There have been several studies of children’s understanding of gravity. Nussbaum and Novak (1976)²² asserted “Five Notions” for children’s understanding of the Earth’s shape and gravity that guided much of the subsequent work. For a comprehensive compilation and review of the research on and recommendations for children’s understanding of gravity, one may refer to Agan and Sneider (2004)¹, Kavanagh and Sneider (2007a¹⁸ and 2007b)¹⁹, and Asghar and Libarkin (2010)². The most common misconceptions held by very young children stem from a strong Earth-centered reference frame, including the idea that things can fall “down” off of the Earth. Middle school and high school students generally hold more sophisticated misconceptions, such as the idea that gravity needs a medium, such as air, to act through, that gravity is confounded with magnetism and rotation, and a general confusion among physical concepts such as weight, mass, and force.

To introduce the methods of the present study, we will concentrate our background review on research that utilizes student-supplied responses, with particular focus on studies done with middle school and high school students, as these investigations helped to guide the questions we asked students. For instance, Palmer (2001)²⁴ asked sixth and tenth grade students to describe the force of gravity on a series of everyday objects that were depicted in various stages of motion near Earth’s surface. The results suggest that student have a situational understanding of gravity, often predicting that the force of gravity is in the direction of an object’s motion. For a brick buried under the ground, many students predicted that the brick would experience zero gravitational force from the Earth. After reviewing several student-supplied responses, Palmer developed seven concept categories to describe how students approach these situations, including categories in which the direction of the gravitational force is tied to the direction of motion of the object in question.

Presumably children’s and high-school students’ misconceptions of gravity persist into college, and the few studies of student understanding of gravity at the college level support this supposition. The methods for researching college student understanding of gravity have been similar to those for researching children’s understanding of gravity, typically using a few questions with diagrams and analyzing student-supplied responses. Piburn et al. (1988)²⁶ used a series of diagrams with different sized planets at various distances from the Sun and asked physical science students which planet a rocket would be easiest to “take off” from, finding that many students viewed the presence of the Sun as a major factor in a planet’s gravity. Dostal (2005)⁹ points out, however, that these questions may be a bit confusing, since real rockets do need to consider the relative position of the Sun. However, results of Piburn’s study allude to deep-seated misconceptions, such as the idea that gravity emanates from the center of an object, and a planet’s gravity is related to magnetism, temperature, composition, and distance from the Sun.

There have been a few studies of student understanding of gravity within Physics classrooms at the college level. These tend to emphasize physics terminology and laboratory experiments on Earth. Sharma et al. (2004)²⁹ investigate Australian college physics students’ conceptions of gravity by phenomenologically categorizing student responses to a question about why an astronaut in a spaceship has zero weight. Gunstone and White (1980¹⁴ and 1981)¹⁵ asked first-year Physics students to compare the experimental results after dropping objects in class. As may be expected, students were reluctant to accept the scientific view, even when their classroom experiment contradicted with their prediction. Graham and Berry (1993)¹³ use a similar scenario by asking students to compare the motions of two balls dropped on the Earth versus on the Moon. Dostal’s Master Thesis (2005)⁹ investigated college student understanding of gravity with emphasis on Physics force diagrams. The multiple-choice and open-ended questions required students to understand the principle of superposition, Newton’s three laws, and proportionality within Newton’s law of gravitation. While these studies include valuable exercises for Physics students grappling with terminology and notation, it is not readily applicable to Astronomy students, who often are not required to draw force diagrams, understand superposition, or articulate the differences between mass, weight, force, and acceleration.

To investigate a context outside of the typical Physics domain, Asghar and Libarkin (2010)² adapted questions from studies that investigate children’s understanding of gravity to research college students enrolled in an introductory geological sciences class. They found that college students’ conceptions of gravity are generally more complex than children’s, but misconceptions still abound. In particular, college students frequently confound gravity with magnetism, rotation, and atmospheric pressure, with only 12% of students holding the correct scientific conception without simultaneously holding alternatives.

