Incorporating Inverse Square Law In Gravity

In summary, we discussed the inverse square law and its implications in relation to calculating the force of gravity between two objects. We also looked at an example where the distance between the objects was increased and how it affected the force of gravity. It is important to use consistent units in calculations to ensure accurate results.
  • #1
Leoragon
43
0
First of all, I'm 13 so I might not comprehend the complex vocabulary or symbols others might use. Second, I just joined!

Okay, let's get to it.

I think I know what the inverse square law is: if a number goes up by x, then the other number is the square of x but in the negative side. Right?

I also think that the force of gravity on a 1kg object on the surface of the Earth (from the average radius) is 9,818,373.084 N . Now what if the distance gets increased by 10 metres? In the equation for the force: F=Gm1m2/r2, do you just add 10 to the r? So it would equal 9,787,623.422 N?

1st equation)
F = 9,818,373.084 N
G = 6.673 X 10-11
m1= 1kg
m2= 5.97219 X 1024 (Earth)
r2 = 40,589,641 (63712)

2nd equation)
F = 9,787,623.422 N
G = 6.673 X 10-11
m1 = 1kg
m2 = 5.97219 X 1024 (Earth)
r2 = 40,717,161 (63812)

If so, where does the inverse square law go?

And is this correct?
 
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  • #2
Leoragon said:
First of all, I'm 13 so I might not comprehend the complex vocabulary or symbols others might use. Second, I just joined!

Okay, let's get to it.

I think I know what the inverse square law is: if a number goes up by x, then the other number is the square of x but in the negative side. Right?

I'm not sure what you mean by "in the negative side", so let me try to explain it for you in words.

Suppose I said the magnitude of some force between two objects increases linearly with separation. That means that if I double the distance between the two objects, the force between the two objects doubles. That is, the factor by which the force increased is the same as the factor by which the separation increased.

Now suppose I said that the magnitude of some force between two objects decreases inversely with the separation. This means that if I double the distance between the two objects, the force between the two objects is cut in half. The factor by which the force changed is 1 over the factor by which the separation changed.

Now suppose I said that the magnitude of some force between two objects increases as the square of the separation. Then if I double the separation between the objects, the force between them is quadrupoled (four times): the factor by which the force increases is the square of the factor by which the distance increased.

If we put these three observations together, you can conclude that if the force between two objects follows and inverse square relationship, then if we double the separation between two objects, the force between them is reduced by 1/4: the factor by which the force is decreased is 1 over the factor by which the separation increased.

Does this make it clearer?

I also think that the force of gravity on a 1kg object on the surface of the Earth (from the average radius) is 9,818,373.084 N . Now what if the distance gets increased by 10 metres? In the equation for the force: F=Gm1m2/r2, do you just add 10 to the r? So it would equal 9,787,623.422 N?

1st equation)
F = 9,818,373.084 N
G = 6.673 X 10-11
m1= 1kg
m2= 5.97219 X 1024 (Earth)
r2 = 40,589,641 (63712)

2nd equation)
F = 9,787,623.422 N
G = 6.673 X 10-11
m1 = 1kg
m2 = 5.97219 X 1024 (Earth)
r2 = 40,717,161 (63812)

If so, where does the inverse square law go?

And is this correct?

The calculations look correct. The inverse square law is the 1/r2 part of the equation for the force: F=Gm1m2/r2.

If the force of gravity were inversely proportional to the separation, then the equation would involve 1/r instead of 1/r2.
 
  • #3
Leoragon said:
First of all, I'm 13 so I might not comprehend the complex vocabulary or symbols others might use. Second, I just joined!

Okay, let's get to it.

I think I know what the inverse square law is: if a number goes up by x, then the other number is the square of x but in the negative side. Right?

I also think that the force of gravity on a 1kg object on the surface of the Earth (from the average radius) is 9,818,373.084 N . Now what if the distance gets increased by 10 metres? In the equation for the force: F=Gm1m2/r2, do you just add 10 to the r? So it would equal 9,787,623.422 N?

1st equation)
F = 9,818,373.084 N
G = 6.673 X 10-11
m1= 1kg
m2= 5.97219 X 1024 (Earth)
r2 = 40,589,641 (63712)

2nd equation)
F = 9,787,623.422 N
G = 6.673 X 10-11
m1 = 1kg
m2 = 5.97219 X 1024 (Earth)
r2 = 40,717,161 (63812)

If so, where does the inverse square law go?

And is this correct?

It is a good idea to use (and keep track of) units.
The weight of a 1 kg object on the surface of the Earth is around 9.8 N.
You are off by 6 orders of magnitude. The reason is using the radius in km whereas G is in standard SI units (N*m^2/kg^2).

For the meaning of the inverse square law, Mute has explained it already.
 
  • #4
The same km<->m-issue occurs at the height difference: It is 10m (6371.000 -> 6371.010), not 10km (6371->6381).
 
  • #5


Hi there! First of all, welcome to the scientific community and thank you for your interest in gravity and the inverse square law. You have a good understanding of the concept - the inverse square law states that the force between two objects is inversely proportional to the square of the distance between them. This means that as the distance between two objects increases, the force of gravity between them decreases.

In the equation you have provided, the correct way to incorporate the inverse square law would be to divide the distance (r) by the square of the distance (r^2). So in your first equation, the distance is 40,589,641, and in your second equation, it is 40,717,161. This means that the force of gravity in the second equation would be slightly less than in the first equation, as you have correctly calculated.

So, to answer your question, the inverse square law is already incorporated in the equation by dividing the distance by the square of the distance. And yes, your calculations are correct! Keep up the good work and keep exploring the wonders of science.
 

1. What is the inverse square law in gravity?

The inverse square law in gravity is a mathematical principle that states that the force of gravity between two objects is inversely proportional to the square of the distance between them. This means that as the distance between two objects increases, the force of gravity decreases exponentially.

2. How is the inverse square law applied in gravity?

The inverse square law is applied in gravity by using it to calculate the force of gravity between two objects. This is done by multiplying the masses of the two objects and dividing by the square of the distance between them. This calculation is used to understand the behavior of objects in orbit and other gravitational interactions.

3. Why is the inverse square law important in gravity?

The inverse square law is important in gravity because it helps us understand and predict the behavior of objects in space. It allows us to calculate the force of gravity between two objects and determine the strength of their gravitational pull. This is crucial for understanding the motion of planets, stars, and other celestial bodies.

4. Are there any exceptions to the inverse square law in gravity?

Yes, there are some situations where the inverse square law does not apply in gravity. For example, when an object is very close to the surface of a planet, the law may not hold true due to factors such as air resistance. Additionally, the law may not apply in extreme situations, such as near black holes or in the early stages of the universe.

5. How does the inverse square law in gravity relate to other laws of physics?

The inverse square law in gravity is related to other laws of physics, such as the laws of motion and the law of universal gravitation. It also plays a role in other areas of physics, such as electromagnetism and optics. Understanding the inverse square law is essential for understanding the fundamental principles of the universe and how different forces interact with each other.

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