# Planets in gravitational well

Planets in gravitational well by Louis Rancourt

Far from any stars in space, gravity coming from one direction is almost cancelled by gravity coming in opposite direction. An object in that position continues in strait line because the net force on the object is zero.

Because of all its atoms, the sun blocks some of that gravity going through the sun. If it was possible to take a picture of only the gravity coming from all region of space, the density of that gravity would be less closer to the sun because of that shielding effect. Gravity density is lower close to the sun and increases according to 1/distance squared. The next drawing represents such a density.

But the sun itself is also an emitter of gravity. That extends to a certain distance from the sun. If it was possible to take a picture of only the gravity coming from the sun without the gravity coming from all region of space, the density of that gravity would be greater closer to the sun and the density decreases according to 1/distance squared.

When these two gravities are added, at a certain distance, the density of gravity from space is almost equal to the density of gravity coming from the direction of the sun.

That makes a kind of big sphere or bubble where gravity is less. That region or bubble is the gravitational well . Planets in that region cannot go in strait line because in doing so, they would enter a region where the gravity from outside is now bigger and they are　pushed back towards the sun. When they approach the sun, the same thing happens in opposite: the gravity coming from the sun is now bigger and the planet is pushed away, In that manner, the planet goes around the sun as satellite.

 distance sun – planet planet planet from sun in m mass kg 1 force in N Mercury 1 5.80E+07 3.30E+23 2 1.30E+28 1 Venus 2 1.10E+08 4.87E+24 3 5.34E+28 2 Earth 3 1.50E+08 5.98E+24 4 3.53E+28 3 Mars 4 2.30E+08 6.42E+23 5 1.61E+27 4 Jupiter 5 7.80E+08 5.69E+26 6 1.24E+29 5 Saturn 6 1.40E+09 5.69E+26 7 3.85E+28 6 Uranus 7 2.80E+09 8.68E+25 8 1.47E+27 7 Neptune 8 4.50E+09 1.02E+26 9 6.69E+26 8 Pluto 9 6.00E+09

Using an arbitrary unit of 10 units for gravity from space, we can compare the different effects on planets of our solar system.

 in log in log distance sending blocking 10 1 1.0000 9.7782 1.00E+02 2 2.0000 9.6532 1.00E+03 3 3.0000 9.4472 1.00E+04 4 4.0000 9.1461 1.00E+05 5 5.0000 8.8921 1.00E+06 6 6.0000 8.3617 Mercury 1.00E+07 7 7.0000 8.0414 Venus 1.10E+08 8 8.0414 7.0000 Pluto 2.30E+08 9 8.3617 6.0000 7.80E+08 10 8.8921 5.0000 1.40E+09 11 9.1461 4.0000 2.80E+09 12 9.4472 3.0000 4.50E+09 13 9.6532 2.0000 6.00E+09 14 9.7782 1.0000

In order to show the gravity well, we must use the log value of the distances. The blue line is for the gravity from space that was partially blocked by the sun and the red line is the gravity emitted by the sun. It goes to almost zero at far distance.

The mass and the speed of the planet will permit to find an equilibrium point and it becomes a satellite to the sun. The centrifugal force has to be equal to the force pushing the planet toward the sun.

The gravity in this graphic represents the net total force when we add opposite forces. Depending on its speed, the planet finds the distance away from the sun where the force towards the sun equals its centrifugal force.

Einstein seems to have a vague idea of that gravity well and tried to explain it with his theory of space time curvature. Space is not curved but its different density will influence objects towards the sun as if it was “curved’ inward.

Following the equation (F = Gmm/dd) there is a possibility to have planets between the sun and Mercury if the speed is big enough. There is no such planet there. This is because of the gravity well described here. A planet closer to the sun would be pushed away by sun radiation of gravity unless it had a very high speed.

This also explains why most comets do not fall into the sun as they should because of the pressure of the gravity emitted by the sun. That gravity will push the comet’s tail away from the sun.

If we add all forces going towards a planet to forces from space coming from other side we have this picture. The sun is at 0 level on y axis in the next graph.

At position 7 to 8, the planet will stay in orbit.This correspond to distances between 1×107 m and 2.3 x 108 m from the sun .Closer distances smaller than 1×107 m, a planet is pushed away from the sun.

These are the figures used in Excel to calculate these positions. in multiple of 10 units.

 forcrces going toward planet opposite in log in log from away from total sending blocking space forces space forces 1 1.0000 9.7782 10 20.7782 -25 1 -4.2218 2 2.0000 9.6532 10 21.6532 -25 2 -3.3468 3 3.0000 9.4472 10 22.4472 -25 3 -2.5528 4 4.0000 9.1461 10 23.1461 -25 4 -1.8539 5 5.0000 8.8921 10 23.8921 -25 5 -1.1079 6 6.0000 8.3617 10 24.3617 -25 6 -0.6383 7 7.0000 8.0414 10 25.0414 -25 7 0.0414 8 8.0414 7.0000 10 25.0414 -25 8 0.0414 9 8.3617 6.0000 10 24.3617 -25 9 0.6383 10 8.8921 5.0000 10 23.8921 -25 10 1.1079 11 9.1461 4.0000 10 23.1461 -25 11 1.8539 12 9.4472 3.0000 10 22.4472 -25 12 2.5528 13 9.6532 2.0000 10 21.6532 -25 13 3.3468 14 9.7782 1.0000 10 20.7782 -25 14 4.2218

In this graph, the sun centre is at 0 on y-axis.

Forces toward the sun from space are below the 0 y axis and forces pushing away from the sun are above the 0 y axis.

These total forces are lowest at the distance where our planets orbit the sun.

N.B. Since we do not know the exact value of the forces due to gravity coming from every directions of space on every kg of matter, we used 10 units in the graph. These units are probably very great and might be measured in the future.