How to Find the Force of Gravity in Physics

Gravity is one of the fundamental forces of physics. The most important aspect of gravity is that it is universal: all objects have a gravitational force that attracts other objects to them. The force of gravity acting on any object is dependent upon the masses of both objects and the distance between them. So, how do you determine the gravitational force of an object? Keep reading to learn how to solve problems with the $Fgrav=(Gm1m2)/d$ equation.

What is the formula for force of gravity?

The formula for gravity is $Fgrav=(Gm1m2)/d$ , where G is the gravitational constant, m1 and m2 are the masses of the objects, and d is the distance between the objects.

Section 1 of 5:

What is the equation for gravity?

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The equation to find the source of gravity is $Fgrav=(Gm1m2)/d$ . When determining the force of gravity between two objects, use the equation $Fgrav=(Gm1m2)/d$ . ^{[1]
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Research source} This equation takes into account the masses of both objects and how far apart the objects are from each other. The variables are defined below: ^{[2]
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- Fgrav is the force due to gravity, measured in Newtons (N)
- G is the universal gravitation constant 6.673 x 10 Nm/kg
- m1 is the mass of the first object
- m2 is the mass of the second object
- d is the distance between the centers of two objects
  - Sometimes you will see the letter r used instead of the letter d . Both symbols represent the distance between the two objects.

Section 2 of 5:

Calculating the Force of Gravity Between Two Objects

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1
Determine the variables of the equation. Depending on the problem, you may be given all but one or two variables. Plug the given variables into your equation and notice what you’re attempting to solve or find. Here’s a refresher of the gravitational force equation and its variables: ^{[3]
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- Equation: $Fgrav=(Gm1m2)/d$
- Fgrav is the force due to gravity, measured in Newtons (N)
- G is the universal gravitation constant 6.673 x 10 Nm/kg
- m1 is the mass of the first object
- m2 is the mass of the second object
- d * or r*** is the distance between the centers of two objects
2
Use metric units for each variable in the equation. For this particular equation, you must use metric units. The masses of objects need to be in kilograms (kg), and the distances need to be in meters (m). If your variables are not already in metric units, convert them before solving the equation.
- Stuck on how to convert your measurements? Try using a conversion calculator online.
If you’re not given the masses of the objects for the equation within a problem, you may need to find them yourself. For smaller objects, you can weigh them on a scale or balance to determine their weight in grams. For larger objects, you may have to look up the approximate mass online. But, most likely, the mass of the objects will be provided to you. ^{[4]
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4
Measure the distance between the two objects. For some problems, you may be asked to do some extra math to reveal the distance between the two objects. The most common example of this is a problem calculating the force of gravity between an object and Earth. In this example, you would need to determine how far away the object is from the center of the Earth. ^{[5]
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- The distance from the surface of the Earth to the center is approximately 6.38 x 10 m.
- You can find resources online with approximate distances from the center of the Earth to objects at various elevations on the surface—just do a quick online search if the information isn’t provided.
5
Plug your variables into the equation to solve. Once you have defined the variables of your equation, you can work on solving the equation. Use the proper order of operations , and be sure that all of your units are in metric units. ^{[6]
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Research source} Here’s an example problem:
- The problem: Determine the force of gravity on a 68 kg person on the surface of the Earth. The mass of the Earth is 5.98 x 10 kg.
  - Make sure all your variables have the proper units. m1 = 5.98 x 10 kg, m2 = 68 kg, G = 6.673 x 10 Nm/kg, and d = 6.38 x 10 m
- Write your equation: $Fgrav=(Gm1m2)/d''=[(6.67x10)x68x(5.98x10)]/(6.38x10)$
  - Multiply the masses of the two objects together. 68 x (5.98 x 10) = 4.06 x 10
  - Multiply the product of m1 and m2 by the gravitational constant G . (4.06 x 10) x (6.67 x 10) = 2.708 x 10
  - Square the distance between the two objects. (6.38 x 10) = 4.07 x 10
  - Divide the product of G x m1 x m2 by the distance squared to find the force of gravity in Newtons (N). 2.708 x 10/4.07 x 10 = 665 N
- The answer: The force of gravity is 665 N.
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Sean Alexander, MS
Academic Tutor
Sean Alexander is an Academic Tutor specializing in teaching mathematics and physics. Sean is the Owner of Alexander Tutoring, an academic tutoring business that provides personalized studying sessions focused on mathematics and physics. With over 15 years of experience, Sean has worked as a physics and math instructor and tutor for Stanford University, San Francisco State University, and Stanbridge Academy. He holds a BS in Physics from the University of California, Santa Barbara and an MS in Theoretical Physics from San Francisco State University.

