Gravitational Force
Gravitational force is the attractive interaction between masses; for point masses or spherically symmetric objects its magnitude follows an inverse-square dependence on center-to-center separation.
What do I need to know for AP Physics 1 Topic 2.6?
Topic 2.6 Gravitational Force: Gravitational force is the attractive interaction between masses; for point masses or spherically symmetric objects its magnitude follows an inverse-square dependence on center-to-center separation.
- Use universal gravitation, distinguish mass from weight, connect near-Earth weight to the broader inverse-square model, and make factor-of-change predictions.
- Practice target: 42 original MCQs and 4 original FRQs for this exact topic.
- Course alignment: current AP Physics 1 framework for the 2026–27 school year and May 2027 exam.
What is Gravitational Force?
Gravitational force is the attractive interaction between masses; for point masses or spherically symmetric objects its magnitude follows an inverse-square dependence on center-to-center separation.
Physics terms this topic teaches directly
Use these as working definitions for the lesson. Each definition is paired with a physical situation so the vocabulary is connected to observable motion or interactions rather than memorized in isolation.
Gravitational force
Gravitational force is the attractive interaction between masses, directed along the line joining their centers; for point masses or spherical bodies its magnitude is Gm₁m₂/r².
Gravity near Earth
Near Earth’s surface, over height changes small compared with Earth’s radius, the gravitational field is approximately uniform and free objects have nearly constant downward acceleration g.
Gravitational field
Gravitational field at a point is gravitational force per unit test mass, g=F_g/m; it points in the direction a small positive test mass would accelerate.
Weight
Weight is the gravitational force acting on an object; near Earth its magnitude is approximately mg.
Apparent weight
Apparent weight is the support force measured by a scale or felt by a supported person, often the normal force; it can differ from mg when acceleration is present.
Understand these ideas here before continuing
You should not have to leave this lesson just to decode its vocabulary. Each concept below is defined here, connected to the physics of this topic, and illustrated with a real situation. A related lesson link is provided only for deeper study.
Force
Meaning here: A vector interaction capable of changing velocity. Gravity is a long-range force between masses.
How this topic uses it: Gravity is one particular interaction force. It can change an object’s velocity even when the object is moving in the opposite direction, as for a ball traveling upward while gravity pulls downward.
Acceleration
Meaning here: A change in velocity per unit time. Gravitational field strength has the same numerical units as gravitational acceleration.
How this topic uses it: Gravitational force produces acceleration through Newton’s second law. Near Earth, free objects of different masses have approximately the same gravitational acceleration when air resistance is neglected.
Center-to-center separation
Meaning here: For point masses or spherical bodies, r in the inverse-square law is measured between centers, not between surfaces.
How this topic uses it: The inverse-square model depends on the distance between mass centers. Using altitude alone for a satellite gives the wrong separation because Earth’s radius must also be included.
Circular orbit
Meaning here: An orbit is continuous free fall in which gravity supplies inward acceleration that continually turns the velocity vector.
How this topic uses it: An orbit combines gravity with changing velocity direction: gravity supplies the inward acceleration while the object’s tangential velocity keeps carrying it around the central body.
How Gravitational Force works
Build the physical model first. The examples below connect the idea to situations you could actually observe before the page turns to equations.
Universal gravity is an inverse-square interaction along the line of centers
Two masses attract each other with force magnitude Gm₁m₂/r², where r is the center-to-center separation. Doubling the separation makes the force one fourth as large. For spherical bodies such as planets, treat the mass as concentrated at the center when using this model. The gravitational field g = GM/r² describes force per unit mass at a location, so a small test mass placed there experiences F_g = mg.
Near Earth, distinguish mass, gravitational force, and apparent weight
When height changes are small compared with Earth's radius, the gravitational field can be treated as approximately constant, commonly g ≈ 10 N/kg in AP Physics 1 estimates. Mass is measured in kilograms; gravitational force or weight is mg in newtons. A bathroom scale does not directly measure mg—it measures the support/normal force. In an upward-accelerating elevator, that normal force can exceed mg; in downward acceleration it can be smaller.
Free fall and orbit are not zero-gravity situations
An astronaut in orbit experiences gravitational acceleration toward Earth while both astronaut and spacecraft fall together, so the support force—and therefore apparent weight—can be near zero. The same idea explains why a freely falling elevator produces weightlessness even though gravity is acting. AP Physics 1 also distinguishes inertial mass, which links force to acceleration, from gravitational mass, which determines gravitational interaction; experiments show these two roles of mass are equivalent.