The only study apart from this one that focuses on college student understanding of gravity in an introductory college astronomy course was done by Feeley (2007)¹¹ for a Masters Thesis. He focused on scenarios on the Moon, including the motion of a pen, a feather, a piece of lead, and a helium-filled balloon released from near the surface. The responses suggested two primary models for student thought, which Feeley called the “air-gravity model” and the “threshold model.” Students who used the air-gravity model reasoned that the Moon has no gravity because it has no air. Students who used the threshold model used the object’s mass to determine its motion, with only heavy objects falling to the surface of the moon and lightweight objects floating away. Feeley also gave students information about Venus and then asked them to compare gravity on Venus to gravity on the Earth. Student responses to this separated into a “planetary rotation model,” the “air-gravity model,” and the Newtonian model.

Published studies on student understanding of gravity at the college level use only a few open-ended questions, or even just one, to explore student ideas about gravity. While these studies are useful in their own right, many misconceptions dealing with gravity are interdependent. The present study is a more comprehensive effort in that it asks students a variety of questions in different contexts and searches for emerging patterns. It is the most comprehensive study that we have found in the literature that is specifically tailored to focus on the concepts of gravity that are important in introductory astronomy courses.

We chose a ten-item free-response format as the best method to probe introductory astronomy student understanding of gravity. This serves three purposes: (1) to explore different representations of gravity in a variety of situations, (2) to allow for analysis via a constant comparative method, as discussed below, and (3) to gain information for distracter responses for a multiple-choice test that represent typical student answers in their typical language. In keeping with our goal of focusing on the causes, effects, and extent of gravity, the questions had little to no emphasis on equations. In order to reliably measure a student’s mental model, we avoided questions where students needed to have heard the answer before, instead emphasizing questions whose answers can be deduced easily by a true understanding of gravity. These are generally different types of questions than those that are asked in textbooks at the end of the chapter. The questions explore the strength of gravity in a variety of environments and contexts—on the moon, in space, in freefall, on planets with orbiting bodies, etc.

In total, 30 questions were developed for the questionnaires, and these questions were divided evenly into three versions: A, B, and C (see Appendix A for a compilation of the questions that were used for this paper). Each section of introductory astronomy in the Fall semester of 2010 was given 30 minutes to complete a different version of the questionnaire. Half of the questions in each version of the questionnaire were composed in text only, and the other half provided a figure of the situation described in the question.

All questionnaires were given to students enrolled in an introductory Astronomy course at Montana State University during the Fall 2010 Semester approximately 3 weeks after the lesson about gravity. There were three sections, two of which were taught by one of the authors. Section 1 included 190 registered students, 143 of which participated in Version A of the gravity survey, giving a response rate of 75%. Section 2 included 191 registered students, 137 of which participated in Version B of the gravity survey, giving a response rate of 72%. And, Section 3 included 54 registered students, 32 of which participated in Version C of the gravity survey, giving a response rate of 59%. Because responses to Version C were low in number, interpretation of student responses to this version should be viewed with caution. Students who typically register for this course are nonscience majors wanting to fulfill their science requirement. Therefore, this may be the only science course these students take in college (Partridge and Greenstein 2003²⁵). Approximately 38% of the students registered for the course were female, but the gender ratio for those students who participated in the gravity questionnaires is unknown.

In analyzing student responses, we followed the model presented by Creswell (2007)⁷ for a grounded theory constant comparative research approach. This approach has been used in many studies on student conceptual understanding (Bailey 2006³, Sharma et al. 2004²⁹, Asghar and Libarkin 2010)², and it has proven to be a reliable method. The central idea to constant comparative research is an open-coding format where the researcher collects data and allows categories to emerge naturally until the information gained is saturated. In constructing categories of student responses to each question, we took an approach similar to what Sharma et al. (2004)²⁹ refer to as a phenomenographic analysis, which de-emphasizes correctness in favor of probing for a complete description of student ideas.

One author compiled student responses by typing each response into a single document and giving each response a number tag so that individual cases could be tracked. In an exploratory fashion, the student responses were read, reread, and rearranged to determine the emergent themes for each question. Once the general themes, or categories, were determined, each author followed the constant comparative method by separately coding the numbered student responses into the determined categories. To illustrate how these codings were compiled and analyzed, consider an example of ten student responses (#1 – #10) to a question that has two conceptual categories, ‘a’ and ‘b.’ Table 1 shows how each rater in this example coded each student response. The raters agreed that four responses (N = 4) fit in Category ‘a’ and three responses (N = 3) fit in Category ‘b.’ The raters did not agree on the categorization of two responses (#5 and #9). For example, Rater 1 coded response #5 in Category ‘b’ while Rater 2 coded it in Category ‘a.’ Also note that both raters deemed response #2 inapplicable to the question.

