How Does Mass Affect Gravitational Force

Short answer

• Mass increases gravitational force in direct proportion. If you double the mass of one object while keeping everything else the same, the gravitational force between the two objects doubles. If you double the mass of both objects, the force becomes four times as strong. That is the core of Newton's law of universal gravitation: the force is proportional to the product of the two masses, and it falls off with the square of the distance between their centers. Mass is not the only factor. Distance matters just as much, and it matters in a different way. Double the distance and the force drops to one quarter of its value. Density and size also shape the gravity you feel at the surface of a planet or a moon, because surface gravity depends on both mass and radius. But when distance and size are held steady, the rule is simple and exact: more mass means a stronger gravitational pull, in direct proportion to the mass added.

More mass means a stronger pull

Every object with mass pulls on every other object with mass. That pull is gravity, and its strength depends first on how much mass is involved. A planet pulls harder than a pebble. A star pulls harder than a planet of the same size but lower mass. The reason is built into the law that describes the force: mass sits in the numerator of the equation, so increasing it increases the force by the same factor.

Think of two bowling balls on a smooth floor, far from anything else. The gravitational force between them is real but far too small to feel, because their masses are small and the gravitational constant is tiny. Replace one bowling ball with a ball of the same size made of lead, which has far more mass in the same volume, and the force between the two balls grows. Replace both balls with lead balls, and the force grows again. Nothing else has changed except mass, and the force has followed mass step for step.

The same pattern scales up to planets and stars. Earth pulls on the Moon with a strong force because Earth is massive. The Sun pulls on Earth with a far stronger force than Earth pulls on the Moon, because the Sun is enormously more massive than Earth, even though the Sun is much farther away. Mass sets the ceiling for how strong the pull can be. Distance then decides how much of that pull is felt at a given separation.

It also helps to notice what mass does not do on its own. Adding mass to an object does not change the gravitational constant, and it does not change the fact that gravity always pulls objects together, never pushes them apart. Mass changes the size of the attraction. It does not change its direction, and it does not turn gravity into a different kind of force.

Newton’s law in plain language

Isaac Newton published his law of universal gravitation in 1687, in his book Philosophiae Naturalis Principia Mathematica, usually called the Principia. The law says that every particle of matter in the universe attracts every other particle with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers. In symbols, the law is written as F equals G times m1 times m2 divided by r squared, or F = G m1 m2 / r^2.

Each symbol has a plain meaning. F is the gravitational force between the two objects, measured in newtons. G is the gravitational constant, a fixed number that sets the overall strength of gravity. The symbols m1 and m2 are the masses of the two objects, measured in kilograms. The symbol r is the distance between the centers of the two objects, measured in meters. The force on each object points toward the other object, and the two forces are equal in size and opposite in direction.

The word product matters here. The force depends on m1 times m2, not on m1 plus m2, and not on the larger mass alone. That is why both masses count. If either mass is zero, there is no gravitational force at all, because the product is zero. If one mass doubles, the product doubles, and so does the force. If both masses double, the product becomes four times as large, because 2 times 2 equals 4, and the force becomes four times as strong.

The constant G is very small. The 2022 CODATA recommended value published by the National Institute of Standards and Technology, NIST, is 6.67430 times 10 to the power of minus 11 cubic meters per kilogram per second squared, with a standard uncertainty of 0.00015 x 10 to the power of minus 11 in the same units. Written out, that is 0.0000000000667430 in those units. Because G is so small, everyday objects exert gravitational forces on each other that are far too weak to notice without sensitive instruments. Only when at least one mass is very large, as with a planet or a star, does the force become obvious in daily life.

The law is called universal because it applies to everything with mass, from dust grains to galaxies. It describes the fall of an apple, the orbit of the Moon, and the motion of planets around the Sun with the same rule. That breadth is what made it a breakthrough: one law for the heavens and for the ground underfoot, with mass as the quantity that sets the strength of the pull.

What doubling and tripling mass actually does

The direct proportion between mass and force is easy to test with numbers, and the numbers are worth working through once, because they remove the guesswork. Keep the distance fixed, change only the mass, and watch the force.

