The physics of artificial gravity (grade 10 and higher)

What is artificial gravity?

Artificial gravity (sometimes referred to as pseudogravity) is the creation of an inertial force that mimics the effects of a gravitational force, usually by rotation.^[1] Artificial gravity, or rotational gravity, is thus the appearance of a centrifugal force in a rotating frame of reference (the transmission of centripetal acceleration via normal force in the non-rotating frame of reference), as opposed to the force experienced in linear acceleration, which by the equivalence principle is indistinguishable from gravity. In a more general sense, “artificial gravity” may also refer to the effect of linear acceleration, e.g. by means of a rocket engine.^[1]

Rotational simulated gravity has been used in simulations to help astronauts train for extreme conditions.^[2] Rotational simulated gravity has been proposed as a solution in human spaceflight to the adverse health effects caused by prolonged weightlessness. However, there are no current practical outer space applications of artificial gravity for humans due to concerns about the size and cost of a spacecraft necessary to produce a useful centripetal force comparable to the gravitational field strength on Earth (g).^[3] Scientists are concerned about the effect of such a system on the inner ear of the occupants. The concern is that using centripetal force to create artificial gravity will cause disturbances in the inner ear leading to nausea and disorientation. The adverse effects may prove intolerable for the occupants

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
• Scissors
• Optional: Duct tape
• Permanent marker
• Tape measure
• Stopwatch
• Volunteer
• Access to open outdoor area or large room free from obstructions like furniture, such as a gymnasium
• Lab notebook

Experimental Procedure

1. 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.
2. 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.
3. 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.
4. 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.
5. 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.
6. 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.
7. To conduct one trial:
   1. Make sure you are in an open area free from obstructions, and that your volunteer is standing a safe distance away with a stopwatch.
   2. Open your accelerometer app and start recording data.
   3. Securely put your phone inside the box with the screen facing up so you can access it.
   4. 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).
   5. 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.
   6. Gently bring the phone to a stop after the volunteer has recorded the time for 10 revolutions.
   7. Record the radius and time for 10 revolutions in a data table like Table 1.

8. 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.
9. 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.
10. Repeat steps 7–9, but swing the phone slightly faster this time.
11. Repeat steps 7–9, but swing the phone as fast as you can (be careful!).
12. Switch to a new radius and repeat steps 7–11. Repeat these steps for each radius you want to test.
13. 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:
15. Equation 3:$$a_c=\frac{4{\pi }^{2}r}{T^2}$$where
    • a_c 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.
16. To calculate your phone’s linear velocity (v), use the equation
18. Equation 4:$$v=\frac{2\pi r}{T}$$
19. For each radius you tested, make a graph of centripetal acceleration (both theoretical and experimental) vs. velocity.
    1. What is the relationship between centripetal acceleration and velocity? Is this what you expect based on Equation 1 in the Background?
    2. What is the relationship between centripetal acceleration and radius? Is this what you expected based on Equation 1 in the Background?
    3. Do your experimental results match your calculations? If they are not the same, what could have caused the difference?
20. 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?

• Can you build a scale-model artificial gravity demonstration using building toys like LEGO® bricks or K’Nex®?