Press release

New law of gravitation

A new law of gravitation has been proposed in a paper recently published by C. K. Raju, an Indian researcher based at Albukhary International University, Malaysia. Newton believed the gravitational force between two objects varies inversely as the square of the distance. Raju's new law of gravitation makes three changes. First, Raju's law uses retarded distance, or “last-seen” distance, instead of the “instantaneous distance” used in Newton's law. This makes Raju's law compatible with special relativity which does not allow forces to travel faster than the speed of light. Secondly, Lorentz covariance, or compatibility with special relativity, further requires that the gravitational force depend also upon the relative velocity between the two objects, unlike Newton's law which depends solely on the distance between them. Third, in contrast to the ordinary differential equations used in Newtonian physics, Raju uses delay differential equations or functional differential equations. This makes Raju’s formulation irreversible and compatible with the everyday experience of irreversible aging which is contrary to the reversibility of Newton’s laws.

The changes dues to Raju's new law make only a tiny difference at the level of the earth or the solar system. However, Raju's law easily explains the flyby anomaly of NASA spacecraft. Careful observation of the motion of several NASA spacecraft showed unaccountable deviations from the predictions of Newtonian theory, even after applying general relativistic corrections. The deviations were systematically linked to the rotation of the earth by NASA scientists. This effect due to the rotation velocity of the earth arises naturally in Raju's theory, though it cannot be explained by either Newtonian gravitation or general relativity.

However, the differences between Raju's law and Newton's law become large at the level of the galaxy. Because a galaxy may contain a trillion stars, the related many-body problem is too hard to solve using general relativity, and is still solved using Newtonian gravitation. This fails to explain the actually observed motions of stars in spiral galaxies. The discrepancy is usually attributed to the existence of hypothetical dark matter. Merely assuming the existence of dark matter does not, however, explain the observed motion of stars in a galaxy. Hence, a further hypothesis is advanced that the dark matter is distributed like a halo around the galaxy, with its density reaching a peak where the luminous matter thins out to zero. Since the gravitational effects of dark and luminous matter are identical, this sharp difference in the distribution of dark and luminous matter seems an artificial hypothesis. With Raju's theory the faster rotation of stars in spiral galaxies (such as the Milky Way) finds a natural explanation without such artificial hypotheses. In a spiral galaxy, unlike a planetary system, there are trillions of stars all rotating in a common direction. On Raju's theory, each star contributes only a tiny velocity drag, but because here are a large number of stars, all rotating in one direction, the total velocity drag is large, and speeds up the stars, as actually observed.

Unlike all previously proposed modifications of gravity, Raju's new law of gravitation can be tested by laboratory experiments. It may help explain the difficulty in obtaining a precise value of the Newtonian gravitational constant G. Since Raju's law makes no speculative hypotheses, assuming only special relativity, if it fails any experimental tests, this too would have fundamental implications across physics.

Raju's theory has an interesting historical angle. Special relativity arose by correcting a mistake about time in Newtonian physics. Raju identifies the origin of this mistake in a novel way as arising from Newton's failure to understand the calculus, then recently imported into Europe from India. Raju's theory carries the correction due to special relativity to its logical conclusion.

It may be recalled that in a book called Cultural Foundations of Mathematics (Pearson Longman, 2007) Raju had earlier detailed evidence for the origin of the differential and integral calculus in India and its transmission to Europe in the 16th c. CE. Raju also has two earlier books on time, Time: Towards a Consistent Theory (Kluwer Academic, 1994) and The Eleven Pictures of Time (Sage, 2003), in both of which he advocated the use of functional differential equations in physics.

Raju received the Telesio Galilei Award 2010, in Hungary, for correcting Einstein's mistake regarding functional differential equations in relativity, and he also played a key role in building India's first supercomputer.

This latest paper, called “Retarded Gravitation Theory”, was presented as an invited talk at the Fifth International School on Field Theory and Gravitation, held in Petropolis, Rio de Janeiro, Brazil, and is published by the American Institute of Physics after peer review.


C. K. Raju, “Retarded gravitation theory”, in: Waldyr Rodrigues Jr, Richard Kerner, Gentil O. Pires, and Carlos Pinheiro (ed.), Sixth International School on Field Theory and Gravitation, American Institute of Physics, New York, 2012, pp. 260-276.


Link to proceedings on American Institute of Physics site:

Further details

A copy of the paper is available online at

Further details about editors, etc. at:

Earlier press reports

For earlier press reports about C. K. Raju, see