If you double the mass of one object, the force doubles. Start with two objects that attract each other with a force of 10 newtons. Double the mass of one of them, and the force becomes 20 newtons. Triple the mass of one of them instead, and the force becomes 30 newtons. Halve the mass of one of them, and the force falls to 5 newtons. The factor you apply to the mass is exactly the factor you apply to the force.

If you change both masses, the effects multiply. Double both masses and the force becomes four times as strong, because the product of the masses has grown by 2 times 2. Triple one mass and double the other, and the force becomes six times as strong, because 3 times 2 equals 6. Halve one mass and double the other, and the force stays the same, because one half times 2 equals 1.

A worked example with real numbers shows how small gravity is between ordinary objects. Take two objects of 1 kilogram each, with their centers 1 meter apart. The force between them is G times 1 times 1 divided by 1 squared, which is just G itself: about 6.67 times 10 to the power of minus 11 newtons. That is roughly 0.0000000000667 newtons. For comparison, the weight of a small apple on Earth is about 1 newton. The gravitational pull between the two 1 kilogram masses is about 15 billion times smaller than that. Double one mass to 2 kilograms, and the force doubles to about 1.33 times 10 to the power of minus 10 newtons. It is still far too small to feel, but the proportion is exact.

The same arithmetic explains why planets dominate. Earth has a mass of about 5.9722 times 10 to the power of 24 kilograms. Put that number into the product m1 times m2, and even after multiplying by the tiny value of G, the result is a force large enough to hold the Moon in orbit and to keep everything on the surface pulled firmly downward. Mass is the lever. The bigger the mass, the bigger the product, and the bigger the force.

Both masses count, and the pull is mutual

Gravity is always a two way pull. Earth pulls on the Moon, and the Moon pulls on Earth with a force of exactly the same size. The Sun pulls on Earth, and Earth pulls on the Sun with an equal force. The two forces are equal and opposite, as Newton’s third law of motion requires. What differs is not the force but the effect: the lighter object accelerates more, because the same force acting on a smaller mass produces a larger acceleration.

That distinction clears up a common puzzle. If Earth and the Moon pull on each other equally, why does the Moon orbit Earth rather than the other way around? The answer is that both bodies do move around their common center of mass, but that point lies inside Earth because Earth is about 81 times as massive as the Moon. Earth wobbles slightly around that point, while the Moon sweeps around it in a wide orbit. The force is shared equally. The motion is not, because the masses are so unequal.

The same logic applies to a person standing on Earth. You pull on Earth with exactly the same force that Earth pulls on you. Your mass is tiny compared with Earth’s, so your pull moves Earth by an amount far too small to measure, while Earth’s pull on you is what you feel as weight. The force is mutual. The visible result is one sided only because one mass is vastly larger than the other.

This also means that the mass of the smaller object is not irrelevant. A heavier satellite feels a stronger gravitational force from Earth than a lighter satellite at the same distance, because the product of the masses is larger. Yet both satellites fall toward Earth at the same rate, because the heavier one also has more inertia to overcome. The force is larger, but so is the mass being accelerated, and the two effects cancel. That is why, in the absence of air resistance, a heavy object and a light object fall at the same rate, even though gravity pulls harder on the heavy one.

Distance matters too, and it matters differently

Mass is only half the story. The other half is distance, and distance acts in the opposite direction and more sharply. In Newton’s law, distance appears in the denominator, squared. That is the inverse square relation: the force is inversely proportional to the square of the distance between the centers of the two objects.

Double the distance and the force falls to one quarter of its value, because 2 squared is 4, and 1 divided by 4 is one quarter. Triple the distance and the force falls to one ninth. Halve the distance and the force becomes four times as strong. Move ten times farther away and the force falls to one hundredth of its value. The falloff is rapid at first and then slows, but it never quite reaches zero. Gravity has an unlimited range in Newton’s picture, even though it becomes vanishingly weak at great distances.

