REVIEW OF PREVIOUS RESEARCH
Student Understanding of Gravity at the K-12 Level
Student Understanding of Gravity at the College Level
IMPORTANT CONCEPTS ABOUT GRAVITY TO FOCUS ON
- The universality of gravity: The same physical principles of gravity apply to every object in the universe.
- Influencing factors: The strength of gravity depends only on the mass of both objects and the distance between them (not size, density, rotation rate, composition, magnetism, etc.).
- The scale and extent of gravity: A body’s gravitational field falls off with distance but approaches zero asymptotically.
- Tidal forces: The Moon’s gravity causes the tidal bulge of oceans on the side closest to and opposite the position of the moon.
- Gravity is an interaction: Gravity is a force of attraction between two masses and is equal for both objects based on Newton’s third Law.
- Equivalence Principle: Gravitational mass and inertial mass are the same quantity.
- Action at a distance: Gravity is a noncontact force and cannot be blocked (for example, by another mass).
Constant Comparative Approach
- S: “Why do astronauts appear to float in their spacecraft?” My response is “there is no gravity in space.”
- I: Okay, and do you still agree with that?
- S: Yes, I do.I: Okay, and what do you define as “space”?
- S: Anything outside of our gravitational pull.
- I: So is there a boundary where something is in our gravitational pull and then not?
- S: I think it gradually decreases from Earth’s surface to nothing at some elevation above earth.
- I: Astronauts orbit Earth just outside our atmosphere, so I guess I’m asking if it [gravity] decreases fast enough to get to be zero just outside our atmosphere.
- S: Yes.
- I: So then is the gravity from the Earth zero at the Moon? Does the Moon feel Earth’s gravity at its location?
- S: No, the Moon has its own gravity.
- I: But the Moon orbits the earth, right?
- S: True.
- I: So why does it orbit the earth?
- S: Because of the gravitational pull between the two masses.
- I: Okay, so it seems that you’re saying that the Moon does feel the Earth’s gravity.
- S: Yes.
- I: So why can the Moon feel Earth’s gravity, but the space station can’t?
- S: Because the space station isn’t a big enough mass.
STUDENT ALTERNATIVE MODELS OF GRAVITY
The Boundary Model
- S. Astronauts are able to float in their spacecraft because they’ve broken out of the atmosphere… once they’ve gotten past the point where earth is able to sustain any kind of atmosphere, then that’s where gravity is weak enough for it [floating] to happen. I don’t think it’s a correlation in any meaningful sense. It’s not like cause and effect or anything.
- I: So it’s not like the atmosphere is causing gravity?
- S: Where the atmosphere is, gravity is strong enough for there to be gravity.
- I: Atmosphere is more of an indicator of where gravity is working?
- S: Yeah, that would be how it works. Yeah.
The Orbital Indicator Model
The Mixing of Forces Model
STUDENT MISAPPLICATION OF THE SCIENTIFIC MODEL
Misapplication of Mass
Only Heavy Objects can Gravitationally Interact
Mass Versus Density
Misapplication of Distance
Misunderstanding What Causes or Creates Gravity
Gravity is Confusing
Appendix A: Questionnaire Results
|Question Conceptual Categories||N||Percent of total||K|
|iAdapted from the TOAST.|
|iiAdapted from Dostal’s (2005)9 Masters Thesis|
|A1. Why do astronauts appear to float in their spacecrafti?||0.84|
|a. There is no gravity in space.||a. 72||a. 50.3%|
|b. Gravity is much weaker in space.||b. 21||b. 14.6%|
|c. They are too far away from Earth or any massive body.||c. 15||c. 10.2%|
|d. They are in a constant state of freefall.||d. 14||d. 9.7%|
|e. The spacecraft’s gravity isn’t strong enough.||e. 3||e. 2.1%|
|A2. If you traveled down a tunnel that reached halfway to the center of the Earth, would the strength of gravity you experience from the Earth change? If so, how? Explain your answer.||0.88|
