Lesson 1 of 5 · Mass, weight & attraction
Gravity is everywhere
7 minute lesson · 3 checks along the way
Your goal for this lessonExplain how mass and distance affect gravitational attraction, and why moving to another world changes weight without changing mass.
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A connection between masses
A dropped pencil and the Moon’s curved journey around Earth belong to the same story. Gravity is a mutual attraction between masses. Earth attracts the pencil, and the pencil attracts Earth. The effects on their motion differ enormously because Earth has so much more . Small everyday objects attract one another too, although those effects are usually overwhelmed by other forces.
Isaac Newton connected falling objects with celestial motion in one mathematical account. In that account, a pair of objects exerts equal and opposite gravitational forces on each other. Equal forces do not mean equal changes of motion: a larger mass is harder to accelerate. Gravity is therefore a relationship between bodies, rather than a power that only planets possess.
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Your mass travels with you
Mass describes how much matter an object contains and how strongly it resists a change in motion. We measure it in kilograms. Gravitational is a force: the local gravitational pull on that mass, measured in newtons. Everyday speech often mixes these meanings, but separating them makes it easier to understand what changes when an astronaut visits another world.
Carry the same sealed instrument from Earth to the Moon and its mass stays the same. Its gravitational weight is smaller on the Moon because the local gravitational acceleration is weaker. The instrument would still resist being pushed sideways. A floor or spring scale supplies a support force; what that scale registers also depends on whether the instrument and scale are accelerating together.
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Distance has a precise meaning
For spherical bodies, viewed from outside, Newton’s model treats gravity as though each body’s mass were concentrated at its center. Increase either mass while keeping the separation fixed and the attraction increases. Increase their center-to-center distance and the attraction decreases. The distance in this rule is not simply height above a planet’s surface: the planet’s radius is part of it too.
The distance rule is an inverse square: double the center-to-center distance while leaving both masses unchanged and the force becomes one quarter as large. Tripling that distance gives one ninth. These comparisons concern the same pair of masses. Moving upward does not cross a boundary where gravity suddenly disappears, and doubling your height above the ground does not generally double your distance from Earth’s center.
Earth from DSCOVR’s EPIC camera on July 6, 2015. Red, green, and blue measurements combine into this color view. The photograph shows our planet; it does not mark an edge where Earth’s gravity stops.
Look closely
Trace the visible edge of Earth. Is that also the boundary of its gravitational influence?
See what to notice
The visible edge separates the sunlit planet from the dark background in this view. Gravity has no matching sharp boundary: its strength decreases with distance. A photograph records arriving light, while measurements of motion help us investigate gravity.
Work through a decision
Use the model, name its limits
Suppose two diagrams place identical probes at different distances from a spherical planet. To compare gravitational attraction, first check that both diagrams use distance from the center. Then keep the planet and probe masses fixed while changing distance. This controlled comparison isolates one cause. A larger-looking planet picture, without mass or scale information, cannot settle which probe feels the greater force.
Newton’s description works extremely well for many ordinary spaceflight calculations. It is still a model. Real planets have uneven mass distributions, other bodies also exert gravity, and Einstein’s general relativity is needed for effects beyond Newton’s description. In this course we begin with slow-moving bodies and an idealized spherical planet, then add the complications that matter to the question.
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Put it together
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