That is why the Sun, despite its enormous mass, does not drag Earth into itself, and why Earth, despite its large mass, does not pull the Moon out of its orbit in a straight line. Distance sets the balance. The Sun is about 333,000 times as massive as Earth, which is why it can hold Earth in orbit from about 150 million kilometers away. If Earth moved much closer to the Sun, the force would grow rapidly. If it moved much farther away, the force would weaken rapidly, and Earth’s orbit would change.

Distance is measured from center to center, not from surface to surface. That detail matters when you stand on Earth. Your distance from Earth’s center is about 6,400 kilometers, the radius of the planet, not zero. If you could somehow stand at Earth’s center, the simple form of the law would break down, because the mass would surround you rather than sitting below you. For objects in space, the center to center rule is what keeps the calculation honest: the Moon is about 384,400 kilometers from Earth’s center, and that is the distance that goes into the law, not the distance from Earth’s surface to the Moon’s surface.

When people ask how mass affects gravitational force, the honest answer therefore has two parts. Mass sets the strength in direct proportion. Distance then scales that strength down by the square of the separation. A massive object far away can pull less strongly than a modest object close by, and a small change in distance can outweigh a large change in mass.

Mass is not weight

One of the most persistent confusions in this topic is the difference between mass and weight, and it is worth clearing up early because the two words are used loosely in everyday speech. Mass is a measure of how much matter an object contains. It is measured in kilograms, and it does not change when the object moves from place to place. Weight is the force of gravity acting on that mass. It is measured in newtons, and it changes with the strength of the gravitational field the object is in.

Your mass is the same on Earth, on the Moon, and in deep space. Your weight is not. On Earth, the acceleration due to gravity at the surface is about 9.81 meters per second squared, so a person with a mass of 70 kilograms weighs about 70 times 9.81, or about 687 newtons. On the Moon, surface gravity is about 1.62 meters per second squared, so the same person weighs about 70 times 1.62, or about 113 newtons, roughly one sixth of the Earth weight. The person has not lost mass. The gravitational field is weaker, because the Moon has much less mass than Earth and a smaller radius, so the force on the same mass is smaller.

The formula that ties the two together is weight equals mass times the acceleration due to gravity, or W = m times g. Here g is not the universal constant G. It is the local acceleration due to gravity, which depends on the mass and radius of the body you are standing on. Near Earth’s surface, g is about 9.81 meters per second squared. Near the Moon’s surface, it is about 1.62 meters per second squared. The two symbols look similar and are easy to confuse, but they are different quantities: G is the same everywhere in the universe, while g changes from place to place.

Scales that report weight in kilograms are using a shortcut. They measure a force and then divide by Earth’s surface gravity to report the mass that would produce that force on Earth. That works fine on Earth, but it would give the wrong mass on the Moon, because the local g is different. Mass is the underlying property. Weight is what gravity does to that property in a particular place.

Why you feel Earth’s gravity and not a person’s

If everything with mass attracts everything else, why do you not feel the gravitational pull of the person next to you, or of a building, or of a mountain? The answer is a matter of scale, and the numbers make it plain.

Earth’s mass is about 5.9722 times 10 to the power of 24 kilograms. A person with a mass of 70 kilograms is about 85 thousand billion billion times less massive. Put those numbers into Newton’s law at the distances involved, and Earth’s pull on you comes out at about 687 newtons, while another person’s pull on you at a distance of a meter is about three hundred billionths of a newton (about a third of a millionth of a newton). The person’s pull is real, and it follows the same law, but it is swamped by Earth’s pull and by friction, air movement, and every other force acting on you.

The same reasoning explains why the Moon, despite its modest mass, raises tides on Earth. The Moon is far less massive than the Sun, but it is far closer, and tides depend on the difference in gravitational pull across Earth’s diameter, not just on the total pull. The Moon’s closeness gives it a strong tidal effect even though its total mass is small. The Sun’s tidal effect is smaller, even though the Sun is far more massive, because the Sun is far farther away and the difference in its pull from one side of Earth to the other is smaller.

It also explains why astronauts in orbit feel weightless even though they are still firmly inside Earth’s gravity. At the height of the International Space Station, Earth’s gravity is still most of its surface strength. The astronauts feel weightless not because gravity has vanished, but because they are in continuous free fall around Earth, falling toward it at the same rate as their spacecraft. Their mass has not changed, and Earth’s mass has not changed. The sensation of weight comes from the floor pushing back, and in free fall there is no floor pushing back.