To measure the degree to which our two codings of student responses about gravity agreed, we used a matrix similar to Table 1 to calculate the Cohen’s Kappa inter-rater reliability statistic, κ, for each question. Inter-rater reliabilities greater than 0.80 are generally accepted as good agreement (Landis and Koch 1977²⁰). If the categorizations for any question resulted in a κ below 0.80, discussions and clarifications were made in an iterative process until acceptable agreement was reached, but no explicit information was exchanged as to which responses each researcher placed in each category.

One of the authors conducted follow-up, audio-recorded interviews to establish credibility of the questionnaires and to gain insight into the complexities of student reasoning. As an incentive, students were offered the chance to win one of five $20 Target gift cards. Fifteen students volunteered for interviews—this included five students who completed version A, nine students who completed version B, and one student who completed version C. All interviews were completed at the end of the semester, between 4our and 7 weeks after the gravity questionnaires were given in class.

The interview format was exploratory. Student ID number was used to match interviewees with their questionnaires completed in class. Students read the question and their written response aloud and were then asked to clarify or expound as necessary. The interviewer was careful to ask probing, but not leading, questions. Some questions required little probing; however, some questions were explored a great length to test the strength of a student’s mental framework. Interviews typically lasted 20–30 minutes.

Appendix A provides a comprehensive summary of questionnaire results. While the questionnaires contained a total of 30 questions, results from only 23 questions are presented. The other seven questions were generally misunderstood by students or provided no new, previously undocumented, information. Each question is displayed with accompanying conceptual categories in the first column and total number, N, of responses that fell within each category according to both raters in the second column (as presented in Section 4C). Note that the number N does not include student responses that were placed in different categories according to each rater, or incoherent or inapplicable student responses, as these responses were not useful in understanding students’ understanding and reasoning on questions. Therefore, the sum of the N values across categories does not match the population outlined in Section 4B. The third column in Appendix A expresses N for each category as a percentage of total respondents, i.e., N was divided by 143 for responses from Version A, 137 for responses from Version B, and 32 for responses from Version C. Finally, the fourth column provides the inter-rater reliability statistic, κ.

Interviews can be categorized as “Consistent,” meaning that a student appeared confident in his or her responses and consistently applied similar reasoning strategies, or “Inconsistent,” meaning that a student was very unsure of his/her responses and changed reasoning throughout the interview. Appendix B summarizes student interview results, including examples of possible working mental models (explained in Section 6).

Question 1A proved to be an excellent starting place to probe students’ mental models. The majority of students answered that astronauts appear to float in their spacecraft because there is no gravity in space. These students were then asked related questions to bring up contradictions in their reasoning. This is demonstrated in the following transcript between a student (S) and interviewer (I):

This example reveals how misconceptions are often intertwined—this student traded in one misconception for another. In answering that there is no gravity in space, the student may appear to conform to the common misconception that gravity needs air to act through. However, thinking about Earth’s effect on the Moon helped this student to realize that Earth’s atmosphere does not affect gravity. Therefore, a more appropriate category for this misconception is that gravity only applies to heavy objects.

Perhaps the most prominent emergent theme is what we call the “boundary model.” A boundary could be the surface of a planet, the edge of the atmosphere, or even an orbit. It may represent a casing that encloses a planet’s gravity, or a “check point” where gravity either disappears or diminishes. With the boundary model, we can explore several student responses.

A combination of Questions A2, B10, and A1 illustrates the boundary idea in very specific regions of Earth—inside the Earth, above the surface, and beyond the atmosphere, respectively. For Question A2 many students (N = 37, 25.9%) reason that the strength of gravity would not change if one traveled down a tunnel to the center of the Earth. The most common explanation for this is that Earth’s gravity is constant throughout, because the Earth is one body (N = 33, 23.1%). In this case it is the Earth’s surface that acts as a boundary, inside of which Earth’s gravity is constant. However, Question B10 illustrates that most students (N = 71, 51.9%) understand that Earth’s gravity diminishes with distance from the surface. Considering further distances from the surface of Earth, the majority of respondents to Question C17 (N=15, 46.9%) assert that one simply must leave the Earth (and its atmosphere) to feel zero gravitational force from Earth. This is a well-document misconception (Watts 1982³⁴, Asghar and Libarkin 2010²) and is supported by typical responses to Question A1 that assert astronauts appear to float in their spacecraft because there is no gravity in space (N = 72, 50.3%). In the “boundary” concept, there are many ways this could make sense: the atmosphere is the casing that holds gravity inside, or the extent of the atmosphere is simply an indicator of the presence of gravity. The latter explanation is clearly articulated in many student responses to Questions A1 and A3. An interviewee discussing his response to A1 asserts:

Combining these typical responses, we arrive at several possible student models for discontinuities, or boundaries, in Earth’s gravitational influence. Variations of the boundary idea in and around Earth are presented in Figure 2.