|a. No change, Earth’s gravity is constant and uniform.||a. 33||a. 23.1%|
|b. Increase, you are closer to the center||b. 19||b. 13.3%|
|c. Increase, there is more pressure.||c. 9||c. 6.3%|
|d. Increase, closest to the densest area.||d. 7||d. 4.9%|
|e. Decrease, more mass above you and less beneath you.||e. 5||e. 3.5%|
|f. Increase, closest to the source of gravity.||f. 5||f. 3.5%|
|g. References interaction with magnetic field||g. 4||g. 2.8%|
|h. Discusses influence from other celestial bodies||h. 4||h. 2.8%|
|i. No change, Earth’s mass is the same.||i. 4||i. 2.8%|
|j. Increase, smaller radius from center.||j. 3||j. 2.1%|
|A3. Is there a relationship between a planet’s gravity and its atmosphere? If so, describe this relationship.||0.85|
|a. No, not that they know of.||a. 29||a. 20.3%|
|b. Yes, gravity holds the atmosphere to the planet.||b. 23||b. 16.1%|
|c. Yes, atmosphere affects the strength of gravity.||c. 17||c. 11.9%|
|d. Yes, gravity determines the thickness and composition of the atmosphere.||d. 10||d. 7.0%|
|e. No, gravity depends on mass and distance and can exist without atmosphere.||e. 10||e. 7.0%|
|f. Yes, atmosphere represents the boundary of gravity.||f. 8||f. 5.6%|
|g. Yes, gravity causes the atmosphere to exist.||g. 6||g. 4.2%|
|h. Yes, the atmosphere exerts pressure.||h. 6||h. 4.2%|
|i. Yes, but not sure what relationship.||i. 5||i. 3.5%|
|A4. How heavy or light does something have to be to create its own gravitational field?||0.93|
|a. Every object has some gravitational field.||a. 61||a. 42.7%|
|b. Very, very heavy.||b. 27||b. 18.9%|
|c. Planet/moon sized.||c. 10||c. 7.0%|
|d. Has gravity only if it has an effect on other objects.||d. 8||d. 5.6%|
|e. Not everything, at least needs to be tangible.||e. 5||e. 3.5%|
|A5. Which person standing on the surface of the Earth experiences a stronger force of gravity? Why?ii||0.86|
|a. Gravity is the same everywhere on the planet.||a. 73||a. 51.0%|
|b. The equator is special.||b. 13||b. 9.1%|
|c. Thinks that South is “down”.||c. 8||c. 5.6%|
|d. Considers rotation.||d. 6||d. 4.2%|
|e. Accounted for the oblateness of Earth.||e. 4||e. 2.8%|
|f. Considers magnetism.||f. 4||f. 2.8%|
|g. Considers position of Sun/Moon.||g. 3||g. 2.1%|
|A6. Each of the following planets has the same mass M, but each is made of a different material. The darker the planet, the denser the material. Describe the strength of gravity that a rocket at distance R from the center of each planet experiences. Why?||0.94|
|a. Same, equal mass and distance from center.||a. 27||a. 18.9%|
|b. Denser material = stronger gravity.||b. 18||b. 12.6%|
|c. Must be "just right" - planet not too dense and rocket not too far (chose B or C).||c. 17||c. 11.9%|
|d. A is the strongest and D is weakest, no explanation.||d. 15||d. 10.5%|
|e. Considers distance from the surface of the planet.||e. 11||e. 7.7%|
|f. A is the weakest and D is strongest, no explanation.||f.8||f. 5.6%|
|g. All same, higher density is compensated by smaller distance to surface.||g. 6||g. 4.2%|
|h. The size of the planet determines gravity.||h. 5||h. 3.5%|
|A7. Describe the strength of gravity on each of the following planets (if any), where more black loops represent stronger magnetic fields.||0.83|
|a. More magnetic fields = stronger gravity.||a. 69||a. 48.3%|
|b. Gravity and magnetism have no relationship.||b. 23||b. 16.1%|
|c. Gravity cannot exist without magnetic fields.||c. 11||c. 7.7%|
|d. Magnetic fields cancel out a planet’s gravity (A is strongest).||d. 4||d. 2.8%|
|B8. Why don’t the planets fall into the Sun?||0.94|
|a. Gravity||a. 33||a. 24.1%|
|b. Orbiting is like falling, centripetal forces.||b. 27||b. 19.7%|
|c. They are on an established orbit.||c. 13||c. 9.4%|
|d. Gravity from other bodies in the solar system is pulling them out.||d. 13||d. 9.4%|
