What is the magnitude of the gravitational force between the earth and a 2kg object?

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by Ron Kurtus

You can find the gravitational force between two objects by applying the Universal Gravitation Equation, provided you know the mass of each object and their separation.

With this equation, you can make calculations to determine such things as the force between the Earth and the Moon, as well as between two large masses.

Questions you may have include:

• What is the Universal Gravitational Equation?
• What is the force of attraction between the Earth and the Moon?
• What is the force of attraction between two other objects?

This lesson will answer those questions. Useful tool: Units Conversion

The Universal Gravitation Equation is:

F = GMm/R2

where

• F is the force of attraction between two objects in newtons (N)
• G is the Universal Gravitational Constant = 6.674*10−11 N-m2/kg2
• M and m are the masses of the two objects in kilograms (kg)
• R is the separation in meters (m) between the objects, as measured from their centers of mass

Force attracting Earth and Moon

To calculate the gravitational force pulling the Earth and Moon together, you need to know their separation and the mass of each object.

Distance

The Earth and Moon are approximately an average of 3.844*105 kilometers apart, center to center.

(Note that the orbit of the Moon around the Earth is not a true circle, so an average separation is used. This also means that the force of attraction varies.)

Since the units of G are in N-m2/kg2, you need to convert the units of R to meters.

R = 3.844*108 m

Mass of each object

Let M be the mass of the Earth and m the mass of the Moon.

M = 5.974*1024 kg

m = 7.349*1022 kg

Force of attraction

Thus, the force of attraction between the Earth and Moon is:

F = GMm/R2

F = (6.674*10−11 N-m2/kg2)(5.974*1024 kg)(7.349*1022 kg)/(3.844*108 m)2

F = (2.930*1037 N-m2)/(1.478*1017 m2)

F = 1.982*1020 N

Note: Notice how all the units, except N, canceled out.

Attraction between Earth and Moon

Result of force

This considerable force is what holds the Moon in orbit around the Earth and prevents it from flying off into space. Inward force of gravitation equals the outward centrifugal force from the motion of the Moon.

(See Circular Planetary Orbits for more information.)

Also, the gravitational force from the Moon pulls the oceans toward it, causing the rising and falling tides, according to the Moon's position.

(See Gravitation Causes Tides on Earth for more information.)

Force attracting large objects

In the same manner, you can calculate the gravitational force attracting two large objects.

Suppose you had an object with mass of 100 kg, another with a mass of 200 kg, and the separation of their centers was 2 meters.

F = GMm/R2

F = (6.674*10−11 N-m2/kg2)(100 kg)(200 kg)/(2 m)2

F = 33370*10−11 N

Simplify:

F = 3.3*10−7 N

That is a very small force attracting the objects together. However, even a smaller force was measured in the Cavendish Experiment to Measure Gravitational Constant.

Summary

You can apply the Universal Gravitation Equation to show the force of attraction between two objects, such as the force between the Earth and the Moon, as well as between two large masses.

Think clearly and logically

Resources and references

Ron Kurtus' Credentials

Websites

Converting units of mass to equivalent forces on Earth - Wikipedia

Weight -

Mass -

Kilogram -

Mass and Weight: the Gravity Force - Engineering Toolbox

Gravitation Resources

Books

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Top-rated books on Gravity

Top-rated books on Gravitation

Questions and comments

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Gravitation topics

This gravitational force calculator lets you find the force between any two objects. Read on to get a better understanding of the gravitational force definition and to learn how to apply the gravity formula. Make sure to check out the escape velocity calculator, too!

Newton's law of universal gravitation states that everybody of nonzero mass attracts every other object in the universe. This attractive force is called gravity. It exists between all objects, even though it may seem ridiculous. For example, while you read these words, a tiny force arises between you and the computer screen. This force is too small to cause any visible effect, but if you apply the principle of gravitational force to planets or stars, its effects will begin to show.

One of the most common examples illustrating the principle of the gravitational force is the free fall.

Use the following formula to calculate the gravitational force between any two objects:

where:

• F stands for gravitational force. It is measured in newtons and is always positive. It means that two objects of a certain mass always attract (and never repel) each other;
• M and m are the masses of two objects in question;
• R is the distance between the centers of these two objects; and
• G is the gravitational constant. It is equal to 6.674×10-11 N·m²/kg².

Did you notice that this equation is similar to the formula in Coulomb's law? While Newton's law of gravity deals with masses, Coulomb's law describes the attractive or repulsive force between electric charges.

1. Find out the mass of the first object. Let's choose Earth - its mass is equal to 5.972×1024 kg. You can enter this large number into the calculator by typing 5.972e24.
2. Find out the mass of the second object. Let's choose the Sun - it weighs 1.989×1030 kg, approximately the same as 330,000 Earths.
3. Determine the distance between two objects. We will choose the distance from Earth to Sun - about 149,600,000 km.
4. Enter all of these values into the gravitational force calculator. It will use the gravity equation to find the force.
5. You can now read the result. For example, the force between Earth and Sun is as high as 3.54×1022 N.

What is the magnitude of the gravitational force between the earth and a 1 kg object on its surface? Mass of the earth is 6 × 1024 kg and radius of the earth is 6.4 × 106 m

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From the universal law of gravitation, the magnitude of the gravitational force (F) between the earth and the body is given by,

$F=G\frac{M\times m}{R^2}$

where $G=6.67\times {10}^{-11}N{m}^2/k{g}^2$ is the universal gravitational constant.

Hence, magnitude of the gravitational force (F) between the earth and the body is given by,

$F=G\frac{M\times m}{R^2}=\frac{6.67\times {10}^{-11}\times 6\times {10}^{24}\times 1}{(6.4\times {10}^6{)}^2}$ = 9.77 N = 9.8 N (approx).