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F=GMm/r^2 (Gravity Formula): The 5 Things You Need To Know

f=gmm/r^2 gravity formula featured image

If you’re seeing it for the first time, the F=GMm/r^2 gravity formula can be a bit of a funky equation.

But get a few key concepts down and it’ll seem clear as day.

Here are the 5 things you need to know.

Anyone who listens to John Mayer, knows he’s fond of saying,

“Gravity, is workin’ against me”

Unfortunately for most beginning physics students this is true – gravity is this mysterious “g” term that we throw into our equations, and know has to do something with apples and the Earth, but that’s about it.

Well today I’m suggesting we buck the system, and get the concept of gravity down first – before learning anything about projectiles, roller coasters, or inclined planes.

Most physics courses de-emphasize a deep understanding of gravity, leaving it until later in the semester. But building a strong foundation with the concept of gravity can turn it around for you, so that gravity works “for you” when the professor starts throwing around “g”s in lecture, and when solving homework and test problems for the rest of the term.

Overall, there are 4 fundamentals ideas associated with gravity, and 1 main application of gravity, found in Classical Mechanics (Physics 101) courses.

(1) Any two objects that have a mass attract each other.

As simple as it sounds. All objects with mass (measured in kilograms) are pulled towards each other at all times.

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The direction of pull for one mass is always the direct 180-degree opposite of the other.

(2) The larger the mass of each object, the stronger the attraction.

And the size of the attractive force is directly proportional to the mass of both objects.

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If either mass gets bigger, the force pulling them together gets bigger by the same amount.

(3) The closer the two objects are, the stronger the attraction.

This attractive force increases towards infinity as the objects get really close together.

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That means the attraction between the objects gets big really fast the closer the objects get.

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(4) And all this attraction occurs from the center of mass of each of the objects.

You’ll learn more about center of mass later.

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For now, just think of the center of mass as the center of the object – i.e. the “average” location of the object’s mass.

So that’s it. Those are the 4 fundamentals of gravity.

Check them out in action:

What would happen if I placed the Sun and the Earth randomly in space…

Notice the relative movement of the two objects. The Sun is much more massive, but still is pulled towards the earth.

(Note: I gave the Earth a little initial push so it would miss the Sun. If they both started stationary they would be pulled straight towards each other and crash together.)

Also notice how friggin’ fast the objects move when they are really close to each other. That’s the exponential increase in force in action as they get closer.

(5) The #1 Application of Gravity in Mechanics

Now, the key application of the principles of gravity in the majority of Mechanics problems is:

An object on Earth’s surface is attracted to the Earth at approximately the same value anywhere on the Earth’s surface, and it’s always framed as “downward.”


Because the distance to the center of the earth is

~ 6,371,000 meters,

whereas the distance to the center of an object like a person is ~3 meters.

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Because of this size discrepancy, the Earth seems flat from your perspective on the surface. And from this vantage point, it seems as though the gravitational force on you is pulling “down.”

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But in reality this force due to gravity is pulling you down towards the Earth’s center in the same way that there is a force pulling “up” on Earth due to your mass.

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Get this down – it’s a cornerstone of at least 50% of problems in mechanics.

The Gravity Formula

Now, there is a formula that describes this behavior:

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Don’t freak out…

These are just symbols that represent the 4 fundamental ideas we discussed earlier.

Each component of the equation is broken down as follows:

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To summarize everything we’ve talked about here, click below for an infographic that overlays each of the formula components on top of the diagrams we just discussed, including a bonus: where the “little g” comes from in all the equations you’ll encounter.

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The payoff??

Now you’ll have the basis to solve:

Projectile problems

(Photo: Zátonyi Sándor)

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Energy problems

(Photo: Rice University)

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and Rotation problems

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And get a leg up on everyone else still wondering where “g” comes from.

Featured image credit: Beth Scupham

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