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Gravitational Interaction – Gravitational Force

Gravitational force is one of the four fundamental forces. It is directly proportional to the masses of the bodies and inversely proportional to the square of the distance between the bodies.

Gravity was the first force to be investigated scientifically. The gravitational force was described systematically by Isaac Newton in the 17th century. Newton stated that the gravitational force acts between all objects having mass (including objects ranging from atoms and photons to planets and stars) and is directly proportional to the masses of the bodies and inversely proportional to the square of the distance between the bodies. Since energy and mass are equivalent, all forms of energy (including light) cause gravitation and are under its influence. The range of this force is ∞ , and it is weaker than the other forces. This relationship is shown in the equation below.

gravitational interaction and gravitational forceThe equation illustrates that the larger the masses of the objects or the smaller the distance between the objects, the greater the gravitational force. So even though the masses of nucleons are very small, the fact that the distance between nucleons is extremely short may make the gravitational force significant. The gravitational force between two protons separated by a distance of 10-20 meters is about 10-24 newtons. Gravity is the weakest of the four fundamental forces of physics, approximately 1038 times weaker than the strong force. On the other hand, gravity is additive. Every speck of matter that you put into a lump contributes to the overall gravity of the lump. Since it is also a very long-range force, it is the dominant force at the macroscopic scale and is the cause of the formation, shape, and trajectory (orbit) of astronomical bodies.

The general theory of relativity is the fundamental theory of gravity. This theory describes gravity not as a force but as a consequence of the curvature of spacetime caused by the uneven distribution of mass. In theories of quantum gravity, the graviton is the hypothetical elementary particle that mediates the force of gravity.

Artificial Gravity

In the 20th century, Einstein’s equivalence principle put all observers, moving or accelerating, on the same footing. Einstein summarised this notion in a postulate:

Principle of Equivalence:

An observer cannot determine, in any way whatsoever, whether the laboratory he occupies is in a uniform gravitational field or is in a reference frame that is accelerating relative to an inertial frame.

This led to an ambiguity as to what exactly is meant by the force of gravity and weight. A scale in an accelerating elevator cannot be distinguished from a scale in a gravitational field. Gravitational force and weight thereby became essentially frame-dependent quantities. According to the general theory of relativity, gravitational and inertial mass are not different properties of matter but two aspects of matter’s fundamental and single property.

Artificial Gravity

An animation of a 50-meter diameter rotating space station. Source: wikipedia.org (P.Fraundorf) License: CC BY-SA 4.0

In situations where gravitation is absent, the chosen coordinate system is not inertial. Still, it is accelerated with the observer. G-forces and corresponding proper accelerations felt by observers in these coordinate systems are caused by the mechanical forces which resist their weight in such systems. The most realistic method of producing artificial gravity, for example, aboard a space station, can be imitated in a rotating spaceship. Objects inside would be pushed toward the hull, which will have some weight. This weight is produced by fictitious or “inertial forces,” which appear in all accelerated coordinate systems. Unlike real gravity, which pulls towards the planet’s center, the centripetal force pushes towards the axis of rotation.

Nuclear and Reactor Physics:
  1. J. R. Lamarsh, Introduction to Nuclear Reactor Theory, 2nd ed., Addison-Wesley, Reading, MA (1983).
  2. J. R. Lamarsh, A. J. Baratta, Introduction to Nuclear Engineering, 3d ed., Prentice-Hall, 2001, ISBN: 0-201-82498-1.
  3. W. M. Stacey, Nuclear Reactor Physics, John Wiley & Sons, 2001, ISBN: 0- 471-39127-1.
  4. Glasstone, Sesonske. Nuclear Reactor Engineering: Reactor Systems Engineering, Springer; 4th edition, 1994, ISBN: 978-0412985317
  5. W.S.C. Williams. Nuclear and Particle Physics. Clarendon Press; 1 edition, 1991, ISBN: 978-0198520467
  6. G.R.Keepin. Physics of Nuclear Kinetics. Addison-Wesley Pub. Co; 1st edition, 1965
  7. Robert Reed Burn, Introduction to Nuclear Reactor Operation, 1988.
  8. U.S. Department of Energy, Nuclear Physics and Reactor Theory. DOE Fundamentals Handbook, Volume 1 and 2. January 1993.
  9. Paul Reuss, Neutron Physics. EDP Sciences, 2008. ISBN: 978-2759800414.

Advanced Reactor Physics:

  1. K. O. Ott, W. A. Bezella, Introductory Nuclear Reactor Statics, American Nuclear Society, Revised edition (1989), 1989, ISBN: 0-894-48033-2.
  2. K. O. Ott, R. J. Neuhold, Introductory Nuclear Reactor Dynamics, American Nuclear Society, 1985, ISBN: 0-894-48029-4.
  3. D. L. Hetrick, Dynamics of Nuclear Reactors, American Nuclear Society, 1993, ISBN: 0-894-48453-2. 
  4. E. E. Lewis, W. F. Miller, Computational Methods of Neutron Transport, American Nuclear Society, 1993, ISBN: 0-894-48452-4.

See above:

Fundamental Interactions