Continued from post number 19 above.
PART FIVE:
Some gravitational calculations.
The theory in the Introduction to Navigation booklet in Star Trek Maps (1980) has another big flaw: Every particle of matter in the universe exerts some gravitational force on every other particle in the universe, no matter how distant. That means that every atom or molecule, every grain of dust and every asteroid, comet, moon, planet, and star in the universe exerts some gravitational force on every other particle in the universe. That means that every object in the universe bends space to a greater or lesser amount at every distance from it, no matter how far.
The degree of space bending according to relativity should be approximately proportional to the degree of gravitational attraction calculated by Newtonian physics.
So if two object attract each other, and all object attract each in Newtonian theory,the strength of that attraction will be inversely proportional to the distance between them.
Assume that the center of the galaxy is about 8,122 ± 31 parsecs (26,490 ± 100 ly) from Earth,as is currently measured, and that the mass of the center of the galaxy is one billion (1,000,000,000) times, or ten billion (10,000,000,000) or one hundred billion 100,000,000,000) times that of the Sun.
In that case the gravitational attraction of the Sun and of the center of the Galaxy, will be equal at a distance from the Sun that is equal to about 26,490 light years divided by the square root of one billion (1,000,000,000), or about 26,490 light years divided by the square root of ten billion (10,000,000,000), or about 26,490 light years divided by the square
e root of one hundred billion 100,000,000,000).
The square root of one billion (1,000,000,000)is 31,622.7766.
The square root of 10,000,000,000) is 100,000.
The square root of one hundred billion (100,000,000,000) is 316,227.766.
Thus the distance from the Sun where the Sun's gravitational attraction, and thus its degree of space curving, should be equal to that of the galactic center, should be about 26,490 light years divided by 31,622.7766 to 100,00 to 316,277.766, and thus about 0.08376876 to 0.2649, to 0.8376873 light years.
Thus a rough calculation would indicate that on an interstellar voyage tens or hundreds of light years long, a starship would pass close enough to a star for the star's gravitational force to be stronger than that of the Galactic center less than only one percent of the time.
So the gravitational attraction and space warping of the galactic center should be dominant in this part of the galaxy, and travelling tensor hundreds of light years closer to or farther from the galactic center will increase or decrease the curvature of space slightly.
Most of the stars, gas, and dust in the galaxy that is not in the galactic center is in the galactic disc, which is about 100,000 light years in diameter and about 1,000 or 2,000 light years thick. The farther a star is "above" or "below" the central plane of the galactic disc, the lesser the gravitational force of the stars in the galactic disc will be.
So the gravitational attraction of the galactic center falls off in concentric spherical layers with increasing distance from the center, and the gravitational attraction of the galactic disc falls off in parallel planes with increasing distance from the mathematical central plane of the galactic disc.
The Milky Way Galaxy is part of the Local Group of Galaxies, which is part of the Virgo Supercluster of galaxies. The Virgo Cluster of galaxies is at the center of the Virgo Supercluster of galaxies, and at the center of the Virgo Cluster of galaxies is the great galaxy M87 or NGC 4486, with a giant black hole in its center. The mass of the Virgo Supercluster
can be mathematically considered to be at the distance of M87.
The calculated distance of M87 is about 16.4 million parsecs or about 53,500,000 light years. Allowing for uncertainty, make the distance about 55,000,000 light years. The Virgo Supercluster is supposed to have a total mass of about 1,000,000,000,000,000 times the mas of the Sun.
The square root of 1,000,000,000,000,000 is 31,622,776.6.. 55,000,000 light years divided by 31,622,776.6 is about 1.739252713 light years. So the Sun's gravity will equal that of the Virgo Supercluster at a distance of about
1.739 light years, which is about two to twenty times the distance at which the Sun's galaxy would equal that of the center of the galaxy.
The Virgo Cluster and galaxy M87 happen to be almost at the direction to one of the galactic poles of the Milky Way galaxy, so the gravitational attraction of the Virgo Supercluster of galaxies will vary only very slightly in different parts of the galactic disc, where most TOS episodes happen.
So throughout the galactic disc the gravitational force from distant but very massive objects, tens of thousands to tens or hundreds of millions of light years away will be dominant, and it will have very gradual gradients with relatively tiny changes in the distances to those distant bodies.
That is very bad news for any theory that the local gravitational force or space curvature within a volume of space determines how fast warp speeds are, since those conditions won't vary greatly over distances of mere tens or hundreds of light years as such a theory would need to explain the different travel times in TOS.
Fortunately there are other theories to explain the varying speeds of warp factors in TOS.
PART FIVE:
Some gravitational calculations.
