Why is acceleration due to gravity constant?

[Surya97]

Hello, I understand that the gravitational force is given by F=G*M1*M2/d^2, and that if an object is more massive, it feels more gravitational force toward the Earth, but also accelerates less due to F=M*A, which cancels out. My question is not why bodies of different weights fall at the same acceleration.

My question is: When the object gets closer to the Earth's core, shouldn't the force change inversely proportional to the distance, causing the force to increase? If so, then why would the object still accelerate at the same rate toward the Earth's core (the force is increasing, but the object has the same amount of mass)? Thank you in advance.

 

[axmls]

It seems you're asking why we assume a constant 9.8 m/s^2 acceleration regardless of the height (near ground level). This is only an approximation, and a very good one. You're right; the force increases as the objects get closer, but when looking at a small mass compared to the earth, moving closer barely changes the force at all, so it is nice to simplify it by saying the acceleration is constant (near the surface). When you start talking about orbiting satellites and whatnot, this approximation is no longer valid.

 

[Delta2]

In physics very often we do approximations or assumptions that are not 100% true , but they simplify the calculations a lot. But you must know to do the proper approximations (depending on the problem we must do the proper approximations) in order your final result or final conclusion to be mostly valid (yet it can't be 100% valid).

 

[Drakkith]

My question is: When the object gets closer to the Earth's core, shouldn't the force change inversely proportional to the distance, causing the force to increase? If so, then why would the object still accelerate at the same rate toward the Earth's core (the force is increasing, but the object has the same amount of mass)?

The general formula for the gravitational force between two objects is F=GMm/r², where M and m are the masses of the two objects, G is the gravitational constant, and r is the distance between the two centers of mass. You can see that because r is in the denominator, the force increases as the two objects get closer. However, because the distances we deal with here in our everyday lives on the surface of the Earth, the distance usually only changes by perhaps a few hundred to a few thousand feet. Since the Earth's radius is about 4,000 miles, a change of even a few thousand feet only changes the force of gravity by a very small amount. Here where I live, we are about 2400 feet above sea level. This increase in altitude of 2400 feet only changes the acceleration of an object by about 0.1 m/s², putting us at around 9.7 m/s² instead of 9.81 m/s². This is a change of around 1%.

 

[Surya97]

Oh, so it does change the acceleration, just by a marginal amount in "normal" situations, so it doesn't matter as much in our everyday lives. Thanks!

 

[ZapperZ]

https://www.physicsforums.com/insights/why-is-acceleration-due-to-gravity-a-constant/

Zz.