In the present study, the misconception that there is no gravity in space was one of the most prevalent. As previously mentioned, this surfaced in student responses to Question A1, but it was also prevalent in responses to Question B10, where 14.6% (N = 20) of respondents reasoned that the strength of the Earth’s gravity on top of Mt. Everest is weaker than at sea level because Mt. Everest is closer to space. In Question B12, a few students asserted that the Apollo spacecraft experienced no gravity because it was in space. And, in Question C23, 12.5% (N = 4) of respondents asserted that two astronauts in space do not experience a gravitational force because there is not gravity in space.

Within the context of the boundary model, it may be reasonable to assume that anytime a student asserts that there is no gravity in space, s/he is working from the idea that “space” is always outside the boundary, whether it be at the surface of a planet or past its atmosphere. As indicated in the interview transcript presented in Section 6B, the boundary may be different for different orbiting objects, extending out farther for more massive objects. The boundary may not define the edge of “space” at all, but rather the conditions for orbiting to occur, inside of which an object falls to a planet, and outside of which an object flies off into space. Responses to Question B8 use the boundary concept in terms of orbits to explain why the planets do not fall into the Sun: “Gravity is pulling the planets towards then Sun but the gravity is not strong enough to actually pull them in,” and, “They are so far away and the Sun doesn’t have enough gravity,” for example. In this case, the “boundary” divides regions where the Sun’s gravity pulls objects in and where it simply holds them in orbit. While this may not be completely incorrect, as planets are in equilibrium, it is clear that students do not understand why the planets are in equilibrium.

An unexpected misconception that was uncovered is that the objects that orbit a planet can act as indicators of its surface gravity. This was strikingly revealed by the majority of student responses to Question B14. This question showed equally sized planets with orbiting satellites or moons at different orbital radii. Categories “a” and “b” show how the “orbiting indicators” concept is generally applied in two opposing ways: (a) A planet’s gravity must be stronger to reach out and hold objects that are far away, or (b) A planet’s gravity must be stronger to pull objects close to it. A typical student response falling in Category “a” is as follows:

“[Planet] A: not much gravity, B and C [have the] same gravity, D [has the] most gravity because it can have a satellite [at the] furthest [distance]. E, F, and G have tides. G has the strongest gravity [because its] moon is furthest away, but E and F both have relatively strong gravity. F might not have tides b/c of [its] two moons.”

This comment contains several interesting concepts. First, in claiming that planet A’s gravity is minimal, the student indicates A’s gravity is not strong enough to hold any objects in orbit. Second, claiming that B and C have the same gravity and less than planet D, the student assumes that the gravity of planets B and C must not reach as far, and must, therefore, be weaker than the gravity of planet D. The student applies this same reasoning for planets E, F, and G. Because the student separated their predictions for the strength of gravity according to planets with artificial satellites and those with moons, s/he possibly expects planet G’s gravity to be stronger since it is able to hold a heavier object, such as a moon, in orbit.

A typical response for Category “b” is as follows: “Probably no surface gravity on A b/c nothing is orbiting it, and a little more surface gravity on B-D b/c a machine is able to stay in orbit, and E-G has the strongest, most surface gravity b/c a moon is able to orbit. E-G probably have tides b/c of the moons.” Like the previous student who fell in Category “a,” this student reasons that Planet A must have weak (in fact, zero!) surface gravity because there is nothing orbiting it. To the student this logically implies that Planet A’s gravity is simply not strong enough to hold objects in orbit. Unlike the previous student, however, this student claims that Planets B and C have more gravity than Planet D, and, similarly, Planets E and F have more gravity than Planet G. The reasoning here is that a planet’s gravity must be stronger to pull an object closer to it.

