lesson
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Every object in the universe with mass exerts an invisible tug on every other mass, stretching across millions of kilometers of empty space. But how do we quantify that pull between giant astronomical bodies like planets and stars?
Newton's Law of Universal Gravitation
In 1687, Isaac Newton published his law of universal gravitation to explain both the fall of an apple on Earth and the orbits of the planets. He discovered that the attractive gravitational force (Fg) between two masses is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers.
📊A clean, modern visual showing two spherical masses, M1 (blue planet, labeled 'Mass M₁') and M2 (orange moon, labeled 'Mass M₂'). A dashed measurement line connects their exact geometric centers labeled 'r (center-to-center distance)'. Two equal-and-opposite inward-pointing force vectors are drawn on each sphere, labeled '+F' and '-F' satisfying Newton's third law. Above the diagram, display the formula in crisp typography: F_g = G * (M1 * M2) / r^2 with a callout box highlighting G = 6.674 × 10⁻¹¹ N·m²/kg² as the Universal Gravitational Constant. Use a light background (#f8f9fa), sleek borders (#e2e8f0), and sharp high-contrast text (#1e2945).
Because of spherical symmetry, a uniform sphere attracts external bodies as if all of its mass were concentrated at a single point mass at its center. The constant of proportionality is the gravitational constant, G=6.674×10−11 N⋅m2/kg2.
How large is this force between actual celestial bodies? Let's compute the gravitational pull holding the Earth and Moon together.
Calculating Gravitational Force
Earth has mass M1=5.972×1024 kg, the Moon has mass M2=7.348×1022 kg, and their center-to-center distance is r=3.844×108 m. Substituting these values into Newton's formula gives:
Fg=(6.674×10−11)(3.844×108)2(5.972×1024)(7.348×1022)=1.98×1020 N
By Newton's Third Law, the gravitational attraction between two objects forms an action-reaction pair. Body A exerts an equal and opposite force on body B (FA on B=−FB on A), regardless of any disparity in their masses.
Even though Earth is roughly 81 times more massive than the Moon, the Moon pulls back on Earth with the exact same magnitude of 1.98×1020 N.
This immense mutual force of nearly 2×1020 N continuously bends the Moon's velocity into an orbit around Earth. But what if we want to measure the strength of Earth's gravity at any point in space, regardless of what object is placed there?