New Formulas for Understanding the Universal Gravitational Constant, G

  • Thread starter JMartin
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In summary, the posting discusses formulas derived from a premise that the universal gravitational constant, G, means that the universe is growing at a constant rate for each kg of mass in the universe. The formula for determining the density at a specific age is given, with the note that mass cancels out. The formula for determining z at a specific age is also provided, along with a simpler formula for determining Ho. However, the conversation also raises questions and concerns about the validity of the premise and the complexity of the topic.
  • #1
JMartin
This posting provides some formulas I derived based on a premise that might seem ridiculous to some people, yet many of the calculated values based on that premise are in line with popular thinking.

The premise is that besides other things, the universal gravitational constant, G, (= 6.67E-11m^3/kg/s^2) means that the universe is growing by 6.67E-11 m^3 per second per second for each kg of mass in the universe. Although it is logical that G can be interpreted that way, it does not mean that mass is responsible for expansion of the universe, merely that it is somehow related. Obviously, the first place that one would look for such a relationship is with gravity, for example, a gravitational law that provides a repelling force for masses that are further apart than a certain distance.

Using the stated premise, one can determine the density of the universe at a specific age with the following formula:

Density = 2 X mass / mass X age of universe^2 X G

Notice that mass cancels out, so it is not necessary to supply it to use the formula.

Since density changes with the expansion of the universe, one can use it to determine z at a specific age of the universe in accordance with the basic premise. That can be done by finding the cube root of the quotient of the density of the universe at the desired age divided by the present density (using an assumed age) and then subtracting 1. However, cancellations allow the following formula to be used:

z = ((present age in seconds ^2 / desired age in seconds ^2) ^ 1/3) -1

Ho for any specific time can also be determined by multiplying the density at that time by the volume of a sphere having a radius of one Mpc to yield the mass contained within that sphere. Consecutively multiplying that mass by G and the age of the universe yields the volume of expansion of the sphere per time. By dividing that volume by the surface area of the sphere, one obtains Ho for 1 Mpc. The formulas is:

Ho = density X volume of 1 Mpc sphere X G X age of the universe / sphere surface area

However, cancellations allow Ho to be obtained by using the following very simple formula:

Ho = 2 X 3.09E22 meters (= 1 Mpc) / 3 X age of universe in seconds X Mpc.
 
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  • #2
Originally posted by JMartin
the universal gravitational constant, G, (= 6.67E-11m^3/kg/s^2) means that the universe is growing by 6.67E-11 m^3 per second per second for each kg of mass in the universe.

If growth is a time rate of change why are its units consitant with a second derivative of volume?

Also, if the universe is growing at a constant volumetric rate, then its radial rate would be increasing at a decreasing rate, which AFAIK, is not consistant with observation.

Using the stated premise, one can determine the density of the universe at a specific age with the following formula:

Density = 2 X mass / mass X age of universe^2 X G

Notice that mass cancels out, so it is not necessary to supply it to use the formula.

how was that derived?

z = ((present age in seconds ^2 / desired age in seconds ^2) ^ 1/3) -1

What is z?

Ho = density X volume of 1 Mpc sphere X G X age of the universe / sphere surface area

However, cancellations allow Ho to be obtained by using the following very simple formula:

Ho = 2 X 3.09E22 meters (= 1 Mpc) / 3 X age of universe in seconds X Mpc.

What is Ho?
 
  • #3
I've worked over these ideas myself, starting with Dirac's Large Number Hypothesis, and I think that on closer investigation you will find that things have to be more complicated than this, and a good deal more complex and subtle than most people involved in cosmology even begin to suspect.
 
  • #4
Or perhaps our superb pattern-detecting brains picking up things in a realm far, far from the one in which the brain evolved?

a.k.a. a cosmic false-positive.
 

1. Why is the universal gravitational constant, G, important?

The universal gravitational constant, G, is important because it is a fundamental constant in physics that helps us understand the force of gravity between two objects. It is used in many equations and formulas to calculate the force of gravity, which is crucial in understanding the motion and behavior of objects in the universe.

2. How was the value of G determined?

The value of G was determined through experiments conducted by scientists, such as Henry Cavendish, in the 18th and 19th centuries. These experiments involved measuring the force of gravity between known masses and using the data to calculate the value of G. It is a difficult value to determine accurately, and modern experiments continue to refine its value.

3. Has the value of G changed over time?

There is currently no evidence to suggest that the value of G has changed over time. However, some theories, such as string theory, propose that the value of G may vary in different dimensions or universes. This is still a topic of ongoing research and debate among physicists.

4. How does G relate to Einstein's theory of general relativity?

Einstein's theory of general relativity explains gravity as the curvature of space-time caused by the presence of mass. G is a crucial factor in this theory, as it determines the strength of the gravitational force between masses and the curvature of space-time. Without G, general relativity would not accurately describe the behavior of gravity.

5. Are there any proposed new formulas for G?

There are ongoing efforts to develop new formulas and theories that may provide a better understanding of G and its role in the universe. These include theories such as quantum gravity and modified gravity, which aim to unify Einstein's theory of general relativity with the principles of quantum mechanics. However, these theories are still in the early stages of development and require further experimentation and testing.

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