Core ideas with real physical examples
Each category keeps the physics statement and the real situation together, so the page does not reduce the topic to abstract definitions.
| Idea/type | What it means | Real example 1 | Real example 2 |
|---|---|---|---|
| Universal attraction | Every pair of masses exerts equal-and-opposite gravitational forces. | Earth pulls a satellite inward while the satellite pulls Earth with equal force magnitude. | A person pulls gravitationally on Earth with the same magnitude that Earth pulls on the person. |
| Inverse-square dependence | Force weakens as 1/r² with center-to-center separation. | Doubling orbital distance makes gravitational force one-fourth as large if masses are unchanged. | Tripling separation makes it one-ninth as large. |
| Weight near Earth | For small height changes near Earth, F_g ≈ mg is a useful local approximation. | A 5 kg backpack weighs about 50 N when g≈10 m/s². | An elevator rider’s gravitational force remains mg even though the scale reading can differ. |
| Free fall/orbit | Objects can feel weightless while gravity still acts strongly. | Astronaut and spacecraft in orbit fall together, producing little normal/support force. | A dropped object and its container can share nearly the same gravitational acceleration. |
| Apparent weight | The magnitude of apparent weight is the support/normal force, so it can differ from gravitational force when the system accelerates. | A scale reads more than mg while an elevator accelerates upward. | A scale can read zero in free fall even though gravity still acts. |
| Inertial vs gravitational mass | Inertial mass controls resistance to acceleration; gravitational mass controls gravitational interaction strength, and experiments find them equivalent. | The same kilogram mass used in F=ma also determines the object’s weight mg near Earth. | Different materials fall with the same gravitational acceleration in the ideal no-drag model because inertial and gravitational mass are equivalent. |
| Gravitational field | A field describes the gravitational effect of a source mass at each location; field strength equals gravitational force per unit test mass. | Near Earth, a 2 kg object in a 10 N/kg field experiences about 20 N of gravitational force. | Farther from a planet, the field arrows/magnitude weaken according to GM/r². |
| Equivalence principle | Locally, an observer in a uniformly accelerating noninertial frame can experience apparent weight effects that are indistinguishable from those associated with a gravitational field. | Inside a windowless rocket accelerating upward, a person feels a floor support force similar to standing in gravity. | In a freely falling elevator, the support force can vanish, producing apparent weightlessness even though gravity still acts. |
| Line of centers | For point masses or spherically symmetric objects, the gravitational interaction acts along the line joining their centers of mass; each body experiences the force toward the other body. | Earth’s gravitational force on a circular-orbit satellite points from the satellite toward Earth’s center. | Two separated uniform spheres attract along the straight line connecting their centers. |
| Near-Earth field value | When the gravitational field does not change appreciably over the motion, AP Physics 1 commonly uses g ≈ 10 N/kg, numerically equal to about 10 m/s² for a freely falling object. | A 3 kg backpack near Earth has weight about 30 N using g≈10 N/kg. | A dropped ball near Earth accelerates downward at about 10 m/s² when air resistance is neglected. |
College Board focus for Topic 2.6
2.6.A–D · Gravitation, gravitational field, near-Earth gravity, apparent weight, and mass equivalence.
Important boundary: Use center-to-center separation for spherical/point-mass gravity; apparent weight is support force, not mg itself.
Equations, variables, SI units and when they apply
| Relationship | Variables / SI units | When to use it | Real example |
|---|---|---|---|
| Fg = Gm1m2/r² | G: N·m²/kg²; m: kg; r: m; F: N | General two-mass gravitational interaction. | If separation doubles, F_g becomes one-fourth. |
| Fg = mg | m: kg; g: m/s²; F: N | Near a planetary surface when g is approximately constant. | A 60 kg person has about 600 N weight if g≈10 m/s². |
| g = GM/r² | G: N·m²/kg²; M: kg; r: m; g: m/s² | Relate gravitational field strength to source mass and distance. | Moving farther from Earth’s center reduces g according to the inverse square. |
Interactive Gravitational Force check
Universal-gravity factor lab
Compare two masses and a separation. The tool calculates gravitational-force magnitude using G.
Adjust a slider to explore the model.
Three real-situation worked examples
Higher altitude
A satellite is moved farther from Earth.
Weight vs scale reading
A rider stands on a scale in an accelerating elevator.
Astronaut in orbit
The astronaut reports apparent weightlessness.
Elevator scale reading
A 60 kg rider accelerates upward at 2 m/s² using g≈10 m/s².
Equivalence of mass
Two objects of different composition fall together in an evacuated chamber.
Common AP mistakes—and the correction
| Common mistake | Correct physics | Real-life check |
|---|---|---|
| Using surface-to-surface distance in the inverse-square formula. | Use center-to-center separation for point/spherical models. | Higher altitude: test the statement against this physical situation. |
| Saying gravity is zero in orbit. | Orbital motion requires significant gravitational acceleration. | Weight vs scale reading: test the statement against this physical situation. |
| Treating mass and weight as the same quantity. | Mass is kg; weight is gravitational force in newtons. | Astronaut in orbit: test the statement against this physical situation. |
| Using constant g across enormous altitude changes. | Use the inverse-square model when r changes significantly. | Elevator scale reading: test the statement against this physical situation. |
| Calling the scale reading “the gravitational force.” | A scale measures normal/support force, which is apparent weight and can differ from mg during acceleration. | Equivalence of mass: test the statement against this physical situation. |
| Treating inertial mass and gravitational mass as unrelated AP quantities. | They describe different roles of mass but have been experimentally verified to be equivalent. | Higher altitude: test the statement against this physical situation. |
Master this topic beyond a formula list
This checkpoint combines the current AP Physics 1 content boundary with representation, experiment/data reasoning, real situations and cross-topic transfer.