This misconception comes up again in Question C21. Instead of satellites or moons orbiting a planet, different ring systems are depicted. Again, Categories “a” and “b” represent the two opposing applications of the “orbiting indicator” misconception. Analogous to Question B14 Category “a,” students in Category “a” of Question C21 predict that the gravity on a planet with more rings and thicker rings must be stronger to hold so much material around the planet. For example, one student asserts, “If E can keep such far-away rings in check, it is exerting more force than B is on its closer-in rings.”

Conversely, Category “b” of Question C21 indicates that planets with less material in orbit have a stronger gravity. A student response in this category is: “The planet with more mass does not have rings, and [for planets with] less mass the planet carries the surrounding objects around it in orbit instead of having it become part of the planet.” Presumably the student is referring to “gravity” when s/he refers to “mass.” This implies that planets with strong gravity will cause all orbiting bodies to spiral inward and impact the planet. If a planet’s gravity is weak, then it may allow some objects to steadily orbit. Again, this is analogous to Question B14 Category “b”, where planets with stronger gravity are able to hold orbiting bodies at smaller radii.

Questionnaire results overwhelmingly support the well-documented (Piburn 1988²⁶, Smith 1988³², Chandler 1991⁶, Graham and Berry 1993¹³, Sharma et al. 2004²⁹, Feeley 2007¹¹, Asghar 2010²) misconception that gravity is confounded with magnetism, rotation, and atmospheric pressure. Question A3 explicitly asks students how gravity is related to atmosphere (if at all), Question A7 explicitly asks how magnetism affects gravity (if at all), and Question B13 explicitly asks how rotation affects gravity (if at all). Perhaps it is understandable for these questions that the majority of students assert that the atmosphere affects the strength of gravity and strong magnetic fields correlate with strong gravity. However, students readily incorporate magnetism, rotation, and atmospheric pressure into their responses to questions that do not address these forces explicitly. All three of these forces are popular responses in Question B9, which asks, “Besides gravity, are there any other forces that hold us to the surface of the Earth?” While it is encouraging that the majority (56.2%, N = 77) of students understand that gravity is the only force holding objects on Earth, 12.4% (N = 17) of students believe that atmospheric forces contribute, 6.6% (N = 9) believe rotation and orbital dynamics contribute, and 2.2% (N = 3) believe magnetic forces contribute. A few students who answered Question A5 even reasoned that people at different latitudes on Earth would experience different forces of gravity because of variations in the magnetic field (2.8%, N = 4) or variations in rotational speed (4.2%, N = 6). A few students refer to these forces again in other questions such as A2 and C18.

Responses to Question B8, “Why don’t the planets fall into the Sun?” illustrate this trend, with 5.1% (N = 7) of students claiming that rotation of the planets and/or Sun counteracts the inward pull of gravity and another 5.1% (N = 7) claiming that repelling magnetic forces counteract the attractive gravitational forces. Responses in category “g” of Question B8 indicate an interesting misconception that could potentially be tied to magnetism. Students in this category reason that planets do not fall into the Sun because, “The planets have their own gravity that repels them from being drug in,” or, “They (the planets and the Sun) are pulling against each other.” The comment, “Gravity is pushing away from the Sun,” indicates that some student may believe that gravity is analogous to magnetism, at times attracting and at other times repelling.

We propose a “mixing of forces model” to describe the types of student responses we observed. Magnetism, rotation, and air pressure seem to be important factors in understanding gravity for some students. The mixing of forces model perhaps could also be used conjunction with the boundary concept presented in Section 6A. To many students, these three factors can modify the reach, or extent, of gravity. Perhaps this can be tied to misconceptions about force and superposition. Perhaps students are drawing on everyday experiences where they (or objects they hold) “feel” lighter or heavier, and they attribute changes in apparent weight to changes in gravity. Since all three versions of the questionnaires contained questions that explicitly address external factors, it is possible that students were cued by questions throughout the survey and they displayed these misconceptions more often than they would have without a prompt. Future research will need to be done to determine exactly how prevalent the mixing of forces model is and how students incorporate it into their mental frameworks.

A few unexpected misconceptions surfaced from the student-supplied responses that do not seem to relate to a specific “mental model” of gravity—they appear to stand on their own as disparate topics. The most surprising misconception observed is the belief that South is “down.” This has been documented in young children (Nussbaum and Novak 1976²²) but certainly not college students. However, 5.6% (N = 8) of the student responses to Question A5 indicate that a person at the North Pole of Earth experiences a stronger gravitational force than a person at the South Pole. Examples of student responses in this category include, “Person A is at the top and wouldn’t fall off,” and, “Person A is at a position where gravity is pulling them directly down.” None of the students who fell in this category volunteered to be interviewed.

