When a spacecraft performs a manoeuver called flyby, in which it comes along a hyperbolic trajectory towards the Earth or other planets, something strange happens. This manoeuver is common practice in interplanetary space travel because it allows the spacecraft to obtain energy from the gravitational interaction alone, without the aid of any propulsion engine. Calculations of the energy transfer attained in this process were performed by the mathematician Michael Minovitch in the early 1960’s at NASA’s Jet Propulsion Laboratory. Later on, the aerospace engineer Gary Flandro proposed the innovative gravity-assist technique that paved the way for the exploration of the Solar System by unmanned spacecraft.

In parallel with aerospace technology, precision measurement, and computation power has improved with time and in the first flyby of the Earth performed by the Galileo spacecraft on December 8, 1990, the navigation team lead by John D. Anderson found something unexpected. The outgoing velocity of the spacecraft was slightly larger than that predicted by orbital models; the discrepancy was only of 3.92 mm per second but enough to raise eyebrows in the physics and astronomy community. The signal for this anomaly was unmistakably clear in both the ranging and the Doppler data. Moreover, the anomaly returned with the second flyby of the Galileo two years later but, in this case, the sign was opposite meaning a decrement instead of an increment of velocity.

The largest magnitude of the anomaly to date has been found in the Earth flyby of the NEAR Shoemaker spacecraft, aimed toward the asteroid Eros. On January 23, 1998, the NEAR spacecraft approached the Earth at a minimum altitude of only 539 km and in the subsequent orbital analysis; it was found that the asymptotic velocity was larger by 13.46 mm per second. Since then, no other mission has found such a large value for a flyby anomaly but discrepancies of the same order of magnitude among theoretical models and observation have been found for the Cassini, Rosetta and Messenger flybys.

Although this difference amounts to the velocity of a snail, it is very important from a fundamental point of view, because it might imply that our present understanding of gravity or inertia is not complete. For a good reason, some of the possible explanations devised involve radical modifications of the present paradigm of physics: a possibility is a halo of dark matter that surrounds the Earth and it is carried along its orbit by Earth’s gravity. McCulloch has also suggested a modification of the law of inertia at small accelerations as a possible cause.

Anyway, at the present stage of this research, the characterization of the anomaly is the most crucial step because it could happen that further analysis would make it vanish like smoke as it happened in the past with many fortuitous findings. On the contrary, if future missions and enhanced mathematical analysis made it obvious that this effect is real, we will have a very important science case for the physics of gravity in the Solar system.

To obtain further evidence on the existence of this anomalous effect, Acedo from the Institute of Multidisciplinary Mathematics at the Polytechnic University of Valencia has developed an orbital model which includes all known sources of perturbations: the Sun, the Moon and the planets, the geopotential model of the Earth (which correspond to the deviations from sphericity), the ocean and the solid tides, magnetic fields, solar wind, atmospheric pressure, among others. Comparing this model with fittings provided by the mission teams to the real orbit, some evidence on anomalous forces acting upon the closest point to the Earth (the so-called perigee) or the orbit have been found. These forces are very small but enough, when integrated along the trajectory, to predict the discrepancies obtained by Anderson et al. on the asymptotic velocities of the spacecraft emerging from these close encounters. This author’s results were recently published in the Astrophysics and Space Science journal (Acedo, 2017).

It seems that the Earth is surrounded by a thin envelope of a few thousand kilometers in which these forces manifest themselves. This means that the forces would be short-ranged and decay very fast with altitude. Moreover, they also depend on the terrestrial latitude and, possibly, on the spacecraft velocity. Nothing like this is predicted by our present accepted theory of gravity, i. e., General Relativity. The reason why this interaction has managed to be hidden until now may be the consequence of the rarity of highly eccentric hyperbolic orbits in nature

Whether this can be ascribed to an unknown fifth force of nature of gravitational origin, or it is the consequence of overlooked conventional effects, only time and further research could tell.

These findings are described in the article entitled Anomalous accelerations in spacecraft flybys of the Earth, published in the journal Astrophysics and Space Science. This work was led by Luis Acedo from Universitat Politècnica de València.

This article cries out for for an understanding of how gravity works!

The laws of atomic gravity are solid and provide solutions to the biggest questions in modern physics. The 3 rules are so simple that high school students easily understand the principles confirming the simplicity by which nature works.

The laws of atomic gravity interconnect the sciences and can be applied to any area of research or study providing a perfect platform for innovation.

Seeking a mathematically adept wizard or group :::)

The three principles of atomic gravity which define how the force of gravity works in quantum atoms are defined both visually and in mathematical relationships and yet the equation eludes the brilliance behind the physics. Perhaps a mathematical mind can be applied to claim the elusive equation of everything?

If you are searching for a path to innovation within your field of study or research or perhaps you are just a mathematical brainiac then feel free to begin by exploring the google docs below.

Principles of Atomic Gravity

https://docs.google.com/document/d/e/2PACX-1vRTa9BoY64I0KsYrM1y7aRMONd7OrFm5RGIgPGA7PolB8hIXjF66azQOTu2yHWpl3uzw614aX6Ks-9q/pub

Zero ‘G’ flight at the Atomic Scale

https://docs.google.com/document/d/e/2PACX-1vRhOSAFyKb9r0kMaEGbLm-skalqF7UAXaqKQDq_RcJCWDAmOQCkbUvIIwih5DALMnqa6p7DzmQxAbzI/pub

If I have seen further it is by standing on the shoulders of giants.

— Sir Isaac Newton

Nature did not deem it her business to make the discovery of her laws easy for us.

— Albert Einstein

Principles of atomic gravity are a North American innovation.

If too busy to investigate the principles no worries floundering will turn to submersion as main stream beliefs slide down under. 🙂

I believe I have the answer to all the gravitational problems besetting physics.

My theory solves both the flyby anomalies and the ‘dark matter’ question.

It teaches a 3rd dimension of universal gravitation that follows Kepler’s idiom: Nature loves simplicity . . .”

I hope to publish one day.

What is required as a comment?

I have read the Valencia paper and am staggered by the depth of detail and scientific scholarship therein. It does not of course solve anything.

PWG