|e. Sun’s gravity isn’t strong enough to pull them in, only to hold them in place.||e. 7||e. 5.1%|
|f. Rotation of planets or the Sun||f. 7||f. 5.1%|
|g. The planets have their own gravity that counteracts the Sun’s.||g. 6||g. 4.4%|
|h. Sun’s magnetic field pushes out.||h. 5||h. 3.6%|
|B9. Besides gravity, are there any other forces that hold us to the Earth’s surface?||0.84|
|a. Nothing else.||a. 77||a. 56.2%|
|b. Atmospheric forces.||b. 17||b. 12.4%|
|c. Rotation and orbital dynamics.||c. 9||c. 6.6%|
|d. Friction.||d. 5||d. 3.6%|
|e. More than one of the above factors||e. 4||e. 2.9%|
|f. Yes, maybe.||f. 4||f. 2.9%|
|g. Magnetic forces.||g. 3||g. 2.2%|
|h. Just provided random Physics terms||h. 2||h. 1.5%|
|B10. The strength of gravity on top of Mt. Everest is 0.25% less than the strength of gravity at sea level. Why is this?||0.83|
|a. Further from core where gravity is stronger.||a. 39||a. 28.5%|
|b. Higher elevation, greater distance from center of mass.||b. 32||b. 23.4%|
|c. Higher in atmosphere, closer to space.||c. 20||c. 14.6%|
|d. Less air pressure, air is thinner.||d. 14||d. 10.2%|
|B11. How would you compare the strength of gravity at the surface of Pluto with the strength of gravity at the surface of the Earth? Explain.||0.91|
|a. Weaker, smaller and less mass.||a. 61||a. 44.5%|
|b. Weaker, further from Sun.||b. 26||b. 19.0%|
|c. Need more information, describes how to compare||c. 9||c. 6.6%|
|d. Weaker, no explanation||d. 7||d. 5.1%|
|e. Greater, for various reasons||e. 7||e. 5.1%|
|f. Weaker, Pluto has less atmosphere||f. 5||f. 3.6%|
|g. They’re different.||g. 4||g. 3.0%|
|h. The same.||h. 2||h. 1.5%|
|B12. When the Apollo spacecraft passed behind the moon from our view on Earth, how did the gravity between the Earth and the spacecraft change (if at all)? Explain.||0.83|
|a. No change, gravity can pull through objects.||a. 31||a. 22.6%|
|b. Moon’s gravity takes over, not feeling Earth’s gravity anymore.||b. 12||b. 8.8%|
|c. Moon blocked/stifled Earth’s gravity.||c. 11||c. 8.0%|
|d. Now BOTH Earth and Moon are pulling.||d. 9||d. 6.6%|
|e. No gravity in space to begin with.||e. 5||e. 3.6%|
|B13. The following planets are viewed from above, with more arrows representing a faster rotation. Describe the strength of gravity (if any) on each planet and how it compares to the other planets.||0.83|
|a. More rotation = more gravity.||a. 48||a. 35.0%|
|b. All have the same gravity.||b. 29||b. 21.2%|
|c. Gravity is non-existent without rotation (A has no gravity).||c. 18||c. 13.1%|
|d. The direction of rotation matters for gravity.||d. 9||d. 6.6%|
|e. More rotation = less gravity.||e. 9||e. 6.6%|
|B14. Compare the surface gravity on each of the following planets with different orbiting bodies. Planet A has nothing orbiting it; B-D have artificial satellites, and E-G have moons. Also, which planets would you expect to have tides?||0.85|
|a. Gravity must be stronger to keep heavy objects near.||a. 30||a. 21.9%|
|b.Gravity must be strong to hold objects that are far away.||b. 15||b. 10.9%|
|c. Same, surface gravity doesn’t depend on what is orbiting.||c. 14||c. 10.2%|
|B15. Compare the strength of the force of gravity for each satellite. Note that Satellite B is twice as big as Satellite A and Satellite C is three times as big as Satellite A.||0.87|
|a. Larger, more massive satellites experience a stronger force of gravity.||a. 72||a. 52.6%|
|b. Same, no explanation.||b. 35||b. 25.5%|
|c. Smaller satellites experience a stronger pull of gravity (b/c more easily affected).||c. 11||c. 8.0%|
|d. Same, gravity pulls on all objects equally.||d. 3||d. 2.2%|
|e. Same, they are at the same distance.||e. 2||e. 1.5%|
|B16. In this diagram, darker planets have a higher density. Which planet would have taller mountains? Why?|
|a. A, lower density means more malleable.||a. 33||a. 24.1%|
|b. B, it’s in between, just right||b. 28||b. 20.4%|