Another interesting misconception is the idea that gravity is a force that pulls an orbiting body along in its orbit, or that gravity establishes an orbit, which then “holds” the object. Responses in Category “c” of Question B8 seem to indicate that this is how some students understand orbiting, reasoning that the planets do not fall into the Sun “because the orbit has been established,” or, “because their orbits keep them in place.” One student even explicitly stated, “When planets are in orbit, the force of gravity between the two bodies is not a direct pull towards each other.” Perhaps this is loosely tied to the mixing of forces model, where the force of gravity is intertwined with rotation or centripetal forces, or perhaps it is just an extension of the “orbital indicator model.”

One more interesting misconception is that gravity can be blocked or stifled, such as when the two objects are not in view of each other. This was most prevalent in responses in Category “c” of Question B12. Students in this category reasoned that when the Apollo spacecraft was behind the Moon, “the Moon was in the way of Earth’s gravity,” or the Moon “interfered with” or “interrupted” the Earth’s gravity. One student stated “Earth had no effect on the spacecraft once behind the moon. It would take effect again once it had view of Earth.” This misconception could potentially relate to that of Category “b” in the same question, where some students appear to believe that an object can only experience the gravity of one object at a time. In this case, when the spacecraft is near the Moon, some students wrote, “the Moon’s gravity was no longer competing with the Earth’s,” or, the spacecraft “was in the Moon’s gravity, not experiencing the Earth’s gravity at all.” Again, this could potentially be tied to the “Mixing of Forces model,” but it seems more related to a misunderstanding of superposition. Perhaps these students are too literal in their interpretation of gravity as a force of attraction between two objects.

Students misapply the factor of mass in determining the force of gravity in a couple ways: (1) assuming that only heavy objects can gravitationally interact and (2) confusing mass and density.

Many students understand that distance between two objects is an important factor in gravity; however, misconceptions occur in how this is applied. For instance, many students become attached to the word “radius.” Scientists often use the variable r for “distance,” but students may interpret this too literally and deduce that r stands for “radius,” and a smaller planet has stronger gravity because it has a smaller radius. This is exemplified in Category “h” of Question A6, with a typical student response: “A is strongest, D is weakest. Masses will be the same but the radiuses [sic] change. The smaller the radius the greater the [gravitational] force.” This misconception crops up again in Category “e” of Question B11. One student reasoned that Pluto’s gravity would be stronger than Earth’s “because the surface is closer to the core.”

An alternative misapplication of the distance variable is mistaking distance as the distance from the surface of a planet. A quote from Category “e” of Question A6 is an example of a student considering the distance from the surface of the planet: “The darker the planet the more dense. Gravity is affected by mass and distance. In the darker shaded planets they will experience more gravity. In the lighter shaded planets they are closer to the planet causing greater gravity.”

Many students do no understand where gravity comes from. One interviewee explicitly states, “I don’t know what creates gravity. I just know it exists.” This is extremely detrimental to understanding how gravity works and how to use the force law, in particular. Despite understanding that mass is an important factor in determining gravity, many students fail to make the connection that the interaction of two masses is in fact the cause of the gravitational force. Because examples and problems in class primarily involve spherical bodies, the center of the object is frequently referenced and students begin to think that the center is somehow different or more special than the rest of the mass. In fact, some students reason that the geometric center of an object is (1) where gravity originates, or (2) the location to which gravity pulls everything.

Question A2 illustrates that many students believe the center of Earth to be somehow different gravitationally than the rest of Earth. 23.1% (N = 33) of students reasoned that gravity would be stronger at the center of Earth than at the surface, with an additional 4.9% (N = 7) implying that this is because the center is the source of gravity, providing comments such as “we are closer to the source of the Earth’s gravity, where gravity originates,” and “you are getting closer to the mass exerting the gravitational force.” The former comment may provide insight into another facet of this misconception—it is not necessarily the center point where gravity originates, but a central region. Some students draw on their knowledge that the core of the Earth is compositionally different than the crust. It is denser, and a student who believes that density, rather than mass, determines gravity would reasonably conclude the center exerts a stronger gravitational force than the crust. Also, the core of Earth is primarily iron, which could potentially factor into a student’s mental model that includes magnetism. And finally, a student who believes pressure (atmospheric or otherwise) to be associated with gravity would logically conclude that the center of Earth exerts a stronger gravitational force than the rest of the Earth.

