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I was told that the gravitational constant is the pulling force between two objects in a distance with mass. Though, doesn't that have the same definition as a gravitational force? I know they're different because of the gravitational force formula, I just don't know what.

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The gravitational constant can be thought of as a measure of how strong the gravitational force is. If you plug in the value of mass and the distance between the two objects, you can find out the force of attraction between them, but you need the gravitational constant for this, as this determines the strength of that attraction.

Notice, $F=Gm_1m_2/r^2 $

If you plug in $m_1,m_2,r=1$ , then you get $F=G$. So, the gravitational constant is equal to the force of attraction between two bodies of unit mass, separated by unit distance. Using this definition, we can find the force between two objects with any random mass and a random separation.

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The gravitational constant is a fixed constant determined experimentally. It can be used to compare the general magnitude of gravitational force in comparison to other types of conservative forces. For example, the electrostatic force between two point charges is given by a very similar equation, but a different constant is used (called the coulomb constant) which is much larger than $G$, hence leading to the conclusion that electric forces are much stronger than gravitational forces

It is by no means equal to the gravitational force. In some sources you may find that the gravitational constant $G$ is defined as the gravitational force of attraction between two unit masses separated by a unit radial distance. However, to disprove this, simply notice that $G$ has units of $\frac {N.m^2}{kg^2}$, while any kind of force has units of $N$, and hence an equality between the two is incorrect. It can be thought of as the numeric value of the force of gravity between two unit masses separated by a unit distance, as given by: $$F = \frac {G(1kg)(1kg)}{1m^2} => F = G.\frac {kg^2}{m^2}$$

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In short, gravitational constant G is the magnitude of gravitational force between 2 objects of unit mass and having a unit distance separation between them.

Only for these objects would gravitational force have a magnitude equal to G. For all other cases, you have to calculate using the masses over distance squared formula.

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See, in Newton's theory of gravity, we say that the force is proportional to the product of the masses of the two objects and inversely proportional to the square of the distance between them. We write this as:

$F\propto m_1 m_2/ r^2 $

To make this an equality , we introduce the constant, say B.

So we have $F = B m_1 m_2/ r^2 $

Now what is the value of this constant?

Just find it out. Take a mass of 5 kg and another mass of 5000 kg, keep them say 100 meters apart and somehow find the amount of force they are exerting on each other. Let us say it is 10 Newton. Then, plugging in all the values we have:

$10 $= $\frac{B * 5*5000}{100^2}$

From the above equation, find the value of B. Then in the future equations, just use its numerical value which will not change ( if it changes, it is no more a constant and the law must be wrong).

Let's say you get the value of B as $0.5 $ then the law becomes:

$F = 0.5 m_1 m_2/ r^2 $

Of course all the above explanation is just to make you understand and the values are all random. The letter B is actually G in the original law and has a certain value = $6.67*10^-{11}$ in S.I. units

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