There is an analogue here. Kepler's Laws are describing the path of planetary motion. The centripetal force in Kepler's laws is the gravitation force as defined by Newtons law of attraction.
Inside the hydrogen atom the centripetal force is the Coulomb force as defined by Coulombs law. For both situations (Kepler and Coulomb) the centripetal forces are in equilibrium with their centrifugal forces.
This is interesting because in both cases centrifugal forces (planetary and ”proton/electron” scale) are physical identical and both contain acceleration generated by the centripetal force. Acceleration can be described as a vector. Like gravity the acceleration vectors have the dimension (m/s^2). This creates a situation where acceleration vectors and the gravity field strength are fully complementary.
So this clears the path for gravity to interfere with the centrifugal force of the electron and therefore influencing its equilibrium with the Coulomb force inside the atom.
Compare the atom in a gravitational field with a balloon under water. The atom represents the balloon and the water represents a gravity field. The deeper the balloon gets submerged the higher (more gravity) the pressure on the balloon. The balloons inside pressure will increase to match the increasing outside pressure, so also with the atom. In similarity the gravity field strength is influencing the distance between the proton and the electron and thus influencing the diameter of the atom
This implies a lot. It would mean that this affects our experienced space-time frame. An example: Say we have a chain of atoms with a length of 1 meter on earth’s surface. We put this chain of atoms in orbit around the Earth at a height of 20.200 km ( height where the GPS satellite are orbiting the earth). The gravity is reduced to appr. 0.56m/s^2. Our "meter of atoms" has an increased relatively length because of the change in distance between all the electrons and protons in this "meter of atoms" causing a relative change in diameter of the atoms. Every day the satellite travels around 78cm more than noticed. because it is rotating around the Earth and after exact 24 hours the distance doesn't match our reference ( earth's meter ) anymore. (See calculating time differencein the blog for full explanation and calculation)
How to examine the influence of gravity
Think of the balloon. When submerged just beneath the surface, the pressure on the top of the balloon is atmospheric, but on the bottom side of the balloon, the pressure is higher. This also occurs in a gravitational field, only the differences in gravitational fields are much smaller. So there is a need to define an infinite small parameter for gravity. “gravity operator” . A infinite small parameter can give a value for an infinite small change in the gravity field on atom sized scale.
Whith the knowledge of the infinite small change in gravity on earth's surface, it is possible to find the small change in gravity acting on the atom. The small difference is interfering with the forces within the atom. The atom adapts by changing the distance between the proton and the electron on a way that equilibrium between Coulomb force and centrifugal force is maintained. This can be arranged by changing the radius between proton and electron. Smaller distance between the particles increases Coulombforce
With help of the coulomb force acting between the proton and the electron in an atom in a gravitational field it is possible to find a value for the radius at the top and at the bottom of the atom.
The value of these radii can be found with use of Keplers law. See the tab of Kepler’s lawfor full explanation
The change in radius of the atom is very small. To make calculations possible, 20 digits are used.
Values for minimum radius where gravity field is highest and max radius where gravity field strength Is lowest are
Calculation of force in direction(x)
For an electron with an eccentric trajectory the resulting centrifugal
force is not constant.
This means that the electron has different values for the centrifugal
force depending on its radius.
The result is a net generated force.
When absorbing the gravitational field into the centrifugal force it is
possible to change the distance between the electron and the proton. See Tie-graph
for more explanation.
The net value for the generated force ( Fgen) of the electron
is pulling on the proton and the result is a total directed force in Nm for the
atom. The amount of change in Coulomb
force/ centripetal force is “like the balloon submerged under water” opposite to maintain equilibrium. But the atom
has free rotation and acts like an polar magnet to complete the equilibrium in
the gravity field.
Now the generated force is directed the atom shows acceleration. When we
stop the atom we experience this force as weight or mass.
Fgen represents a value for kinetic energy with
The importancy here is that if gravity is considered
as in Newtons laws ( the appel falls to the ground), mass is a constant and has
the dimension () or better
known as kg. Fgen however contains a force in Nm (Newton
meter) and represent the kinetic energy of the electron. So the kinetic energy
of the apple forces it towards the ground (there
is no difference for the observer)