Newton's law of universal gravitation

Hello everybody.

Is there any way to apply the gravitational force on a body in its most general expression?


I would impose m1.
m2 is my model which has a finite dimension.


There’s the NEWTON option for *DLOAD. I always wondered who would use that but unsurprisingly it’s you :wink:

It looks like you could do orbital mechanics with this and dynamic.


How did I miss that?
I looked up NEWTON in the manual but only saw references to the Newton-Raphson numerical method and Newton’s second law. It really didn’t make sense that the gravitational constant would appear under *PHYSICAL CONSTANTS and then not be used.
This is good news because the Coulomb force have exactly the same shape. There is an analogy to the electric field just converting the different constants.

Thank you very much Victor !!

Hi Victor,

I think your help deserves some promo footage for Mecway :wink: and Calculix.
This simple test runs in 2:30 min. It’s linear dynamics with arbitrary initial velocities in the three components to check convergence.
Enough to understand why so few planets survived in the solar system. Only those areas at the right distance, density and initial velocities are able to find an stable orbit one around each other. The impacts could probably be simulated moving to Nonlinear dynamics + contact.
I have no doubt that any student or fan of celestial dynamics will be happy about this possibility in CalculiX.

NOTE: Some distance and time units scaling are needed to avoid rounding errors. Keep in mind we are managing very large dimensions with gravitational constant O(1Ee-11) , millions of Km and days/years time periods



It is a bit absurd to answer myself, but I do not want to raise false expectations.

Applying the analogy to an electrostatic calculation has not been so simple.

First because the charge is not uniformly distributed over the surface as density is in the volume and second because, even if only as a first approximation, Calculix does not admit neither densities nor a negative gravitational constant to be able to model the electrostatic repulsion of charges of the same sign.

Anyway, the gravitational part is not bad at all.

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Beautiful animation @Disla !