Earth, the Moon, and the Sun compared

A short comparison of familiar bodies makes the mass rule concrete. The numbers below are rounded teaching values, and each one comes from the sources listed at the end of this article.

Earth has a mass of about 5.9722 times 10 to the power of 24 kilograms and a surface gravity of about 9.81 meters per second squared. The Moon has a mass of about 7.35 times 10 to the power of 22 kilograms, which is about 1.2 percent of Earth’s mass, or about one eighty first of Earth’s mass. Its surface gravity is about 1.62 meters per second squared, about one sixth of Earth’s. The Moon’s mass is much smaller, and its radius is also smaller, so the two effects partly offset each other. The result is a surface gravity that is weaker than Earth’s, but not as weak as the mass ratio alone would suggest.

The Sun has a mass of about 1.989 times 10 to the power of 30 kilograms, about 333,000 times Earth’s mass. Its surface gravity is about 28 times Earth’s surface gravity. That factor of 28 is much smaller than the mass factor of 333,000, because the Sun’s radius is about 109 times Earth’s radius, and surface gravity depends on mass divided by radius squared. The Sun’s huge mass is spread over a huge volume, so the gravity at its visible surface, while very strong, is not 333,000 times stronger than Earth’s.

Jupiter, the largest planet in the solar system, has a mass of about 1.898 times 10 to the power of 27 kilograms, about 318 times Earth’s mass. Its surface gravity is about 2.5 times Earth’s, again far less than the mass ratio, because Jupiter is much larger than Earth and its mass is spread over a much greater radius. These comparisons show the same lesson from three directions: mass drives the force up, but radius and distance pull the felt gravity back down.

The Earth Sun distance also belongs in this picture. Earth orbits the Sun at a mean distance of about 150 million kilometers, a distance covered in more detail in our guide to how far Earth is from the Sun. That distance, combined with the Sun’s enormous mass, sets the strength of the Sun’s pull on Earth and the speed Earth must travel to stay in orbit. If the Sun were less massive, Earth would need to move more slowly to stay in the same orbit. If the Sun were more massive, Earth would need to move faster. Mass, distance, and orbital speed are linked, and changing one changes the balance of the others.

The scale of the Sun itself is hard to picture from mass alone. About 1.3 million Earths would fit inside the Sun by volume, a comparison explored in our article on how many Earths can fit in the Sun. Volume and mass are different quantities: the Sun’s volume is vast because it is large, and its mass is vast because it contains so much matter. Both facts matter for gravity, but it is mass, not volume, that goes into Newton’s law.

Density and size: why mass alone does not set surface gravity

Mass alone does not decide how strong gravity feels at the surface of a world. Surface gravity depends on mass and radius together, through the relation g equals G times M divided by R squared, where M is the mass of the body and R is its radius. Two bodies with the same mass can have very different surface gravities if their radii differ, because the smaller body packs the same mass into a smaller volume and puts its surface closer to its center.

Density is the bridge between mass, size, and surface gravity. Density is mass divided by volume. A small, dense body can have a surprisingly strong surface gravity for its mass, because its surface sits close to a large amount of matter. A large, low density body can have a modest surface gravity despite a large total mass, because its surface sits far from most of its matter. Jupiter is the familiar example: its mass is 318 times Earth’s, but its surface gravity is only about 2.5 times Earth’s, because its radius is about 11 times Earth’s and the radius is squared in the relation.

The Moon shows the other side of the same rule. Its mass is only about 1.2 percent of Earth’s, yet its surface gravity is about 17 percent of Earth’s, because its radius is only about one quarter of Earth’s. The small radius partly compensates for the small mass. If the Moon were the same mass but larger, its surface gravity would be weaker still. If it were the same mass but smaller and denser, its surface gravity would be stronger.

