# Weight

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Weight is a property of objects in a gravitational field. The weight of an object is the force exerted on it by the gravitational field, usually one caused by a single very large (planet-sized or larger) object.

Newton's Law of gravitation gives the force f exerted by gravity as:

${\displaystyle f=G\,{\frac {M_{\mathrm {1} }M_{\mathrm {2} }}{R_{\mathrm {E} }^{2}}}}$

Force is equal to mass multiplied by acceleration, and thus the weight of an object is equal to its mass multiplied by the acceleration it experiences due to the gravitational attraction of the nearby larger object. This acceleration is given as:

${\displaystyle a=G\,{\frac {M}{R^{2}}}}$ (where R is the distance from the center of mass of the larger object)

On the surface of Earth, the weight of an object is approximately equal to its mass multiplied by 9.8 m s−2, with minor local variations due to the irregularity of the earth's surface. On other planets, the weight of an object of a given mass will be different than its weight on earth, and thus moving the object will require different amounts of force. Most sources of force are not dependent on their weight, and so most actions will have different results in different gravitational fields. The classic example of this is to consider a person jumping on different planets. Due to the different gravitational fields of the different planets, the person's weight will be different, but the force produced by his muscles will be essentially the same, as the force is produced by a chemical reaction. Therefore, a person can jump significantly higher in a weaker gravitational field, such as occurs on earth's moon, but will be unable to jump as high in a stronger gravitational field, such as occurs on Jupiter.

## Units

In SI units, weight is measured in units of force, the newton and its derivatives. In U.S. customary units, weight is measured in pounds-force and other units which are fractions or multiples of the pound. One pound-force is the weight of 0.453 592 37 kg subject to a standard gravity of 9.80665 m s−2, or approximately 4.448 N.

Note that the pound, without the "-force" qualifier, is considered a unit of mass.

## Apparent Weight

Objects that are either in a downward vertical freefall or in an orbit around a planet such as Earth are often referred to as being "weightless," or as "experiencing weightlessness." However, this is a misnomer. As mentioned earlier, weight is the force exerted on an object by a gravitational field, and this force is certainly present in order for objects to either pick up speed as they fall vertically, or maintain an orbit rather than travel in a straight line away from the planet. However, for a person falling or orbiting, these situations feel no different than floating in space far away from any planet or other source of gravity.

To characterize these situations more accurately, we can instead say that a person or object's apparent weight is zero. In this context, apparent weight is the reading one would get from a scale located under the person or object. Apparent weight can be zero, equal to the true weight, less than (but nonzero) the true weight, or greater than the true weight. The following examples illustrate each of these possibilities.

• As mentioned already, a person or object in vertical freefall or in orbit around a planet has zero apparent weight. A scale under the person or object would have a reading of zero.
• A person or object standing at rest on the ground has an apparent weight equal to their true weight. A scale under the person would indicate the person's weight, and is in fact how weight is typically measured.
• A person on an elevator that has a downward acceleration has an apparent weight that is less than their true weight. Note that a downward acceleration is not the same as a downward motion, and occurs for either (1) an object moving upward while slowing down, or (2) an object moving downward while speeding up. In either case, the person would feel lighter than normal, and a scale under the person would have a reading that is less than their true weight.
• A person on an elevator that has an upward acceleration has an apparent weight that is more than their true weight. Note that an upward acceleration is not the same as an upward motion, and occurs for either (1) an object moving upward while speeding up, or (2) an object moving downward while slowing down. In either case, the person would feel heavier than normal, and a scale under the person would have a reading that is more than their true weight.