2026–27 mastery checklist
- Use Newton’s universal gravitation for point masses or spherically symmetric bodies with center-to-center separation.
- Describe gravitational field as force per unit test mass and relate near-Earth field strength to g.
- Distinguish mass, gravitational force/weight, apparent weight and weightlessness.
- Recognize equivalence of inertial and gravitational mass within the course model.
Must-not-miss relationship
F_g = Gm_1m_2/r² and g = F_g/m. Near Earth, F_g ≈ mg when g can be treated as uniform.
Two anchor situations
An astronaut in orbit can be weightless in the apparent-weight sense while Earth’s gravitational force remains substantial.
A bathroom scale reads the support/normal force, so its reading can differ from mg in an accelerating elevator.
Diagram / graph / equation / claim
Draw a gravitational field vector map around one spherical body, then overlay the force on a positive test mass and compare the r-dependence.
How to test the physics
Use a smartphone accelerometer/scale-style setup in a safe elevator or simulated cart system to distinguish support-force reading from gravitational force conceptually.
Use center-to-center distance for spherical/point-mass gravity. Do not replace universal gravitation with near-Earth mg when r changes significantly.
Carry universal gravity into gravitational potential energy and satellite/orbit models.
Connect to Topic 6.6 orbital motionGo beyond memorizing the equation
This topic now combines model selection, physical intuition, a worked transfer problem, graph/data analysis, answer verification, and the four current AP free-response reasoning modes.
Choose the model before calculating
Choose the gravitational model: near-Earth constant g or universal gravitation. For spherical bodies use center-to-center separation.
Why the physics works
Universal gravitation decreases with the square of separation, while the near-Earth model treats the small variation in r as negligible.
Solve this before opening the solution
A 2 kg object is near Earth where g≈10 m/s². Find its weight. If a point-mass gravitational field is evaluated at twice the original distance from the source, how does field magnitude change?
Reveal complete reasoning
Solution: Weight=mg=20 N downward. Doubling r makes g_field one-fourth as large because it scales as 1/r².
Physics check: A field cannot become negative in magnitude; direction points toward the attracting mass.
What should you plot?
For a point/spherical source, plot measured field magnitude g versus 1/r².
What does the graph mean?
A straight-line relation supports the inverse-square model, with slope GM.
How this exact topic can appear in each current FRQ mode
F_g = Gm_1m_2/r² and g = F_g/m. Near Earth, F_g ≈ mg when g can be treated as uniform.
Draw a gravitational field vector map around one spherical body, then overlay the force on a positive test mass and compare the r-dependence.
Use a smartphone accelerometer/scale-style setup in a safe elevator or simulated cart system to distinguish support-force reading from gravitational force conceptually.
Carry universal gravity into gravitational potential energy and satellite/orbit models.
Distinguish mass from weight, identify the source mass and center-to-center r, and state the attractive direction.
Continue with the exact topic question banks
Use the focused banks for skill practice. The five full model papers are reserved for whole-exam simulation.
Topic 2.6 quick questions
What is the first thing I should identify in a Topic 2.6 problem?
Use universal gravitation, distinguish mass from weight, connect near-Earth weight to the broader inverse-square model, and make factor-of-change predictions.
Should I memorize an equation before understanding the physical model?
No. Start by identifying the system, interactions, directions and representation. Then choose the relationship whose assumptions match the situation.
Where should I practice this exact topic?
Use the direct 42-MCQ and 4-FRQ Topic 2.6 banks on this page. The five-model-paper page is reserved for full-exam simulation.
Is this aligned to the May 2027 AP Physics 1 exam?
Yes. The course content remains based on the Fall 2024 framework for 2026–27; the Fall 2026 update changes the May 2027 exam timing and question count, not this Unit 2 topic sequence.
Where Topic 2.6 appears in AP-style released work
These are original topic summaries and alignment notes, not reproduced College Board question text. One released FRQ can legitimately connect to several topics.
Orbiting spacecraft and circular-motion derivation
Direct connection to gravitation, circular motion and orbital period.
Mathematical RoutinesCart on incline and gravitational-acceleration experiment
Links kinematics, dynamics and experimental determination of gravitational acceleration.
Experimental Design & AnalysisPendulum comparison, work and elastic restoring behavior
Connects gravitational context, work/energy and oscillator period reasoning.
Qualitative / Quantitative TranslationRecent public FRQs are the safest format reference. Older released questions can still contain excellent physics, but the course and exam changed; use the atlas alignment notes before treating a legacy question as a current-format simulation.