|c. C, more material to make mountains.||c. 22||c. 16.1%|
|d. A, has less gravity.||d. 15||d. 10.9%|
|e. C, more geologic activity||e. 7||e. 5.1%|
|f. Need more information.||f. 6||f. 4.4%|
|C17. How far away from the Earth do you have to go to feel zero gravitational force from the Earth?||0.95|
|a. Outside of the Earth.||a. 15||a. 46.9%|
|b. On the scale of much larger than the solar system.||b. 5||b. 15.6%|
|c. On the scale of nearby bodies and the solar system.||c. 4||c. 12.5%|
|C18. What determines the strength of the gravitational interaction between two objects?||0.95|
|a. Mass and/or distance, but incomplete.||a. 16||a. 50.0%|
|b. Complete: Mass of both objects and distance between them.||b. 11||b. 34.4%|
|c. Variables other than mass and distance.||c. 2||c. 6.3%|
|C19. How would the motion of a baseball thrown upward from the surface of the Moon differ from that on Earth? Describe how fast it will go and where it will end up.||0.93|
|a. Will land back on surface.||a. 20||a. 62.5%|
|b. Will travel away from the moon.||b. 4||b. 12.5%|
|c. Will float.||c. 4||c. 12.5%|
|C20. Assume that planets A and B have the same mass M, but planet A is made of a denser material and planet B is bigger. Make an “X” about where a rocket that is launched from planet A begins to experience a stronger force of gravity from planet B. The black dot shows the halfway point for reference. Explain your choice.||1.00|
|a. Recognizes that pull of gravity would be equal at halfway point||a. 13||a. 40.6%|
|b. Closer to B, no explanation||b. 8||b. 25.0%|
|c. B has more gravity because it is larger.||c. 6||c. 18.8%|
|d. A has more gravity because it is more dense.||d. 3||d. 9.4%|
|e. Closer to A, no explanation||e. 1||e. 3.1%|
|C21. Compare the force of gravity at the surface of each of the following planets that have different ring structures.||1.00|
|a. More material around a planet = stronger gravity.||a. 13||a. 40.6%|
|b. Less material around a planet = stronger gravity.||b. 5||b. 15.6%|
|c. Planets with rings far away = more gravity.||c. 4||c. 12.5%|
|d. All the same.||d. 2||d. 6.25%|
|C22. A person is living on a planet where there has been a huge hole carved out. Draw an arrow that shows the direction of the gravitational force he experiences. Explain your choice.||0.96|
|a. Toward new center of mass.||a. 11||a. 34.4%|
|b. Toward geometric center.||b. 7||b. 21.9%|
|c. Toward left surface.||c. 4||c. 12.5%|
|d. Toward the gap.||d. 3||d. 9.4%|
|C23. Two astronauts are floating in space far away from any planets or stars. Do they experience any gravitational force? If so, from what and will its effects be measurable? If not, why not?||1.00|
|a. Yes, from each other.||a. 12||a. 37.5%|
|b. Yes, from something else.||b. 6||b. 18.8%|
|c. No, there is no source nearby.||c. 6||c. 18.8%|
|d. No, there is no gravity in space.||d. 3||d. 9.4%|
|e. No, no explanation||e. 4||e. 12.5%|
Appendix B: Interview Results
|Student and Major||Version||Cor I||Working models||Notes|
|1 University Studies||B||C||Correct scientific model|
|2 Undeclared||B||I||Boundary model—The Sun is only strong enough to hold us in place.||Very unsure of answers, not sure where gravity comes from. Not sure if magnetism and rotation matter.|
|3 Undeclared||A||C||Boundary model—Different boundaries for different masses. The moon experiences Earth’s gravity but the space station does not.|
|4 History||A||C||Boundary model, Misapplication of Mass: Density|
|5 Undeclared||B||I||Orbital indicator model||Very unsure.|
|6 Undeclared||A||C||Boundary model—Earth’s gravity is constant within the atmosphere and then starts diminishing just past the atmosphere. Orbital indicator—An object’s gravity can be measured by its effects on other objects. It is relative; sometimes a body can have a gravitational field if it is the largest object nearby.||There is no gravitational force between Mars and Earth because Mars is not orbiting the Earth. Mars only interacts gravitationally with the Sun. Magnetic fields and gravity definitely have a relationship; they are not separate.|