Many responses to Question C22 further demonstrate the misconception that gravity originates from the center of an object. Depicting a planet whose center of mass is offset from its geometric center unambiguously untangles student conceptions. While 34.4% (N = 11) of respondents correctly drew an arrow representing the gravitational force toward the center of mass, 21.9% (N = 7) drew an arrow to the geometric center. In the latter case, one student adds that, although gravity still points to the geometric center, “it may be weaker than normal.” Again, students may understand that mass is a factor in a planet’s gravity, but they do not understand its role exactly. Alternatively, a few students (9.4%, N = 3) appear to believe gravity to be caused by a lack of mass, as these students drew arrows pointing into the hole of the planet. Since version C had so few respondents, we can only speculate as to students’ reasoning in this process. However, arrows to the hole may allude to the misconception that gravity is measured by its effects on other bodies—a person could fall into the hole but would merely remain on the surface at the side without a hole.

Student responses to Question A2 unveil the subtle interplay between mass and distance. In considering how gravity changes upon traveling down a thin tunnel to the center of Earth, some students who understand the proper relationship between gravity and distance (i.e., they wrote Newton’s law of gravitation) reason that gravity increases because “the radius is smaller.” Perhaps these students assumed that, since the Earth’s mass is constant, they could consider only distance. They ignore how the relative distribution of mass affects gravity at a point inside the Earth. While a truly proper explanation for the decrease of gravity requires a Gaussian approach, students who answered correctly (3.5%, N = 5) reasoned that gravity would decrease because, “Some of the mass of the earth would be behind you and pulling in the opposite direction of the rest of the earth,” and there is “less mass between you and the center of the body of mass.”

The misconceptions presented above are not necessarily mutually exclusive and may contribute to each other. For example, a student who asserts that the Earth’s magnetic field and/or rotation can push out and extend the Earth’s gravitational field may simultaneously hold the boundary model misconception and the orbital indicator misconception. Even students who correctly apply the scientific model may also simultaneously reason with alternative models. We speculate that students that mix seemingly contradictory models are operating from what Bao and Redish (2006)⁴ call a “mixed model state,” within which individual models are triggered by situational cues. While seemingly contradictory to the expert, students might use one model in a certain situation and a different model in a different situation. We found that, in general, only when pushed with questions (such as in interviews) do students begin to question their framework and modify it accordingly.

Despite the multitude of misconceptions about gravity that students can possess, the majority of responses to most of the questions fell within a category that fit with the correct scientific model of Newtonian gravity. However, unlike Piburn (1988)²⁶, we do not conclude that this means that students mostly have a reasonable understanding of gravity. Section 7 elucidates the many ways that students get lost in their attempts to reconcile Newton’s law of gravitation with their intuition. They learn that mass and distance are the primary factors that determine the strength of gravity, but in many cases they do not know how to apply these factors: Is the “distance” the radius of a planet or the distance of an orbiting body from the surface of a planet? Are mass and distance the only factors that determine gravity? How does mass relate to density? It was rare for a single student to possess the correct scientific model without simultaneously relying on an alternative model to answer certain questions. This is in agreement with the results found by Asghar and Libarkin (2010)². We suspect that students are trying to “assimilate,” rather than “accommodate” in Piagetian terms (Vosniadou and Brewer 1987³³), what they are taught about gravity with their previous knowledge.

When intuition takes precedence, students often deduce the strength of gravity based on its effects, or what we would feel like in that situation. They have a hard time distinguishing between apparent weight and gravitational force. The orbital indicator model may be part of a broader mental framework that gravity can be understood in terms of its effect on other objects. For example, student responses that fell in Category ‘b’ of Question B14 indicate that a small satellite orbiting Earth would experience a stronger gravitational force than a larger satellite, because “it is easier to move.” Furthermore, responses in Category ‘d’ of Question A4 (5.6%, N = 8) indicate that some students believe a planet’s gravity to be defined only in terms of its effects on other objects. Responses in this category describe how heavy or light something must be to create its own gravitational field with such responses as: “Heavier than all other objects near it,” “Depends upon how big other objects are,” and “It would depend on where it is placed. If the object is on earth it would have no gravitational field, but if it were in space it would have one.” Determination of gravity based on its effects has been documented by Noce (1988)²¹ in children and by Asghar and Libarkin (2010)² in college geology students. Perhaps this misconception relates to misconceptions about forces in general. Students think in terms of the effort it would take to move an object, with the bigger, stronger objects being “in control over the smaller objects.”

