When we contemplate the beauty of the night sky, we are not aware that these bright stars are not actually in those positions. Due to a physical phenomenon related to the propagation of light, what we observe are virtual positions, displaced with respect to their real locations in the universe.

Knowing the precise location of celestial objects is crucial for studying the cosmos, and even more relevant if it is, for example, an asteroid that could impact the Earth.

This is because the light rays coming from the object are bent by an intense gravitational field, such as that of the Sun. The light that reaches us from them does not travel in a direct path.

Effect of the curvature of light rays, due to the intense solar gravitational field, on the positioning of a distant star. Credits: NASA.

The effect is greater when the light beams approach the massive body. But even at large angular separations between the emitting body (which can be a star) and the reflector (the Sun), these deviations can become very significant, especially when investigating high-precision astrometry .

A detailed knowledge of the initial positions of celestial bodies allows us to describe their orbits around the Sun more accurately, something that is particularly relevant when dealing with smaller bodies such as asteroids and even exoplanets in their movement around distant stars.

Combining optics and general relativity

This phenomenon of light deflecting when passing through a gravitational field had been known since Newton’s time. Thinking of light as tiny projectiles, the German scientist Johan Georg von Soldner obtained a first result for the angle of deflection of starlight when it grazes the solar disk . He obtained an astonishing 0.87 arc seconds (i.e. an angle 372,414 times smaller than a right angle).

It was not until the development of Einstein’s theory of general relativity that this value was doubled to the world-famous 1.75”. This result was confirmed experimentally by the British astronomer Arthur Eddington during his famous solar eclipse expeditions of 29 May 1919. That famous eclipse proved Einstein right and catapulted him to worldwide fame.

This NASA animation illustrates the effect of light rays bending as they approach an intense gravitational field such as that of the Sun. Credits: NASA, ESA, and Goddard Space Flight Center/K. Jackson.

Studying the mirage

Eddington claimed that the calculation could also be carried out (with a high degree of accuracy) in an alternative way, based on considerations of geometrical optics.

In this way, the effect of the curvature of light rays could be explained on the basis of the well-known phenomenon of mirages, caused by the curvature of light rays (refraction) in layers of air of varying density.

Illustration of a mirage in the desert when the warmer layers of air (close to the surface) have a different refractive index than the upper (colder) layers. As a result, the paths of the light rays coming from the object (the camel’s head), which pass through the different layers of air, reach the observer describing a curved path. Credits: Encyclopedia Britannica.

In a recent study published in the British astrophysics journal Monthly Notices of the Royal Astronomical Society , we propose a new theoretical result that would improve (in relation to previous studies) the precision in the positioning of objects in the universe, such as minor asteroids or distant galaxies.

In our work we address the calculation of the angle of deflection of light using this method (called Material Medium Approach or MMA), which dates back to the 1920s.

The PPN method to make Einstein’s equations easier

The exact calculation of this angle is not an easy task, since it involves solving complex differential equations within the framework of Einsteinian general relativity.

Approximate analytical solutions are often used based on the so-called post-Newtonian method (PPN) , which expresses Einstein’s complicated equations in terms of deviations from Newton’s law of universal gravitation up to different orders.

This PPN approach is widely used in astronomy to correct the positions of distant stars. This is what the European Space Agency’s GAIA observatory does, for example, to provide a highly detailed map of the stars in the Milky Way.

Our MMA calculation method accurately reproduces the angle of light deflection for a gravitational field like that of the Sun. And we find differences.

Discrepancy between the first-order PPN formalism and our new exact equation (optical MMA method) for the angle of light deflection, for solar system bodies (left panel) and extrasolar sources (right panel). The main light deflector is considered to be the Sun, with larger differences (in reddish-orange tones) for bodies in the asteroid belt.

Although they may seem like small discrepancies, they could be very significant in the positioning of minor objects in the solar system.

But all this will depend on the angular size of the star we are aiming at.

A better description of the orbits of minor bodies

One potential application of this new development would be a better determination of the orbits of smaller bodies around the Sun, such as asteroids. Greater precision in their initial positioning will lead to better prediction of their orbit.

An example of the application of our new result to the precise localization of asteroids and minor bodies in the Solar System. The illustration shows the particular cases of the asteroid Apophis (left panel) and Dimorphos (right panel).

We have taken two examples: the asteroids Apophis and Dimorphos . In both cases, the virtual positions recorded by a telescope (in orange) are displaced with respect to the real positions , calculated using the first-order PPN approximation (in red) and our exact MMA equation (in blue).

In the case of the asteroid Apophis, which is larger in angular size, this discrepancy in its positioning would not seem so relevant, although it would have to be taken into account in future calculations.

However, for Dimorphos there would be a significant delocalization, with possible implications for the proper calculation of its orbit.

Proxima Centauri and its exoplanet

Moving away from the Solar System, our theoretical result would also be applicable to the precise positioning of the closest star to the Sun, Proxima Centauri , and the exoplanet orbiting it, Proxima Centauri b .

Artist’s impression of the exoplanet Proxima Centauri b. Credits: ESO/M. KORNMESSER.

According to our calculations, the error committed would be similar to the angular size of said star, so a correction would then be necessary when carrying out a detailed study of the orbit of Proxima Centauri b.

A more precise map of the distribution of distant galaxies

Our theoretical result could also help in the more precise localization of distant galaxies distorted and magnified by large amounts of intermediate mass, such as galaxy clusters, through the so-called weak gravitational lensing phenomenon .

This could lead to more accurate maps of the mass distribution in galaxy clusters, which is particularly important in the era of the Euclid Space Telescope we are currently immersed in.

The mirage we see in the sky really becomes important when we need a precise calculation of the celestial object. We are getting more and more precise.

Author Bio: Oscar del Barco Novillo is Associate Professor. Department of Physics (Optics area) at the University of Murcia