This is why astronomers care about both mass and radius when they describe a planet. Mass alone tells you how strongly the planet pulls on other bodies at a distance. Mass plus radius tells you how strongly it pulls on something standing on its surface. A planet could be massive yet easy to stand on if it is also very large and low in density, and a small planet could be hard to stand on if it is dense and compact. When you read that a newly found exoplanet has a certain mass, remember that its surface gravity is still unknown until its radius is measured too.

The same principle applies on the scale of stars and galaxies. A galaxy contains an enormous total mass, spread over an immense volume, so the gravity felt at any one point inside it is the sum of many distant contributions rather than the pull of a single compact body. Our article on how many galaxies there are gives a sense of how many such systems exist, and each one is held together by the combined mass of its stars, gas, and dark matter. The law is the same. The geometry is what changes.

How scientists first measured the strength of gravity

Newton gave the world the law, but he did not know the value of G. The constant was not measured in his lifetime, and for more than a century after the Principia, physicists could compare gravitational forces but could not state their absolute size. The breakthrough came from a laboratory experiment with lead spheres, a suspended rod, and a very thin wire.

Henry Cavendish performed the experiment in 1797 to 1798. He used an apparatus devised by the geologist John Michell, who had died in 1793 before he could carry it out. The apparatus was a torsion balance: a wooden rod hung from a thin wire, with a small lead sphere weighing 0.73 kilograms at each end, and a much larger lead sphere weighing 158 kilograms placed near each small sphere. The gravitational attraction between each pair of spheres twisted the wire by a tiny amount, and Cavendish measured that twist to work out the force.

Cavendish did not set out to measure G. As Encyclopaedia Britannica records, he and Michell conceived the experiment as a way to determine Earth’s density, and the formulation of Newton’s law involving the gravitational constant did not appear until the late 19th century. Cavendish compared the tiny pull between the lead spheres with the pull of Earth on the same small spheres, and from that ratio he found Earth’s mean density to be 5.48 times that of water, close to the modern value of 5.51 grams per cubic centimeter. Once Earth’s density and size were known, its mass followed, and later physicists could combine that result with Newton’s law to derive a value for G.

The experiment also proved something larger than a number. It showed that Newton’s law worked on the scale of a laboratory bench, not only on the scale of planets and moons. Gravity between lead spheres a few centimeters across followed the same rule as gravity between Earth and the Moon. That was the first direct evidence that the law was truly universal, and it opened the way for the precise measurements of G that continue today. Modern determinations still use refined versions of the torsion balance, and the value remains one of the least precisely known fundamental constants, because gravity is so weak between laboratory masses that every measurement must fight noise from vibration, temperature, and air movement.

What mass does not do

Several common ideas about mass and gravity sound plausible but do not survive a careful look at the law. Clearing them up is part of understanding what mass actually does.

First, mass does not change how fast an object falls. In the absence of air resistance, a heavy object and a light object dropped from the same height hit the ground at the same time. Gravity pulls harder on the heavy object, because the product of the masses is larger, but the heavy object also has more inertia, so it needs more force to accelerate at the same rate. The two effects cancel exactly, and the acceleration is the same. Air resistance breaks the tie in real life: a feather falls slowly because air pushes back on it, not because gravity treats it differently.

Second, mass does not make gravity act faster or slower. The force depends on the masses and the distance at a given moment. It does not depend on how fast the objects are moving, in Newton’s picture, or on their temperature, color, or composition. Two objects of the same mass attract each other with the same force whether they are made of iron, rock, or ice, provided their centers are the same distance apart. Composition matters for density and size, and therefore for where the surface sits, but the law itself cares only about mass and distance.

Third, adding mass to a small object does not make it noticeably more attractive to things around it unless the added mass is very large. Put a heavy backpack on your back and your gravitational pull on the room does increase, in strict proportion to the added mass, but the increase is far too small to feel or measure without laboratory instruments. The proportion is exact and the effect is real. It is simply tiny, because G is tiny and human scale masses are tiny compared with planetary masses.

Fourth, mass does not shield gravity or block it. There is no known material that blocks gravitational attraction, and putting mass between two objects does not reduce the force between them in Newton’s law. The intervening mass adds its own gravitational pull, but it does not cancel the pull of the objects on either side. This is one reason gravity is so different from magnetism or electric charge, where shielding and cancellation are everyday facts.

