Testing gravity with interstellar precursor missions

Abstract

We consider how the trajectory of an interstellar precursor mission would be affected by the gravity of the Sun in Newtonian and Milgromian dynamics (MOND). The Solar gravity is ≈ 50% stronger in MOND beyond a distance of ≈ 7000 astronomical units, the MOND radius of the Sun. A spacecraft travelling at 0.01 c reaches this distance after 11.1 years. We show that the extra gravity in MOND causes an anomalous deceleration that reduces its radial velocity by ≈ 3 cm/s and the twoway light travel time from the inner Solar System by ≈ 0.1 seconds after 20 years. A distinctive signature of MOND is that the gravity from the Sun is not directly towards it. This is due to the non-linear nature of MOND and the external gravitational field from the rest of the Galaxy, which we self-consistently include in our calculations. As a result, the sky position of the spacecraft would deviate by up to 0.2 mas over 20 years. This deviation is always in the plane containing the spacecraft trajectory and the direction towards the Galactic Centre. By launching spacecraft in different directions, it is possible to test the characteristic pattern of angular deviations expected in MOND. This would minimize the chance that any detected anomalies are caused by other processes like drag from the interstellar medium. Such confounding factors could also be mitigated using an onboard accelerometer to measure non-gravitational forces. We briefly discuss how the gravity theories could be conclusively distinguished using a Cavendish-style active gravitational experiment beyond the Sun's MOND radius.

The Global Stability of M33 in MOND

“…Φ has a rather complicated behaviour if internal and external fields are comparable (e.g. Thomas et al 2018;Banik & Kroupa 2019). However, it is possible to obtain Φ analytically if the boundary is external field dominated, i.e.…”

“…An interesting situation where disk precession does matter is the bifurcation apparent at large r in our cylindrical rz projection (Figure 15). * Banik & Kroupa (2019) provides a visualization of the point mass gravitational field when gext = 1.78 a 0 , the value appropriate to the Solar neighbourhood of the Milky Way (McMillan 2017). This is because the mean height of the disk is z ∝ sin φ, where φ is the azimuthal angle measured from the line of nodes with respect to the initial disk plane (in this case, the x-axis).…”

The local dark sector

“…With these caveats in mind, rough orders of magnitude allow us to expect to be able to send a probe of mass less than 1000 kg to hundreds of AU in two to four years, which would make it a viable mission. Recently, [19] showed how a similar mission (though in a slightly different context) can be feasible.…”

“…We could in particular enter a new intermediate regime that bridges GR in the Solar System and "dark energy gravitation" at cosmological scales. Additionally, we would approach MOND's acceleration, thereby allowing us to directly test MOND [19].…”

Detailed numerical implementation of the wide binary test

“…Only one force library is needed because all WBs in the Solar neighbourhood feel almost the same Galactic external field, but the library must be stretched and scaled to cover different M (Banik & Zhao 2018b). This force library is visualised in (Banik & Kroupa 2019). The WB orbit library in MOND exploited this symmetry and was similarly expensive to prepare, though the Newtonian WB orbit library took ≈ 5× less as it considered only one WB mass (arbitrarily fixed at 1.5 M⊙) and did not need to consider different angles between the orbital pole and the Galactic EFE (towards the Galactic centre).…”