Is there a quantification of gravitational attraction at the atomic level?

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The discussion centers on the quantification of gravitational attraction at the atomic level, specifically regarding hydrogen atoms and protons. Participants reference Newton's law of gravitation, which states that gravitational force is proportional to the product of two masses divided by the square of the distance between them. The Higgs field is mentioned as a contributor to mass, but its direct connection to gravity remains unclear in current theories. A notable example illustrates the weakness of gravitational attraction, showing that two hydrogen atoms would take millions of years to move closer due to gravity alone. Overall, the conversation highlights the complexities of understanding gravitational forces at such small scales.
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What I'd like to know is has anyone figured out a system of units for gravitational attraction? I can't find anything on google. For instance, given a hydrogen atom or even just a proton, is there a quantification of how much gravitational attraction it exerts on everything else around it (I suppose at a given distance)

I'm not talking about weight here, since that changes based on the setting of the mass in question


Second questions, is there a layman's explanation of the relationship between mass (which I understand is thought to be created by higgs bosons) and the actual gravitational force being provided by mass? Does one (the higgs) cause gravity, or are both mass and gravity produced by something else and are simply correlated?

Thanx!
 
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Sounds to me like you are just looking for Newton's equation for gravitational force. Are you familiar with it?
 
I can't answer your second question but your first one is, just as Russ pointed out, Newton's law of gravitation.

GM1M2 / d^2

G= Gravitational constant
M1= Mass one
M2= Mass two

divided by their distance squared.
 
The Higgs field is part of the explanation for mass. Most of the mass of nucleons comes from internal energy.

Gravity is a force (proportional to mass) described by Newton's law and more precisely by general rerlativity. Current theory has no direct connection with Higgs field.
 
Just to show how weak the force of gravity is between atoms, A. J. Mallmann in an article in The Physics Teacher v 32 1994 calculated that two hydrogen atoms initially at rest and 1.0 mm apart attracted only by gravity would take 2 million years for them to "fall" to a separation of 0.5mm. Very interesting.
 
I do not have a good working knowledge of physics yet. I tried to piece this together but after researching this, I couldn’t figure out the correct laws of physics to combine to develop a formula to answer this question. Ex. 1 - A moving object impacts a static object at a constant velocity. Ex. 2 - A moving object impacts a static object at the same velocity but is accelerating at the moment of impact. Assuming the mass of the objects is the same and the velocity at the moment of impact...

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