Sean Alexander, MS
Academic Tutor

If you come across a harder problem, take your time. Physics can be difficult to understand. If you’re having a hard time figuring out the concept or problem, take a deep breath. Try to approach the problem from a different angle, or take a break and come back to it later.
6
Use the equation $Fgrav=mg$ to calculate an estimated force of gravity. As academic tutor Sean Alexander explains, on Earth, the force of gravity causes objects to accelerate at a rate of 9.8 m/s. If you’re calculating the gravitational force of an object on Earth, you can simplify the lengthy $Fgrav=(GMearthm)/d$ to $Fgrav=mg$ . ^{[7]
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- If you want a more exact approximation of force, you can still use the equation $Fgrav=(GMearthm)/d$ .
- Be sure your variables are in metric units (kilograms and meters) before trying to solve.
7
Solve the equation $Fgrav=mg$ to determine the gravitational force on Earth. Once you have defined the variables of your equation, you can plug them in and solve. Be sure that all of your units are in metric, and you’re using the proper order of operations to solve. ^{[8]
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Research source} Let’s use the same equation from above and see how close the approximation is:
- The problem: Determine the force of gravity on a 68 kg person on the surface of the earth.
- Convert the variables to the proper units: m = 68 kg, g = 9.8 m/s.
- Write the equation: Fgrav = mg = 68*9.8 = 666 N.
- The answer: With F = mg, the force of gravity is 666 N, while using the more exact equation yields a force of 665 N. As you can see, these values are almost identical.

Section 3 of 5:

What is the formula for Newton’s Second Law of Gravity?

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The formula for the Second Law of gravity is F = ma . Newton’s Second Law of Motion states that any object will accelerate when acted upon by a net or unbalanced force. In other words, if a force is acting upon an object that’s greater than the forces acting in the opposite direction, the object will accelerate in the direction of the larger force. This law can be summed up with the equation F = ma , where F is the force, m is the mass of the object, and a is the acceleration. ^{[9]
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- Using this law, we can calculate the gravitational force of any object on the Earth's surface, given the known acceleration due to gravity.

Section 4 of 5:

Example Problems

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1

How much force does it take to hold an apple with a mass of 0.1 kg on Earth?

F = mg
F = 0.1 x 9.8
F = 0.98 N ^{[10]
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2

A man hits a gold ball (0.2 kg), which accelerates at a rate of 20 m/s². What amount of force acted on the ball?

F = ma
F = 0.2 x 20
F = 4 N ^{[11]
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Section 5 of 5:

FAQs

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1

Is 9.8 the force of gravity? Yes, the exact value of g , or the force of gravity, is 9.80665 m/s², which is usually rounded to 9.8 m/s². This is the average value of the gravitational force on Earth. ^{[12]
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Research source} This number is typically used in most physics problems as the value of g , unless otherwise stated.
2
What is Newton’s Law of Gravity? Sir Isaac Newton’s Law of Gravity (also known as the Law of Universal Gravitation) states that every particle attracts every other particle in the universe, creating a proportional force. In other words, gravity is the reason objects fall or stay in place. ^{[13]
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- Fun facts: Heavier objects have a stronger force of gravity between them, and objects that are close to each other have more gravity between them.
3

What is the constant force of gravity? In the gravity equation, the constant force of gravity is represented by the variable G or g— the universal gravitational constant. ^{[14]
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Research source} On Earth, the gravitational constant is 9.8 m/s². ^{[15]
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4
What is the gravitational force between the Earth and the Moon? The gravitational force between the Earth and the Moon is 1.988 x 1020 N. How did we come to this conclusion? Check out the work below: ^{[16]
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- Equation: Fgrav = (Gm1m2)/d
- G = 6.673 x 10 Nm/kg
- m1 = 5.98 x 1024 kg (the mass of the Earth)
- m2 = 7.35 x 1022 kg (the mass of the Moon)
- d = 3.84 x 108 m (the distance between the Earth and the Moon)
- Plug the variables into the equation.
- F = 1.988 x 1020 N

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How do I find the mass of the moon?

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Check out same steps as mentioned below. But remember gravity on moon is 1/6th of gravity on earth.

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A mass of 25 kg weighs 123 Newtons on another planet. What is the gravity on the planet?

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The "gravity" on the surface of a planet is it's acceleration (the rate of increase in speed as an object falls). Fg (the force of gravity) is m x g (acceleration of gravity), in m/(s squared), so g is Fg / m = 123 N / 25 kg ~= 4.92 m/(s squared).

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How do I find the value of acceleration due to a gravity at a height of 2R from the surface of the earth?

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If you want to know what the gravity would be when you are 3 earth-radii away from the center of earth, then the gravity would be 1/9th normal gravity. You're multiplying by 3 on the bottom, so 1/3, but then it's squared. Acceleration would then be 1.09 meters per second squared.

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How to Find the Force of Gravity in Physics

What is the formula for force of gravity?

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What is the equation for gravity?

Calculating the Force of Gravity Between Two Objects

What is the formula for Newton’s Second Law of Gravity?

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