Universal Gravitation Governs Every Orbit
Nova stands at the edge of a moonlit observatory deck, pointing a telescope toward Jupiter while orbital diagrams and gravitational field lines glow on a tablet in her other hand, planets tracing arcs across the star-filled sky above.
- State Newton's law of universal gravitation and identify each variable in the equation F = Gm₁m₂/r².
- Explain how gravitational force changes when mass or separation distance is altered, using the inverse-square relationship.
- Apply the inverse-square relationship to predict how gravitational force changes when mass or distance is altered by a given factor.
- Predict the direction and relative magnitude of gravitational force between two objects given their masses and separation.
- Explain why all orbital motion — from satellites to planets — arises from the same gravitational law Newton derived.
Key terms
- Universal gravitation
- Newton's law that any two masses attract along the line joining them with force F = Gm₁m₂/r².
- Gravitational constant G
- The fixed proportionality constant 6.674 × 10⁻¹¹ N·m²/kg² that scales the strength of gravity everywhere in the universe.
- Inverse-square law
- The dependence of force on one over distance squared, so tripling separation reduces force to one-ninth.
- Centripetal force
- The net inward force required to keep an object moving along a curved path; for orbits, gravity supplies it.
Decoding the Equation
The law F = Gm₁m₂/r² states that gravitational attraction grows linearly with each mass but shrinks with the square of the center-to-center distance. Doubling either mass doubles the force, while doubling the distance quarters it because the 1/r² term dominates. The constant G is extremely small, which is why gravity between everyday objects is negligible and only becomes commanding when at least one mass is planetary in scale. Crucially, gravity is always attractive and acts along the line connecting the two centers, never repelling.
An Orbit Is Continuous Falling
Newton's insight was that the Moon and a thrown stone obey the same law: an orbit is simply free-fall with enough sideways speed that the surface curves away as fast as the object falls toward it. Gravity is never canceled in orbit; it is the centripetal force that bends the path into an ellipse. Because gravity follows an inverse-square law, the resulting closed orbits are precisely the ellipses Kepler had earlier extracted from observation, unifying terrestrial and celestial motion under one principle.
Worked examples
A probe moves from distance r to distance 3r from Earth's center. How does the gravitational force change?
- Use the inverse-square law: F ∝ 1/r².
- The distance multiplies by 3, so the force multiplies by 1/3² = 1/9.
- Therefore the new force is one-ninth of the original.
Answer: The gravitational force drops to one-ninth of its original value, not one-third.
Activity
Rank these three pairs of objects from strongest to weakest gravitational force between them, dragging the cards into order. Tip: compare the masses and distances using F = Gm₁m₂/r² — you do not need exact numbers, just relative size.
Practice
If both masses in a gravitational pair are doubled while the distance stays the same, calculate how the force changes and explain each factor.
Explain why a planet keeps orbiting the Sun instead of either flying away or falling straight in, referring to its sideways velocity.
Common mistakes to avoid
- Tripling distance reduces gravity to one-third.Gravity follows the inverse-square law, so tripling distance reduces the force to one-ninth, not one-third.
- In orbit, velocity cancels gravity so there is no net force.Gravity is not canceled; it acts as the centripetal force continuously bending the planet's path into an orbit.
Check your understanding
A space probe moves to a distance three times farther from Earth than its original orbit. How does the gravitational force Earth exerts on the probe change?
Newton's law of universal gravitation is called 'universal' because it
Which statement best explains why a planet continues to orbit the Sun rather than flying away or falling straight in?
Recap
Newton's universal gravitation, F = Gm₁m₂/r², applies to any two masses anywhere, growing with mass and falling as the inverse square of distance; it explains orbits as continuous free-fall and reproduces Kepler's ellipses from a single principle.
Reflect
Why was it revolutionary for Newton to claim that the force pulling an apple down is the very same force holding the Moon in orbit?