# Accumulation of Mass

The recent post by shamrock5585 got me thinking. Most models of stellar formation and stuff basically involve an accumulation of mass through gravity building larger and larger mass. However, even if we assume that all the particles are of neutral charge we can still expect a dipole-dipole force as the particles get closer (through taylor series expansion). However, (if we briefly consider gravity as a newtonian force instead of in terms of general relativity) I would be inclined to think that, due to the very small size of the constant G, that the dipolar term (although it is of the order 1/r^3) would be dominant as the particles begin to closely pack and yet I don't think I've ever heard of dipolar attraction being an important factor of stellar formation (although i'm a computational quantum many-body guy not an astro guy).

I guess my question is, is dipolar attraction ever considered in these sorts of models?

D H
Staff Emeritus
The Earth (and any real astronomical object) is not a perfect sphere. A precision gravity model requires a treatment of the non-spherical shape. Spherical harmonics are one obvious choice. The obvious origin for such a spherical harmonics expansion is the center of mass. The center of mass spherical harmonics expansion has a zero dipole moment because a non-zero value would require a negative mass. So, no dipole moment for Newtonian gravity.

Higher order terms can be quite important, at least at close range. For example, the Earth's zonal quadrupole moment, J2, is one of the major perturbing factors in satellite orbits and dominates all other perturbing factors at geosynchronous satellites. Quadrupole moments only go so far. People have developed 360x360 spherical harmonics models for the Earth's gravitational field (http://cddis.nasa.gov/926/egm96/egm96.html" [Broken]. JPL has developed Lunar gravity models up to degree and order 160.

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I'm not talking about the earth though I'm talking about stellar formation where you have a dust cloud which accumulates atom by atom, dust speck by dust speck to make a solar system.

D H
Staff Emeritus
What difference does it make, conceptually? There is a zero dipole moment in the center of mass spherical harmonics expansion of the gravitational field for any collection of mass because there is no such thing as negative mass.

One problem with a dust cloud is that the spherical harmonics model will be time-varying, but if you want to get real picky, so is the Earth's. The Earth rotates once per day, but this problem can be addressed by developing the spherical harmonics in a rotating frame that rotates with the Earth. Even so, the Sun and Moon cause tides, which results in a daily variation in the rotating frame spherical harmonics coefficients. Mass migrates northward during winter (northern hemisphere) and southward during summer, causing an annual variation in the coefficients. Mountains rise up and erode and continents move around, causing longer term variations.

Bottom line: An extremely detailed Earth gravitational model will have time-varying spherical harmonics coefficients. The same is true for a dust cloud.

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But individual atoms and molecules do experience a dipole-dipole force (the van der waals force). And I'd imagine that the magnitude of that force is either of the same order or larger then the gravitational attraction at the distances between particles of a dust cloud.

NOTE: I am talking about an ELECTRONIC dipole-dipole force (from electron orbitals) not a gravitational dipole force coming from expanding the graviational force.

D H
Staff Emeritus
Electric dipoles result because there is such a thing as negative charge. There is no such thing as negative mass. A similar situation occurs in magnetism, except in magnetism there is no monopole moment rather than no dipole moment.

D H
Staff Emeritus