Overview of the Force of Gravity
About 4 min read
(updated 9 February 2022)
Gravity is a force that attracts objects toward the Earth. It is an approximation of the gravitational force that attracts objects of mass toward each other at great distances.
The equation for the force of gravity is F = mg, where g is the acceleration due to gravity. Units can be designated in metric (SI) or English system. The equation also indicates the weight of an object (W = mg).
The major feature of this force is that all objects fall at the same rate, regardless of their mass. Gravity on the Moon and on other planets have different values of the acceleration due to gravity. However, the effects of the force are similar.
Questions you may have include:
- What is the gravity equation?
- What is the most outstanding characteristic of gravity?
- What is gravity elsewhere?
This lesson will answer those questions. Useful tool: Units Conversion
Gravity equation
According to Newton’s Law of Universal Gravitation, gravitation is the force that attracts objects toward each other. For objects relatively close to the Earth, this force is called gravity, and its equation is:
F = mg
where
- F is the force pulling objects toward the Earth
- m is the mass of the object
- g is the acceleration due to gravity; this number is a constant for all masses of matter
- mg is the product of m times g
Acceleration due to gravity
The acceleration due to the force of gravity on Earth is designated by g. Its value is:
g = 9.807 meters per second-squared (m/s2) in the metric or SI system of measurement
g = 32.2 feet per second-squared (ft/s2) in the English system of measurement
In the equation F = mg, you must use the same measurement system for mass, m, as you do for g.
Weight and mass
The weight of an object of a given mass is the force of gravity on that object:
w = mg
where
- w is the weight in newtons (N) or pound-force (lb)
- m is the mass in kilograms or pound-mass (lb-mass)
Weighing an object
You can find the weight of an object on a calibrated scale—usually with a spring resisting the force of the weight.
The mass of an object can be measured with a balance scale, comparing with an object of a given mass.
Objects fall at the same rate
The most outstanding characteristic of gravity is the fact that all objects fall at the same rate—assuming the effect of air resistance is negligible. This is because the acceleration due to gravity, g, is a constant for all objects, no matter what their mass.
This seems counterintuitive, since you would expect a heavy object to fall faster than an object that weighed less. But it is a fact. Try dropping two objects at the same time, from the same height, making sure they are heavy enough not to be affected by air resistance. You will see they hit the ground at the same time.
(See Equivalence Principle of Gravity for more information.)
Gravity elsewhere
When you talk about gravity, you mean gravitation near the Earth. However, the same gravity equation holds for objects near the Moon or other planets, except that the value of g is different. In those cases, you typically tell where the gravity is, such as “gravity on the Moon” or “gravity on Mars.”
Gravity on the Moon
The force of gravity on the Moon is approximately 1/6 of that on the Earth for a given mass. Thus:
Fm = mgm
where
- Fm is the force or weight on the Moon
- m is the mass of an object
- gm is the acceleration due to gravity on the Moon
The value for gm is 1.6 m/s2 or 5.3 ft/s2.
Weight and mass on the Moon
The value for gm is approximately 1/6 of the value for g on Earth. Thus, an object on the Moon would weigh about 1/6 of its weight on Earth.
Using a spring scale, if you weigh 60 kg (132 pounds) on the Earth, you would weigh only 10 kg (22 lbs) on the Moon. However, using a balance scale on both Earth and the Moon, your mass would be the same.
Dropped objects
If you dropped two objects of different weights on the Moon, they would fall to the ground at the same rate. You wouldn’t have to worry about the effect of air resistance, since there is no air on the Moon.
Since gm = g/6, the objects would fall at a slower rate.
(See Gravity Equations for Falling Objects and then apply gm to get the different values.)
Summary
Gravity is the force that pulls objects toward the Earth. It is a special case of gravitation. The equation for the force due to gravity is F = mg, resulting in the fact that all objects fall at the same rate, regardless of their mass. Gravity on the Moon and gravity on other planets have different values of the acceleration due to gravity, but the effects of the force are similar.
Be as great as you can be
Resources and references
Websites
Force of Gravity – Universe Today Magazine
Earth’s gravity – Wikipedia
How does gravity work? – How Stuff Works
Standard gravity – Average value, as compared to variation due to position on Earth – Wikipedia
International Gravity Formula – Variation of gravity with distance from equator – Geophysics dept. University of Oklahoma
I feel ‘lighter’ when up a mountain but am I? – National Physics Laboratory FAQ