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Why don't people on the "other side" of the earth fall off?
Every object in the universe attracts every other object with a force (gravity) that is proportional to the masses of the objects and inversely proportional to the squared distance between objects. Since the earth is so massive it attracts us (no matter where we stand) with a force strong enough to keep us from falling off. Read on for a more detailed explanation.

Fact 1. Fact 3.

Mass is a measure of how much matter is in an object. On earth, mass and weight are effectively the same thing.¹

Fact 2.
The earth's mass is approximately 6,000,000,000,000,000,000,000,000 kg (13,000,000,000,000,000,000,000,000 lb).² Gravity is an attractive force between any two objects in the universe. The force attracting any two bodies is proportional to the product of their masses and is inversely proportional to the squared distance between them. Below, the gravitational attraction is stronger for the right-most pair of objects because they are more massive and closer together.

The attractive force of gravity acts between the center of two objects. In the case of people standing on the earth's surface, the effect of gravity is to attract us towards the center of the earth. As a result, no matter where you stand on the earth, you don't fall off.

Gravity is also the reason why the moon (and satellites) orbit the earth and why we orbit the sun. But then why doesn't the moon crash into the earth? The moon is, in fact, constantly falling towards earth, it is just that it keeps missing. With an initial motion along the path of the orbit, the moon can continually fall towards earth without ever reaching it. This is illustrated on the right in the above diagram, where a cannon is shown firing a cannonball. If the speed of the cannonball is too slow it will crash into the earth. If the speed is too fast, the cannonball will escape the gravitational attraction of the earth. But, if the speed is just right, then the cannon ball will continually fall towards the earth, but never reach it -- it will orbit the earth.³

¹ An object's weight is a measure of how much gravity is acting on it. An object weighs less on the moon because the moon's mass, and therefore gravitational attraction, is less. An object's mass, however, is the same no matter where it is.
² A typical plane with people, cargo and fuel has a mass of 70,000 kilograms (kg) (154,322 pounds (lb) or 77.16 tons). If we compare the mass of the earth to the distance between the earth and the sun, then the mass of a plane would be approximately the diameter of an atom.
³ Objects will orbit the earth only if they are above earth's atmosphere, where particles in the earth's atmosphere do not slow it down.

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Why don't people on the "other side" of the earth fall off? Every object in the universe attracts every other object with a force (gravity) that is proportional to the masses of the objects and inversely proportional to the squared distance between objects. Since the earth is so massive it attracts us (no matter where we stand) with a force strong enough to keep us from falling off. Read on for a more detailed explanation.
Fact 1.	Fact 3.
Mass is a measure of how much matter is in an object. On earth, mass and weight are effectively the same thing.¹ Fact 2. The earth's mass is approximately 6,000,000,000,000,000,000,000,000 kg (13,000,000,000,000,000,000,000,000 lb).²	Gravity is an attractive force between any two objects in the universe. The force attracting any two bodies is proportional to the product of their masses and is inversely proportional to the squared distance between them. Below, the gravitational attraction is stronger for the right-most pair of objects because they are more massive and closer together.
The attractive force of gravity acts between the center of two objects. In the case of people standing on the earth's surface, the effect of gravity is to attract us towards the center of the earth. As a result, no matter where you stand on the earth, you don't fall off. Gravity is also the reason why the moon (and satellites) orbit the earth and why we orbit the sun. But then why doesn't the moon crash into the earth? The moon is, in fact, constantly falling towards earth, it is just that it keeps missing. With an initial motion along the path of the orbit, the moon can continually fall towards earth without ever reaching it. This is illustrated on the right in the above diagram, where a cannon is shown firing a cannonball. If the speed of the cannonball is too slow it will crash into the earth. If the speed is too fast, the cannonball will escape the gravitational attraction of the earth. But, if the speed is just right, then the cannon ball will continually fall towards the earth, but never reach it -- it will orbit the earth.³
¹ An object's weight is a measure of how much gravity is acting on it. An object weighs less on the moon because the moon's mass, and therefore gravitational attraction, is less. An object's mass, however, is the same no matter where it is. ² A typical plane with people, cargo and fuel has a mass of 70,000 kilograms (kg) (154,322 pounds (lb) or 77.16 tons). If we compare the mass of the earth to the distance between the earth and the sun, then the mass of a plane would be approximately the diameter of an atom. ³ Objects will orbit the earth only if they are above earth's atmosphere, where particles in the earth's atmosphere do not slow it down.