This is a tricky question to answer because the correct answer to this question would qualify a person to win the Nobel Prize.
The Current Day Understanding of what Magnetic and Gravitational Fields are.
The standard answer given by most physicists would be to say NO.
This is because in the current model called the Standard Model that comes from Quantum Theory no one really knows what a magnetic field is and no one knows what a gravitational field is.
Examples of explanations physicists might give are as follows:
Thus relationship between gravitational field and magnetic field is simply that these are fields. Sohail Ahmed
So far there is no known relationship. If you discover one, you will surely win the Nobel prize. Jess H. Brewer
NO, There is no relationship between magnetic strength and gravity until now since no-one has yet succeeded in relating the electromagnetic force & gravity. Vipul Kachare
Neither is a force. They only appear to be forces because we need to use force to overcome the directional momentum. Both are characterized by a change in apparent strength inversely proportional to the square of the distance between them. Thus, as that distance decreases, the change in momentum increases accordingly, and the net effect is acceleration. Robert Glodowski
Typically the answers vary somewhat and because this question is really about discovering whether there is a mechanical relationship between the two force types. In some cases some scientists are not even willing to recognize these two fields as being fields of force.
The bottom line is current day physicists do not know what a magnetic field is and what a gravitational field is. If they did they we would have solved the Unified Field Theory Problem.
The Unified Field Theory Problem Defined
Electromagnetism and gravity emerge as aspects of a single fundamental field.This is the Albert Einstein Version. I am certain that this is the proper version that needs to be solved. My only adjustment is to deconstruct electromagnetism back into the electrostatic force and the magnetic force. This means the new version of the Unified Field Theory would be to unite the three fundamental forces of nature as stemming from the one fundamental field.
In the theory of Super Relativity unification has been accomplished by defining that there are three fundamental forces. The three forces are the electrostatic field, the magnetic field and the gravitational field. Maxwell successfully united electrostatic field to the magnetic field. This was done by discovering the relationship of the motion of electrostatic charge which causes the emergence of the magnetic field.
Definition of the Single Fundamental Field
Now that the primary forces of nature have been successfully defined it is time to define what the fundamental field is. Since the three greatest physicists ever to live all designed their models using the aether concept I followed in there footsteps. The three physicists were Newton, Maxwell and Einstein. I decided that the aether concept was then and is now the correct model to use. Therefore the I regard the aether as being the single fundamental field. There is an abundance of evidence that I have compiled in my book “Master of Reality” that proves the existence of the aether.
Summarizing
I have now established that there are three fundamental forces that all manifest as forces of attraction or repulsion via the phenomenon known as action at a distance. Action at a distance can only be physically possible if there exists a fundamental field that is continuous, all pervading and omnipresent. This means that the forces of attraction and repulsion occur in a local manner. These fields of force act upon distant objects via stresses and tensions within the aether medium. So magnetism, the electrostatic field and the gravitational field are three different aspects of the fundamental aether field.
I am now closing in on answering your question. So my answer to your question is YES they are related fields in the aether medium. They appear as being unrelated because they are different types of bending of space. The relationship that exists between the magnetic field and the gravitational field is established by the motion of charges through the aether medium(the fundamental field).
The Magnetic Field of Force
The magnetic field is a particular type of bending of space in which magnetic attraction happens as a result of charges moving in the same direction. Magnetic repulsion occurs between charges which are moving in opposite directions. This results in a polarized field of force. As the charges move in a conductor the lines of force emerge from north pole and then circle around and enter into the south pole. Clearly what is happening is that space is reacting to the charges that are moving within it. Space reacts by rotating around the charge as the charge moves within the aether. The magnetic field of force is a torsional reaction to moving charge.
The Gravitational Field of Force
The formation of the gravitational field is just another type of bending of space. The gravitational field according to the Theory of Super Relativity is non-polarized. A non-polarized field that is a homogenous gradient field that surrounds a rapidly spinning sphere. Gravity is a contraction of space caused by the accelerated motion of electromagnetic fields.
The Specific Gravitational Model Example
The Gravitational Field of force is caused by the accelerated motion of unbalanced charged particle fields. An example is the motion of quarks inside the neutron and proton. The quarks move in a rapid trefoil shaped pattern of motion. This is an highly accelerated motion. The dynamic geometric pattern of trefoil motion is also precessing and because of this additional motion a transformation from trefoil structure to a spherical structure happens. The spherical rotation causes a contraction of space just as Einstein predicted in his happiest thought.
This is an excerpt from Amir D. Aczel’s Book entitled “God’s Equation” page 59.
*“Einstein followed the line of reasoning that began with the “happiest thought” of his life. Still at the Swiss patent office, he conducted one of his famous thought experiments. Einstein imagined a circle spinning in space. The center of the circle did not move, but its circumference was moving quickly in a circular direction. Einstein compared what happens in several reference frames, a standard tool he had used in developing the special relativity theory. He concluded, using his special relativity, that the boundary of the disk contracted as it spun. There was a force acting on the circle at the boundary – the centrifugal force – and its action was analogous to that of a gravitational force. But the same contraction that affected the outer circle left the diameter unchanged. Thus, Einstein concluded, in a way that surprised even him, the ratio of the circle to the diameter was no longer pi. He deduced that in the presence of a gravitational force (or field) the geometry of space was non-Euclidean.
This is what happening for the neutron and the proton as they are equivalent to rapidly spinning spheres. This is how the neutron and the proton generate their so called rest mass. This is how the gravitational field is generated.
Summary
So to answer your question the magnetic field and the gravitational field are two different aspects of the single fundamental field (the aether). The gravitational field is a gradient field of contraction. The magnetic field is a torsional (twist or Rotational field) reaction to moving charge. Both fields are generated by the motion of electromagnetic particles within the aether medium.