How does one exactly calculate gravity? How to portray a visual?

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Discussion Overview

The discussion centers around the calculation of gravitational force using the formula F=G((m1)(m2))/d^2 and how to visually represent this equation. Participants explore various methods for creating visualizations, considering both the mathematical and conceptual aspects of gravity.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • Some participants reiterate the gravitational formula and express interest in visualizing it.
  • One suggestion involves creating a graph with force on the vertical axis and distance on the horizontal axis, assuming constant masses.
  • Another proposal includes a graph with force versus the product of the masses while keeping distance constant.
  • A three-dimensional graph is suggested, with force on the z-axis, distance on the x-axis, and mass product on the y-axis.
  • Participants mention the possibility of plotting gravitational potential energy against distance.
  • One participant points out that searching online can yield various visual resources, though they caution that some may be misleading, particularly those related to general relativity rather than Newtonian gravity.
  • There is a clarification that the formula applies specifically to point or spherical masses and that different geometries would require different equations.
  • A request is made for actual drawings or images to aid in understanding the visual representation.

Areas of Agreement / Disagreement

Participants generally agree on the need for visual representations of the gravitational formula, but there are differing views on the best methods to achieve this and the appropriateness of certain visual analogies. The discussion remains unresolved regarding the most effective visualization techniques.

Contextual Notes

Some limitations are noted, such as the specific applicability of the gravitational formula to spherical or point masses and the potential for confusion with visualizations from general relativity.

infinite.curve
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I know of the equation F=G((m1)(m2))/d^2.

So the distance between two masses are squared then divided out of the out come of the masses times the gravitational constant.

My question: how to make a visual representation of this formula?
 
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infinite.curve said:
I know of the equation F=G((m1)(m2))/d^2.

So the distance between two masses are squared then divided out of the out come of the masses times the gravitational constant.

My question: how to make a visual representation of this formula?

It somewhat depends on what you want to show with your visual representation.

One way would be to draw a graph with the force between the two objects on the vertical axis and the distance between them on the horizontal axis, assuming the masses are constant.

Another way would be to draw a graph with the force between them on the vertical axis and the product of the two masses on the horizontal axis, assuming that the distance between them is constant.

Another way would be to draw a three-dimensional graph with the force between the objects on the z-axis, the distance between them on the x-axis, and the product of the masses on the y-axis.

And yet another way would be to draw a graph with the gravitational potential energy on the vertical axis and the distance between them on the horizontal axis.

There are more possibilities, but these between them cover most of the interesting visual representations.
 
infinite.curve said:
I know of the equation F=G((m1)(m2))/d^2.

So the distance between two masses are squared then divided out of the out come of the masses times the gravitational constant.

My question: how to make a visual representation of this formula?

Google is your friend: Using the search terms "visualization of gravity" hundreds of U-tubes, images, and articles appear. Just try it.
 
infinite.curve said:
My question: how to make a visual representation of this formula?
As Nugatory suggested making a graph of the force as a function of some of variables is the most useful way to visualize a formula. A vector diagram can be also useful but you usually can't get all of the info in the formula using one.

Bobbywhy said:
Google is your friend: Using the search terms "visualization of gravity" hundreds of U-tubes, images, and articles appear. Just try it.
In this case this is kind of a bad advice since what you get, is a bunch a of videos,pictures and animations of the pretty misleading rubber membrane analogy model from GR. The OP asks about the visualization of the Newtonian formula.
 
All the responses are ever much appreciated.

Can anyone actually draw it and clip on a picture?

I get the idea, but want to be certain of what I am picturing.
 
infinite.curve said:
I know of the equation F=G((m1)(m2))/d^2.

So the distance between two masses are squared then divided out of the out come of the masses times the gravitational constant.

This isn't the equation for any two masses. This is for two spherical or point masses. The equation between a rod and a sphere would be different. You can get creative with different geometries.

As others have said, you can plot the force as a function of separation distance.
 
Mmm_Pasta said:
This isn't the equation for any two masses. This is for two spherical or point masses. The equation between a rod and a sphere would be different.

Yes, that is true. So what would be the equation for a rod and a circle?

In regards of how to make a visual representation, I got it. Thank you.
 

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