Finally, mass on its own does not decide whether an object can hold an atmosphere or keep a moon in orbit. Those outcomes depend on mass, radius, temperature, distance from the Sun, and the history of the body. A massive planet close to its star can still lose light gases if it is hot enough, and a low mass moon can keep a thin atmosphere if it is cold enough and far enough from its star. Mass is the starting point for those questions, not the whole answer.

Mass, gravity, and orbits

Orbits are where the mass rule shows its most elegant result. A planet stays in orbit because its forward motion balances the inward pull of gravity. If the central body were more massive, its pull would be stronger at the same distance, and the orbiting body would need to move faster to stay in the same orbit. If the central body were less massive, the orbiting body would need to move more slowly. The mass of the central body, the distance of the orbit, and the orbital speed are tied together by the same law.

That is why the Sun’s mass matters so much for the solar system. The Sun holds all eight planets in orbit, not because it is close to them, but because it is so massive that its pull remains strong across hundreds of millions of kilometers. Earth, with far less mass, holds only one natural satellite, the Moon, and it holds it at a much smaller distance. Jupiter, the most massive planet, holds dozens of moons, because its mass gives it a gravitational reach that smaller planets cannot match.

The mass of the orbiting body matters far less than the mass of the central body, because the orbiting body’s mass appears on both sides of the calculation: it increases the force, but it also increases the inertia that must be accelerated. For a satellite that is much lighter than its planet, the orbital speed depends almost entirely on the planet’s mass and the distance of the orbit. That is why satellites of very different sizes can share the same orbit at the same speed, and why the Moon’s orbital period depends mainly on Earth’s mass and the Earth Moon distance, not on the Moon’s own mass.

Mass also shapes the structure of the solar system over long times. Planets grew by gathering mass, and as they gathered mass their gravity grew stronger, which let them gather still more mass. That feedback is part of how small rocky bodies became planets and how Jupiter became large enough to shape the orbits of asteroids and comets around it. Gravity rewards mass with more mass, up to the limits set by the material available and the heat generated as it gathers.

On the largest scales, the same rule holds galaxies and clusters of galaxies together. The total mass of a galaxy, including the dark matter that outweighs its visible stars, sets the strength of its gravitational hold on its stars and gas. Without that mass, the stars would drift apart. With it, they trace orbits around the galactic center that last for billions of years. The law that describes a falling apple also describes a galaxy, with mass as the quantity that sets the strength at every scale.

Frequently asked questions

Does more mass always mean more gravity?

Yes, when distance and size are held fixed. Double the mass of one object and the gravitational force between the two objects doubles. Double both masses and the force quadruples. But the gravity you feel at the surface of a planet also depends on its radius, so a more massive planet is not automatically harder to stand on. A large, low density planet can have a modest surface gravity despite a large total mass, because its surface sits far from its center.

Does mass affect gravity or does gravity affect mass?

Mass affects gravity in the sense that mass is the source of gravitational attraction: more mass produces a stronger pull. Gravity does not change an object’s mass. It changes its weight, which is the force gravity exerts on that mass in a particular place. An object’s mass stays the same on Earth, on the Moon, and in space, while its weight changes with the local gravitational field.

How does mass affect gravitational force between two objects?

The force is directly proportional to the product of the two masses. If you increase either mass, the force increases by the same factor. If you increase both masses, the factors multiply. The relation is F equals G times m1 times m2 divided by r squared, where G is the gravitational constant and r is the distance between the centers of the two objects.

Why do heavier objects not fall faster?

Gravity pulls harder on a heavier object, but the heavier object also has more inertia, so it resists acceleration more strongly. The two effects cancel, and in the absence of air resistance all objects fall at the same rate. Air resistance is what makes a feather fall more slowly than a stone in everyday conditions, not a difference in how gravity acts on their masses.

Does the Moon have less gravity because it has less mass?

