Authors: Indranil Banik and Pavel Kroupa
First Author’s Institution: Helmholtz-Institut für Strahlen und Kernphysik (HISKP), University of Bonn, Germany
Status: Published in MNRAS (open access on ArXiV)
Humans have long dreamed of conquering the stars. Yet, even with the best of today’s technological capabilities, such an endeavour could take centuries. Since Newton’s incident with an apple, his theories of motion and universal gravitation have remained largely accepted save Einstein’s 1915 overhaul. Still, there remains observations that Newtonian dynamics cannot fully describe. One such observation is that of a galaxy’s rotation curve. We would expect a galaxy to rotate more slowly the further we move away from its center. It turns out that the rotation remains the same, and in some cases increases. The common solution to this problem is to invoke dark matter. This invisible matter accounts for the “missing mass” that enables galaxies to spin more than they otherwise should. MOdified Newtonian Dynamics (MOND) is an alternative theory of gravity that also attempts to account for these rotation curves. Instead of invoking dark matter, MOND alters the gravitational acceleration. This paper shows how this modified acceleration can alter the trajectory of interstellar probes.
To the MOND And Back
MOND modifies the gravitational acceleration by introducing an empirical constant a0. The distance from a star at which the modified acceleration and usual Newtonian acceleration differ by this constant a0 is called the MOND radius. For the Sun, the MOND radius is roughly 7kAU (i.e 7000 times the average distance from the Earth to the Sun). For comparison, the closest star to the Sun, Proxima Centauri, is roughly 268kAU away. In today’s paper, the authors consider a spacecraft travelling at 0.01 c where c is the speed of light. At this speed, it would take approximately 400 years to reach Proxima Centauri, but only 11 years to reach the MOND radius.
As expected, Figure 1 shows very little deviation between MOND and Newtonian mechanics for positions well within the MOND radius. However, there is a significant boost to the gravitational acceleration, particularly in the direction away from the galactic center (the negative x axis). Overall, gravitational acceleration in MOND is stronger than the expected Newtonian acceleration.
Modified Newtonian Trajectories
To examine the changes on spacecraft trajectories, the authors considered only the part of the journey beyond 2kAU from the sun. This limit corresponds to the point at which MOND starts to have non-negligible effects (see the change in the shade of blue in Figure 1).
Figure 2 shows how the stronger gravity that exists under MOND leads to a small but no doubt significant reduction in the velocity of an interstellar probe. Players of Kerbal Space Program would no doubt appreciate how small changes in velocity can
sometimes often result in catastrophic consequences. In this case, the changes are extremely small. The reduction of 3 cm/sec after 20 years corresponds to a two-way light travel time of 0.1 seconds, or a distance of 10−4 AU. Furthermore, the velocity reduction also results in the probe changing direction over time (see Figure 5 in the paper). Observers can thus verify MOND by measuring both the change in the downrange distance (i.e how far away the probe is) and the change in its angular position (which can be determined by interferometry).
Touching the Sky
Before humans can feasibly travel to other stars, precursor probes will necessarily have to be sent at relatively low speeds. As such, these probes could not only chart our next stage in space-faring capability, but also reveal the inner workings of gravity. MOND is not alone in challenging accepted theories of gravity: many other theories, such as the five-dimensional Kaluza-Klein theory and the elusive theory of everything have attempted to incorporate gravity as part of an overarching picture of how the Universe works. This paper shows that MOND is testable for it will affect the trajectories of interstellar spacecraft. All that’s left now is to reach for the stars.