|Mixing of forces—The more magnetic fields, the stronger the gravity.|
|7 Health Promotion||B||I||Misapplication of mass: Both mass and density matter, but mostly density. Boundary model—To a certain extent past the atmosphere, gravity is gone and then you float. If earth did not have an atmosphere, gravity would probably stop inside of Earth. Gravity needs something to permeate through. Mixing of forces—Rotation might affect gravity.||Unable to reconcile why planets do not fall into the Sun. Reasons that planets far away must be more massive for being at such a large distance, but then later reasons that the surface gravity of Jovian planets is less than terrestrial because they are less dense. Very confused about orbiting; it never ‘clicked’ in class. “Just don’t know.” Admitted to guessing, sees contradictions, but cannot reconcile them.|
|8 Architecture (took intro physics)||B||C||Mixing of forces—The strength of the gravitational force on Mt. Everest is less than at sea level because it is further from the center and from the center of rotation. Orbital indicator—We could look at bodies in the solar system and count how many moons they have and how fast they are orbiting to figure out the planet’s surface gravity. Scientific model||Discusses how rotation would change gravity, but when further questioned, admits that gravity is constant and rotation would change the force that is felt.|
|9 University Studies||B||C||Mixing of forces—Planets do not fall into the Sun because their magnetism counteracts the Sun’s magnetism. All the heavy metals and iron in Earth’s core is pulling us down with magnetism. Also, Venus has a much stronger gravity than Earth b/c its atmosphere is so thick.||Claims that most of the answers are just common sense, they just seem right.There is a complicated interaction between magnetism, rotation, and gravity. There is probably a scientific equation that describes it. Pluto’s surface gravity is much weaker because it is further from the Sun and it is not geologically active.|
|10 Business Marketing (took general Physics in high school)||A||I||Boundary model—Earth’s atmosphere represents where gravity drastically decreases. Also, Earth’s gravity is constant in the Earth. When you are flying in a plane nothing feels lighter. Mixing of forces—Atmosphere causes stronger surface gravity. Also, gravity is determined by a combination of mass and magnetism. Misapplication of mass—Earth’s mass is the minimum mass for an object to have its own gravitational field. Denser materials have stronger gravity.||Unable to reconcile how gravity operates in space. Earth has gravity because of its mass and it is rotating on axis. Does not understand her own written answers. Having a gravitational field means being able to affect other objects. Nothing orbits the moon, so it must not create its own gravitational field. Same for Mercury and Venus. Very unsure, guessing at times. Scientists are unable to predict the strength of gravity at the center of the Earth, because they have never been there.|
|11 University Studies||A||C||Boundary model—Earth’s atmosphere might be able to block outside gravitational forces. Source of gravity—Originally under the impression gravity comes from something outside Earth, but realized throughout the interview that it comes from a planet. Mixing of forces—Magnetic fields can counteract gravity. Scientific model—Every object that has mass must have a gravitational field, because it wouldn’t make sense for there to be a cut-off mass.||Saw inconsistencies in his written answers; rethinks several responses to be more consistent with gravity depending on mass and distance. Uses information about the moon, other planets, and the Sun to try to reason through questions. Wondered if there was really a way to know all the answers with certainty. Was not sure about the difference between mass and density.|
