# The Law of Universal Gravitation: Definition, Importance & Examples Video

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• 0:02 Newton's Apple
• 1:39 Gravity Gets Weaker…
• 3:43 Gravity is Everywhere
• 5:00 Lesson Summary
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Lesson Transcript
Instructor: Sarah Friedl

Sarah has two Master's, one in Zoology and one in GIS, a Bachelor's in Biology, and has taught college level Physical Science and Biology.

Gravity is what pulls us toward Earth, but it's also what pulls Earth toward us. This is explained by the law of universal gravitation, which describes how all objects in the universe have this important force between them.

## Newton's Apple

You've probably heard this story before: one day Isaac Newton was sitting under an apple tree when one of the apples fell from the tree and hit him on the head. This fortunate event was what led Newton to discover gravity, and the rest is history!

We don't know the exact events leading to Newton's discovery of gravity or if he ever even sat under that tree. What we do know is that Newton really was a smart guy who was able to reason WHY an apple would fall from a tree to the ground. Newton understood that objects pull on each other - the earth pulls the apple to the ground, but the apple also pulls back on the Earth.

The most important part about this is not only that objects pull on each other, but that two objects attract each other with a force that is proportional to the product of their masses and inversely proportional to the square of the distance between them. This is known as Newton's law of universal gravitation. What this means is that for any two objects in the universe, the gravity between these two objects depends only on their mass and distance.

We can also express this relationship in equation form: F = G * (m1*m2) /d^2, where F is the gravitational force, G is the universal gravitational constant 6.67 x 10^-11 Nm^2/kg^2, m is the mass of each object, and d is the distance between their centers.

## Gravity Gets Weaker with Distance

The distance between two objects is an important component of the law of universal gravitation. It's not just how far away the objects are from each other, it's the SQUARE of that distance. So, for example, if two objects are 3 kilometers away from each other, you can't just divide by 3 to get the gravitational force - you have to divide by 3 x 3, which is 9.

And if the objects are 9 kilometers away from each other you have to divide by 81. So, even though the objects are only 3 times as far from each other, the force is actually going to be 9 times weaker - that's a big difference!

This idea of an exponential decrease describes the inverse-square law. As you just saw, increasing the distance only a small amount decreases the force by a large amount, because the square of the distance is inversely proportional to the force.

It might help to think about this concept with a can of spray paint and a wall. The paint can will spray paint out in all directions from the nozzle, not just in a straight line, right? So, let's say you have your can of paint and you stand very close to the wall - only 1 meter away. When you spray the wall your paint covers a certain area; let's call it one unit.

If you move away from the wall to a distance of 2 meters, the paint you spray toward the wall will cover a larger area but with the same amount of paint as before. The area you cover is not twice as big - it's four times as big because your can sprays paint in all directions - the area is both twice as tall and twice as wide as before. If you step back yet again, this time to a distance of 3 meters, the area your paint covers is now 9 units because it is BOTH three times as tall and three times as wide as your original unit of area. Remember, you're still spraying the same amount of paint but over a larger area, so, the paint is 'weaker' all around.

## Gravity Is Everywhere

You may have heard that there is no gravity in outer space. Well, I hate to be the one to do this, but I am going to bust that myth right now! Gravity is EVERYWHERE! It's just that when it becomes weak enough it may feel like there's no gravity anymore.

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