# Acceleration due to gravity 1

## Acceleration g

And for the sake of this, we're going to assume that the distance between the body, if we're at the the surface of the Earth, the distance between that and the center of the Earth is just going to be the radius of the Earth. It's going to be this mass right over here. But if you want the acceleration, we just have to remember that force is equal to mass times acceleration. Even on the surface of the Earth, there are local variations in the value of the acceleration of gravity g. Use the Gravitational Fields widget below to investigate how location affects the value of g. And so the magnitude of our acceleration due to gravity using Newton's universal law of gravitation is just going to be this expression right over here. So force divided by mass is equal to acceleration. This EE button means, literally, times 10 to the negative If you just multiply this by 1, Because now we're placing the center of mass of our object-- whether it's a space station or someone sitting in the space station, they're going to be kilometers higher. Now it's times 10 to the sixth. Use the Value of g widget below to look up the acceleration of gravity on other planets. So you divide this by meters squared. So during the free fall, the only force acting on the object is the gravitational force of the earth. So let's get my calculator out.

So this will be in the case of Earth. So we're adding kilometers. This is-- 1, 2, 3, 4, 5, 10 to the sixth meters. But there's other minor, minor effects, irregularities. This is a scalar quantity right over here. It's going to be the gravitational constant times the mass of the Earth divided by the distance between the object's center of mass and the center of the mass of the Earth.

### Acceleration due to gravity 1

The kilograms cancel out with these kilograms. To accelerate at 9. And this will give us the magnitude of the acceleration on that mass due to gravity. And this is a misconception. And in this case, it is the other mass. Like, for example, the acceleration due to gravity on the moon is different from that of the earth. There are slight variations in this numerical value to the second decimal place that are dependent primarily upon on altitude. But if you want the acceleration, we just have to remember that force is equal to mass times acceleration. But it's moving so fast that it keeps missing the Earth. And I just want to make sure that everything is the same units. If the velocity and time for a free-falling object being dropped from a position of rest were tabulated, then one would note the following pattern. It is the same thing as 6,, meters. And so you might say, well, what's going on here? And then I want to multiply that times the mass of Earth, which is right over here. Because if you multiply it by a mass, it tells you how much force is pulling on that mass.

And this is a misconception. So there's an important thing to realize.

## Acceleration due to gravity value

So 6, kilometers-- actually, let me scroll over. So if you want the acceleration due to gravity, you divide. And that tells us that the force of gravity between two objects-- and let's just talk about the magnitude of the force of gravity between two objects-- is equal to the universal gravitational constant times the mass of one of the bodies, M1, times the mass of the second body divided by the distance between the center of masses of the bodies squared. So then we get 6. And then think about how it changes as we get further and further away from the surface of the Earth. The numerical value for the acceleration of gravity is most accurately known as 9. If the velocity and time for a free-falling object being dropped from a position of rest were tabulated, then one would note the following pattern. I just wrote Earth really, really small. And if you wanted to solve for acceleration you just divide both sides times mass. So let's divide both sides by that mass. So this is just the magnitude of the acceleration.

And then what I want to do is figure out, well, one, I want to compare it to the value that the textbooks give us and see, maybe, why it may or may not be different.

Read the Concept of Acceleration here for better understanding of this topic. It is 6. Use the Value of g widget below to look up the acceleration of gravity on other planets. You multiply that times the mass of the Earth, which is in kilograms. Now let the ball come down on its own. Now, with that out of the way, what I'm curious about is what is the acceleration due to gravity if we go up kilometers?

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