|12 University Studies||B||C||Scientific model—Orbiting is analogous to the coin toss machines in the Mall. The mass of a body determines the strength of its gravity, which explains why the Moon and Pluto have less gravity. The Earth’s gravity comes from its whole mass. You measure distance from the center, but there is nothing magical about the center that gives it gravity. Mixing of forces—More rotation causes less gravity, in analogy to a merry-go-round.||References answers to other questions to reason. Realizes there is a difference between air pressure and gravity, but each affects the motion of a rocket leaving Earth.|
|13 Film||B||C||Scientific model—Gravity is determined only by mass and distance. Rotation does not matter. A planet’s surface gravity is determined by its mass. The bodies orbiting a planet do not affect it’s gravity. Boundary model: The edge of the atmosphere is an indicator of where gravity drastically decreases.||Reasons through questions with ease. Uses mass and distance consistently as factors that determine gravity. Very sure of answers. Does not question reasoning at all throughout the interview.|
|Misapplication of Scientific Model: Gravity is strongest at the center of the Earth. Gravity originates in the core.|
|14 Psychology||C||I||Boundary model—Gravity diminishes greatly after atmosphere. Scientific model—Mass and distance determines gravity. The mass of both objects matters: The Earth gravitationally interacts more with the Moon than the Space Station because the Moon is more massive. Misapplication of the Scientific model—Only very massive objects have gravity. Planet do not feel each other’s gravity, because they are feeling the Sun’s gravity. Empty space (a hole or void) can cause gravity. Orbital indicator—Rings extend the size of a planet. A planet’s physical size determines the extent of its gravitational field.||Originally says there is no gravity in space, but then discusses how objects in space are affected by gravity in other questions. States that mass and distance determines gravity, but then uses density and physical size of a planet to reason through questions. Sometimes reasons that objects can only feel gravity from one object at a time, and sometimes discusses how an object can experience gravity from multiple bodies. Changes answer on C23 from correct answer, saying it does not make sense now—the astronauts are not massive enough to exert a gravitational force on each other. Objects must be at least the size of a moon to have gravity. Originally reasons that gravity can be determined by apparent weight and its effects on other objects (i.e., up for upward moving objects; a brick buried under the ground would not feel gravity because it cannot move down much farther). However, with more questioning he changes to saying that gravity on Earth is always down. Gravitational force would pull toward the opening in Question C22 because it would try to seal itself up.|
|15 Geology||B||C||Scientific model—A planet’s mass alone determines its gravity. Rotation and atmospheric pressure do not affect the strength of gravity. The force of gravity between two bodies depends directly on the mass of both objects. The Earth’s gravity is measured from its center because that is the average location of all the mass.||Not entirely confident in the scientific model—thought maybe density could be a factor, but did not include density in reasoning through responses. Could not figure out why the planets do not fall into the Sun. Thought maybe it had to do with the expansion of space, but not sure.|
|Category ‘a’||Category ‘b’||Not applicable|
|Rater 2||Category ‘a’||#1, #3, #6, #10||#5|
|Category ‘b’||#9||#4, #7, #8|