measure
- Access to open outdoor area or large room free from obstructions like furniture, such as a gymnasium
- Lab notebook
- Make sure your string is strong enough to do this project. Grab the string with your hands about 30 cm apart, and yank on the string as hard as you can. If the string breaks, it is not strong enough to twirl your phone around. If needed, get some stronger string.
- Construct a padded box to hold your phone (Figure 5). This box will protect your phone while you twirl it around (and just in case the string breaks or you accidentally let go). Your phone should be laid down flat (not at an angle) and fit snugly inside the box without sliding around, but should also be easy to remove so you can access the screen.
Figure 5. Padded box to hold the phone, with holes for string.
- Poke two small holes in opposite sides of the box, a few centimeters from the edge. Optionally, you can reinforce the edges of these holes with duct tape. Thread the string through them. Instead of tying a knot in the string, you can just hold on to both ends of the string when you twirl it (Figure 6). A knot could come undone, causing your box to fall.
- Go to an open area that is free of obstructions (a soft surface, like grass, is best) and practice swinging your phone around in a radius of 1—2 m, gently at first! Make sure you can do so safely and that your box and string do not break.
Figure 6. Overhead view of the experiment. Note how the box has one long piece of string threaded through it, so you can hold on to both ends, as opposed to tying a knot in the string and only holding on to one end.
- Most modern smartphones contain accelerometers, which are electronic sensors that can measure acceleration. With permission, search for and download an accelerometer app on your phone. Most of these apps will record acceleration in three directions labeled X, Y, and Z (Figure 7). You should find an app that lets you record data (as opposed to just displaying instantaneous data). For your experiment, you will want to record the acceleration that points along the radius of your circle (inward in Figure 6), not tangential to the circle or up/down (out of the screen in Figure 7).
Figure 7. Example of the X, Y, and Z axes on a phone.
- Using a tape measure, masking tape, and a permanent marker, mark the radii that you plan to test along your string. For example, you could test in 0.5-m increments. It will become difficult to twirl the string with a radius longer than a few meters, but try to go as high as you can.
- To conduct one trial:
- Make sure you are in an open area free from obstructions, and that your volunteer is standing a safe distance away with a stopwatch.
- Open your accelerometer app and start recording data.
- Securely put your phone inside the box with the screen facing up so you can access it.
- Hold the string at one of your length markers, and start twirling the string above your head. Do your best to twirl the string at a constant speed, just fast enough to keep the string mostly horizontal (so the box is not dragging on the ground).
- Once you have the phone twirling at a constant speed, your volunteer should use the stopwatch to time how long it takes you to do 10 full revolutions. You will do 10 revolutions and calculate an average, to account for variations in the rotation speed.
- Gently bring the phone to a stop after the volunteer has recorded the time for 10 revolutions.
- Record the radius and time for 10 revolutions in a data table like Table 1.
|Time for 10 Revolutions
|Period for 1 Revolution |
| Linear Velocity
|Experimental Centripetal Acceleration
|Calculated Centripetal Acceleration |
- Find the average experimental centripetal acceleration over your 10 full revolutions. To do this, you may need to crop your recorded data. Figure 8 shows an example of one complete trial. Note how the data has "ramp up" and "ramp down" periods at the beginning and end. You only want the data from the middle part where the phone was spinning at a roughly (but not perfectly) constant speed. Some apps will let you crop the data and will automatically calculate an average value for you. For other apps, you may need to export the data to a computer and analyze it in a spreadsheet program to calculate the average.
Figure 8. Screenshot of recorded accelerometer data.
- Repeat step 7 two more times, for a total of three trials at this radius and speed. Do your best to swing the phone at the same speed each time.
- Repeat steps 7–9, but swing the phone slightly faster this time.
- Repeat steps 7–9, but swing the phone as fast as you can (be careful!).
- Switch to a new radius and repeat steps 7–11. Repeat these steps for each radius you want to test.
- Now, for each one of your trials, calculate a theoretical centripetal acceleration and record this value in your data table. You can do this using Equation 1 from the Background, but it is easier to convert this equation to a form that uses the period of rotation, T, instead of the linear velocity:
- ac is the centripetal acceleration, in meters per second squared (m/s²)
- r is the radius, in meters (m)
- T is the period for one revolution, in seconds (s). Note that since your volunteer recorded the amount of time for 10 revolutions, you will need to divide that time by 10 to get the period for 1 revolution.
- To calculate your phone's linear velocity (v), use the equation
- For each radius you tested, make a graph of centripetal acceleration (both theoretical and experimental) vs. velocity.
- What is the relationship between centripetal acceleration and velocity? Is this what you expect based on Equation 1 in the Background?
- What is the relationship between centripetal acceleration and radius? Is this what you expected based on Equation 1 in the Background?
- Do your experimental results match your calculations? If they are not the same, what could have caused the difference?
- Based on your experiments and background reading, do you have any recommendations for a space station that can generate artificial gravity similar to Earth's, but not cause motion sickness or other problems for astronauts?
Ask an Expert
- If you do not want to risk twirling your phone around on a string, you can do a smaller-scale version of this experiment using a salad spinner. See the Science Buddies project Separating Butter with a Salad Spinner Centrifuge.
- Can you build a scale-model artificial gravity demonstration using building toys like LEGO® bricks or K'Nex®?
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