The theory in the Introduction to Navigation booklet in Star Trek Maps (1980) has another big flaw: Every particle of matter in the universe exerts some gravitational force on every other particle in the universe, no matter how distant. That means that every atom or molecule, every grain of dust and every asteroid, comet, moon, planet, and star in the universe exerts some gravitational force on every other particle in the universe. That means that every object in the universe bends space to a greater or lesser amount at every distance from it, no matter how far.
The degree of space bending according to relativity should be approximately proportional to the degree of gravitational attraction calculated by Newtonian physics.
The equation for universal gravitation thus takes the form:
{\displaystyle F=G{\frac {m_{1}m_{2}}{r^{2}}},}
where F is the gravitational force acting between two objects, m1 and m2 are the masses of the objects, r is the distance between the centers of their masses, and G is the gravitational constant.
So if two object attract each other, and all object attract each in Newtonian theory,the strength of that attraction will be inversely proportional to the distance between them.
Assume that the center of the galaxy is about 8,122 ± 31 parsecs (26,490 ± 100 ly) from Earth,as is currently measured, and that the mass of the center of the galaxy is one billion (1,000,000,000) times, or ten billion (10,000,000,000) or one hundred billion 100,000,000,000) times that of the Sun.
In that case the gravitational attraction of the Sun and of the center of the Galaxy, will be equal at a distance from the Sun that is equal to about 26,490 light years divided by the square root of one billion (1,000,000,000), or about 26,490 light years divided by the square root of ten billion (10,000,000,000), or about 26,490 light years divided by the square
e root of one hundred billion 100,000,000,000).
The square root of one billion (1,000,000,000)is 31,622.7766.
The square root of 10,000,000,000) is 100,000.
The square root of one hundred billion (100,000,000,000) is 316,227.766.
Thus the distance from the Sun where the Sun's gravitational attraction, and thus its degree of space curving, should be equal to that of the galactic center, should be about 26,490 light years divided by 31,622.7766 to 100,00 to 316,277.766, and thus about 0.08376876 to 0.2649, to 0.8376873 light years.
Thus a rough calculation would indicate that on an interstellar voyage tens or hundreds of light years long, a starship would pass close enough to a star for the star's gravitational force to be stronger than that of the Galactic center less than only one percent of the time.
So the gravitational attraction and space warping of the galactic center should be dominant in this part of the galaxy, and travelling tensor hundreds of light years closer to or farther from the galactic center will increase or decrease the curvature of space slightly.
Most of the stars, gas, and dust in the galaxy that is not in the galactic center is in the galactic disc, which is about 100,000 light years in diameter and about 1,000 or 2,000 light years thick. The farther a star is "above" or "below" the central plane of the galactic disc, the lesser the gravitational force of the stars in the galactic disc will be.
So the gravitational attraction of the galactic center falls off in concentric spherical layers with increasing distance from the center, and the gravitational attraction of the galactic disc falls off in parallel planes with increasing distance from the mathematical central plane of the galactic disc.
The Milky Way Galaxy is part of the Local Group of Galaxies, which is part of the Virgo Supercluster of galaxies. The Virgo Cluster of galaxies is at the center of the Virgo Supercluster of galaxies, and at the center of the Virgo Cluster of galaxies is the great galaxy M87 or NGC 4486, with a giant black hole in its center. The mass of the Virgo Supercluster
can be mathematically considered to be at the distance of M87.
The calculated distance of M87 is about 16.4 million parsecs or about 53,500,000 light years. Allowing for uncertainty, make the distance about 55,000,000 light years. The Virgo Supercluster is supposed to have a total mass of about 1,000,000,000,000,000 times the mas of the Sun.
The square root of 1,000,000,000,000,000 is 31,622,776.6.. 55,000,000 light years divided by 31,622,776.6 is about 1.739252713 light years. So the Sun's gravity will equal that of the Virgo Supercluster at a distance of about
1.739 light years, which is about two to twenty times the distance at which the Sun's galaxy would equal that of the center of the galaxy.
The Virgo Cluster and galaxy M87 happen to be almost at the direction to one of the galactic poles of the Milky Way galaxy, so the gravitational attraction of the Virgo Supercluster of galaxies will vary only very slightly in different parts of the galactic disc, where most TOS episodes happen.
So throughout the galactic disc the gravitational force from distant but very massive objects, tens of thousands to tens or hundreds of millions of light years away will be dominant, and it will have very gradual gradients with relatively tiny changes in the distances to those distant bodies.
That is very bad news for any theory that the local gravitational force or space curvature within a volume of space determines how fast warp speeds are, since those conditions won't vary greatly over distances of mere tens or hundreds of light years as such a theory would need to explain the different travel times in TOS.
Fortunately there are other theories to explain the varying speeds of warp factors in TOS.
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