Partly, yes. The Moon’s mass is about 1.2 percent of Earth’s mass, and that is the main reason its surface gravity is weaker, at about 1.62 meters per second squared compared with Earth’s 9.81. But radius matters too. The Moon’s radius is about one quarter of Earth’s, which partly offsets its small mass. If the Moon had the same mass but a larger radius, its surface gravity would be weaker still.

Can an object have mass but no gravity?

No, in Newton’s picture every object with mass exerts a gravitational pull on every other object with mass. The pull may be far too small to notice, as it is between two people or two small stones, but it is not zero. Even a single atom exerts a gravitational pull, although the force is unimaginably small. There is no known way to switch gravity off or to shield an object from it.

Does distance matter more than mass?

It depends on the numbers. Mass changes the force in direct proportion, while distance changes it by the square of the factor. Doubling the mass doubles the force, but doubling the distance cuts it to one quarter. In practice, a small change in distance can outweigh a large change in mass, which is why the Moon raises stronger tides on Earth than the far more massive Sun does. Both factors must be considered together, never one alone.

Sources & references

• * National Institute of Standards and Technology, NIST Reference on Constants, Units, and Uncertainty, CODATA Value: Newtonian constant of gravitation, 2022 CODATA recommended values. G equals 6.67430 times 10 to the power of minus 11 cubic meters per kilogram per second squared, standard uncertainty 0.00015 x 10 to the power of minus 11 in the same units. Opened and read 5 November 2026.
• * Encyclopaedia Britannica, Cavendish experiment, Definition and Facts, published 17 January 2019. The experiment was performed in 1797 to 1798 by Henry Cavendish, using apparatus devised by John Michell; small spheres 0.73 kilograms, large spheres 158 kilograms; Earth's mean density found as 5.48 times that of water, close to the modern value of 5.51 grams per cubic centimeter; the experiment was devised to determine Earth's density, not to measure G. Opened and read 5 November 2026.
• * Coble, McLin, and Cominsky, Big Ideas in Cosmology, Physics LibreTexts, Section 7.3: Gravity Is a Universal Force, San Francisco State University, Chico State University, and Sonoma State University, with NASA educational material. Newton's law of universal gravitation, F equals G times m1 times m2 divided by r squared; the Moon's orbit radius 384,400 kilometers; surface distance from Earth's center about 6,400 kilometers; Cavendish measured G just before the turn of the 19th century, more than 50 years after Newton's death. Opened and read 5 November 2026.
• * NASA and Sonoma State University Swift Education and Public Outreach, Newton's Law of Gravitation. Two objects with masses m1 and m2 attract each other with a force directly proportional to the product of their masses and inversely proportional to the square of the distance between them; objects near Earth fall at the same rate independent of their masses. Opened and read 5 November 2026 via search result text.
• * University of Illinois, Physics Van, Weight vs. Mass. Mass is a measure of how much matter an object contains; weight is the force gravity exerts on that mass; the Moon's mass is 7.3477 times 10 to the power of 22 kilograms and Earth's mass is 5.9736 times 10 to the power of 24 kilograms. Opened and read 5 November 2026 via search result text.
• * University of California, Santa Barbara, ScienceLine. Earth's mass is 5.9724 times 10 to the power of 24 kilograms and the Moon's mass is 0.07346 times 10 to the power of 24 kilograms; surface gravity on the Moon is 1.62 meters per second squared, or 0.165 of Earth's 9.8 meters per second squared; the Moon has about one eightieth of Earth's mass. Opened and read 5 November 2026 via search result text.
• * University of Virginia, Gravity Fact Sheet, Physics 152, Michael Fowler. The Sun has a mass of 1.99 times 10 to the power of 30 kilograms; Jupiter's mass is 318 times Earth's mass and its surface gravity is 2.54 times Earth's; the Sun's surface gravity is 28 times Earth's. Opened and read 5 November 2026 via search result text.
• * University of Illinois, Geophysical and Astrophysical Constants. Mass of Earth 5.97 times 10 to the power of 24 kilograms; mean surface gravity 9.81 meters per second squared; mass of Moon 7.35 times 10 to the power of 22 kilograms; surface gravity of the Moon 1.62 meters per second squared. Opened and read 5 November 2026 via search result text.