The Effective Center Of Gravity

I wonder if our view of gravity requires some modification. According to all that I can see in science texts and on the internet, the strength of a gravitational force is subject to the inverse square law. In other words if an object is twice as far away, the gravitational force it exerts will be 1/4, if three times as far away, it will be 1/9. Also, the gravity of a spherical body such as a moon, planet or, star behaves as if it were coming from the center of mass of the body.

Yet, I find that this cannot be completely correct. These principles are not wrong in themselves but this neglects to take into account the geometric nature of spheres. Since essentially all sources of significant gravitational forces in the universe will be spherical in shape, it is vital that our view of the nature of gravity be amended to include this.

Our present concept of gravity which I described in the first paragraph would only be complete if the mass of a gravitational source was concentrated in an infinitesimal point or was at an infinite distance.

Suppose we have a satellite or spacecraft at a certain distance from a planet. Imagine a geometric plane that divides the planet into two equal hemispheres and is perpendicular to a straight line from the spacecraft through the center of the planet. For the sake of simplicity, we will assume that the planet is of uniform density.

Our present concept of gravity considers that the center of mass of the planet and it's center of gravity is one and the same and that it's gravitational force acts as if it is originating from this point. My reasoning is that this would only be the case if the perpendicular bisector plane divided the planet's mass so that all of the mass in the forward hemisphere was closer to the spacecraft than all of the mass in the further hemisphere.

Since a line of equal distance from the spacecraft will form a circle or sphere, this can only be true if the planet was at an infinite distance from the spacecraft so that the arc of a circle centered on the spacecraft that passed through the planet would be a straight line or that all the mass of the planet was concentrated in an infinitesimal point.

In the case of a satellite or spacecraft a finite distance from a spherical body such as a planet, a perpendicular bisector plane as described above cannot divide the planet into two equal hemispheres so that all of the mass in the forward hemisphere is closer to the spacecraft than all of the mass in the further hemisphere. The perpendicular bisector plane must pass through the center of the planet and since the line a given distance from the spacecraft forms a sphere or circle, that means that some of the mass in the forward hemisphere of the planet, around the outside of the planet, will be further from the spacecraft than some of the mass in the further hemisphere, around the center of the planet, and thus it's gravitational influence on the spacecraft will be greater.

This means that the effective center of gravity of the earth is different for all objects at different places on the earth's surface or in the space above the earth because a circle drawn from any given outside point that divides the earth in half will have a different arc for each outside point. The effective center of gravity of a planet relative to a spacecraft or other object approaching the planet is the planet's actual center of mass when the spacecraft is at an infinite distance away and moves along the same axis toward the spacecraft as it approaches the planet. This is because when there is less distance to the planet, there is a greater proportional difference between the gravitational effects of it's near and far sides.

A circle centered on the spacecraft and dividing the planet in half is what we must use to determine the center of gravity relative to the spacecraft. But it cannot be such a simple circle because then the relative center of gravity of the planet will be further away from the spacecraft than the planet's center of mass, and this makes no sense since the closer hemisphere of the planet to the spacecraft must have more of a gravitational effect on the spacecraft than the further half. The relative center of gravity of the planet must be closer to the spacecraft than the planet's center of mass, since the gravitational effect of mass falls off with distance.

The model that I have come up with to determine the relative center of gravity for the planet with regard to a Spacecraft A is to create an imaginary Spacecraft B at an altitude above the planet equal to that of Spacecraft A, but on the diametrically opposite side of the planet. Draw a circle centered on Spacecraft B which divides the planet exactly in half. The point on this circle directly between the mass center of the planet and Spacecraft A will be the relative center of gravity of the planet with regard to Spacecraft A.

This may throw off our understanding of the strength of gravity because since practically all sources of significant gravity are spheres, it has been acting over lesser distances than had been previously thought. I have been unable to find any reference to this anywhere.

This means that the effective center of gravity of a body orbiting the earth, such as the moon continuously changes, tracing a circle around the earth's actual center of mass on the plane of the moon's apparent orbit. This acts to churn the earth's liquid iron core and strengthen it's magnetic field as I described in the posting "The Moon And Earth's Magnetic Field" on this blog.

You may notice that this concept is similar to that of tides. Tidal forces occur whenever there is a difference between the actual center of mass and the effective center of gravity. This is why the tidal effect of the moon on the earth is more than twice that of the sun, even though the sun's gravitational pull on the earth is about 168 times that of the moon. The moon is 400 times as close to us as the sun so that the difference between the center of mass and the effective center of gravity is far greater.