One other noteworthy trend is that many students were very unsure of their answers to questionnaires. This was obvious in several written responses where students explicitly state, “Not sure,” or, “I have no clue.” However, it was especially prevalent in the interviews. Five of the 15 interviewees (33%) were categorized as “Inconsistent” in their reasoning (see Appendix B). Even those who were categorized as “Consistent” did not seem entirely confident in their answers. As they reviewed their written responses, several rambled and wavered back and forth before making a decision. Interviewee #4 felt the need to express: “…. oh, and I worded everything so I sound confident, but I’m not super confident.”

For a body in orbit around a planet, the gravitational force law requires the mass of both the body and the planet; however, in calculating the acceleration due to gravity, only the mass of the planet needs to be considered. Understanding this distinction may not be necessary for introductory astronomy students, so in many questions we simply refer to “gravity,” rather than specifying the “force,” “acceleration,” or “field.” In hindsight, this may not have been entirely appropriate, as some students misinterpreted questions. Question B15 highlights this ambiguity—two common response categories were that ‘a’: Larger, more massive satellites experience a stronger force of gravity, and ‘d’: Gravity pulls on all objects equally. Category ‘a’ is the correct response for gravitational force, and Category ‘d’ is the correct response to gravitational acceleration. Question A4 shows similar confusion: 5.6% (N = 8) of respondents reason that an object only has gravity if it has an effect on another object. While it is true that gravitational force requires two objects, the concept of a field allows one to think about a single object’s gravity. It is impossible to distinguish what the student meant or if they have misconceptions about these topics at all. In future multiple-choice versions that incorporate these questions, we will be more specific with terminology to eliminate ambiguity.

A students’ understanding of gravity is closely related to his/her understanding of other physical concepts, such as air pressure, the presence of an atmosphere, momentum, kinematics, and magnetism. For this reason, gravity can serve as a proxy for student’s understanding of many general physical concepts. Gravity is a concept that everyone has heard of and has daily experience with, so it is an excellent starting point for studying and reshaping students’ mental models. In the Constructivist framework, defining the preconceptions and misconceptions that students work from is a critical first step in helping them restructure their mental models.

The present study used exploratory, open-response format questionnaires to explore student misconceptions about gravity, which allowed themes to emerge naturally in students’ typical language. This is the first comprehensive study tailored specifically to introductory college astronomy students’ understanding of gravity. A variety of contexts were explored, including the strength of gravity in and around Earth, in terms of the solar system, and in hypothetical situations. Fifteen student interviews supplemented student responses as a deeper probe of misconceptions. In addition to the typical documented misconceptions about gravity, previously undocumented misconceptions were observed. In fact, the breadth of questions allowed a description of possible student mental models. We defined three possible alternative mental models about gravity—the boundary model, the orbital indicator model, and the “mixing of forces model.” These alternative models are the first to rigorously generalize student ideas about gravity. Additionally, we explored certain surprising disparate misconceptions and common misapplications of the scientific model in terms of mass, distance, and the cause of gravity. Taken as a whole, our proposed alternative models and description of misapplications of the scientific model offer a new language for astronomy researchers and educators to use in understanding their students’ ideas about gravity. These models give educators a vantage point from which to understand their students’ background knowledge and to navigate potential pitfalls in learning the scientific model. The results can lead to immediate formative assessment in the classroom and instructional development.

The student-supplied responses and interviews in the present study provide ample information about gravity conceptions in the natural language of students. While information about where these conceptions come from and exactly how students’ mental models are structured and used is still in the speculative stage, the project is ongoing and will be developed further in future work. As mentioned earlier, categories that represent misconceptions will be used for distractor choices in an up-and-coming, multiple-choice Newtonian Gravity Concept Inventory (NGCI), which has the potential to provide an independent measure of the mental models presented in Sections 6,7. Student interviews will continue to be used to supplement the NGCI results with a qualitative approach in an effort to provide a holistic picture of introductory astronomy student understanding of gravity.