Gravity, fields & mass
You will be able to: Use center-to-center distance to compare gravitational forces and field strengths.
Why does gravity weaken with distance?
Imagine moving a small satellite from one orbital distance to twice that distance from Earth’s center. Earth still pulls it, but with one quarter of the force. Distance enters the law twice.
A useful starting point: Net force and acceleration →
Words and symbols before equations
- Gravitational field g
- Force per unit test mass, in N/kg; equivalent to m/s².
- Separation r
- Distance between the centers of spherical masses, in m.
- G
- Universal gravitational constant, about 6.67×10⁻¹¹ N·m²/kg².
- Inertial / gravitational mass
- Mass measures resistance to acceleration and participation in gravity; experimentally these are equivalent.
What this picture assumes
Fixed source and test masses, spherically symmetric or point masses. Ratios are dimensionless. Reference force F₀ and field g₀ occur at r₀.
Connect the picture to the physics
Every pair of masses attracts. For point masses or nonoverlapping spherically symmetric bodies, the force magnitude is Gm₁m₂/r². It acts along the line joining their centers.
The field created by a spherical body of mass M is g=GM/r² outside it. Multiplying by a small object’s mass gives its weight there: F=mg. Field strength describes the source and location, not the test mass.
Near Earth’s surface over small height changes, g is approximately constant. At large heights use distance from Earth’s center: r=R+h. Because inertial and gravitational masses are equivalent, different freely falling objects share the same acceleration in the same field when other forces are negligible.
A worked example, step by step
At radius r, a satellite experiences force F and field g. Compare the force if its mass doubles and its distance becomes 3r. Compare the field at 3r.
- The satellite mass contributes a factor 2 to force.
- Tripling distance contributes a factor 1/3²=1/9.
- New force is 2F/9. The new field is g/9 because field does not depend on satellite mass.
- The satellite’s acceleration is also g/9 if gravity is the only force.
Height above the surface is not the r in the inverse-square law.
Does a heavier falling object feel more gravity? Why not accelerate faster?
Compare with an explanation
It feels proportionally more gravitational force but has proportionally more inertia. The ratio F/m is unchanged.
Predict. Change one thing. Explain.
Keep the source and test masses fixed. Change r/r₀ from 1 to 2 and 3. Compare F/F₀ with 1, 1/4 and 1/9. The graph is a model prediction, not measurements.
F/F₀ = g/g₀ = 1.
Fixed source and test masses, spherically symmetric or point masses. Ratios are dimensionless. Reference force F₀ and field g₀ occur at r₀.
Explain what you noticed: Which quantity changed? Which stayed fixed? Use a force or motion relationship to justify your prediction.
Apply the idea to a fresh problem Practice →Show what you understand.
Two original questions are a starting check, not proof of mastery. Explain your choice before revealing the answer.
Original written challenge
4 points · self-check · not an official AP questionA planet has twice Earth’s mass and twice its radius. (a) Write the field comparison, (b) calculate surface g using Earth g=10 N/kg, (c) find the weight of a 3 kg object, and (d) state its mass there.
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Compare with the answer and four-point rubric
- 1 point: g_planet/g_Earth = 2/2².
- 1 point: 5 N/kg.
- 1 point: 15 N.
- 1 point: 3 kg; changing gravitational field changes weight, not mass.
Accept equivalent correct methods and explanations. This is a Refresh Kid teaching rubric, not an official AP scoring guideline.
Retrieve it before you reveal it.
RECALL 1What is g measured in?
N/kg, equivalent to m/s².
RECALL 2Which distance does gravity use?
Center-to-center separation.
RECALL 3Why do ideal falling objects share acceleration?
Gravitational force and inertia both scale with mass.
Revisit these tomorrow and a week later. Try a fresh problem and explain why the method applies.
Gravity, fields & mass
- F_g=Gm₁m₂/r²; g=GM/r².
- Use center-to-center distance and spherically symmetric or point masses.
Remember: Height above the surface is not the r in the inverse-square law.
Conditions: Fixed source and test masses, spherically symmetric or point masses. Ratios are dimensionless. Reference force F₀ and field g₀ occur at r₀.
Refresh Kid · Unit 2 · Objectives 2.6.A, 2.6.B, 2.6.D · Review edition
Framework, scope and review status
Mapped to College Board CED, Topic 2.6, objectives 2.6.A, 2.6.B, 2.6.D. CED effective Fall 2024, current PDF ©2026; checked September 16, 2026. Fall-2026 corrections also checked. The lesson breakdown and questions are original Refresh Kid work, not official topic subdivisions.
Implementation and automated checks are separate from independent teacher review and observation of students. Both human review stages remain pending. This is a review edition, not a certified or validated assessment.
Optional further resource: College Board’s released questions and scoring guides. Papers can combine units; this link is an archive, not an assignment of every question to this lesson.
Our learn, explore, practice and recall sequence is informed by the IES learning guide. The exact Refresh Kid implementation has not been evaluated for learning effectiveness.
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