A search for Planet Nine with small spacecraft:Three-body, post-Newtonian, non-gravitational, planetary and Kuiper Belt effects

Abstract

A hypothetical gravitating body in the outer Solar System, the so-called Planet Nine, was proposed to explain the unexpected clustering of the Kuiper Belt Objects. As it has not been observed via telescopes, it was conjectured to be a primordial black hole (of the size of a quince) that could be gravitationally detected by laser-launching or solar sailing many small spacecraft. Here, we study various aspects affecting such a search for Planet Nine. Our basic observable is the angular displacement in the trajectory of a small spacecraft which will be mainly affected by the gravity of Planet Nine, augmented with several other 3-body, non-gravitational, post-Newtonian, planetary, and Kuiper Belt effects. First, we calculate the effect of the Sun in the framework of the circular restricted three-body problem of the Sun--Planet Nine-spacecraft for the two particular initial conditions. Then, we study the effects of Kuiper Belt and outer planets, namely Jupiter, Saturn, Uranus, Neptune, as well as non-gravitational perturbations such as magnetic and drag forces exerted by the interstellar medium; and the solar radiation pressure. In addition, we investigate the post-Newtonian general relativistic effects such as the frame-dragging, Schwarzschild effect, and geodetic precession on the spacecraft trajectory. We show that the leading order angular displacement is due to the solar radiation pressure for the lower spacecraft velocities, and the drag force for the higher spacecraft velocities. Among the general relativistic effects, the frame-dragging has the smallest effect; and the Schwarzschild effect due to Sun has the largest effect. However, none of the general relativistic effects produces a meaningful contribution to the detection.

arXiv comment29 pages, 10 figures, matches the published version

References in corpus (22)

• Evidence for a Distant Giant Planet in the Solar System
• The Planet Nine Hypothesis
• The Breakthrough Starshot System Model
• What if Planet 9 is a Primordial Black Hole?
• Constraints on the location of a possible 9th planet derived from the Cassini data
• Generation of Highly Inclined Trans-Neptunian Objects by Planet Nine
• Constraints on the location of a putative distant massive body in the Solar System from recent planetary data
• Solar Obliquity Induced by Planet Nine
• Mass of the Kuiper Belt
• Electromagnetic forces on a relativistic spacecraft in the interstellar medium
• Preliminary constraints on the location of the recently hypothesized new planet of the Solar System from planetary orbital dynamics
• Science opportunities with solar sailing smallsats
• Perspectives on effectively constraining the location of a massive trans-Plutonian object with the New Horizons spacecraft: a sensitivity analysis
• A search for Planet Nine using the Zwicky Transient Facility public archive
• Tilting Uranus via Secular Spin-Orbit Resonance with Planet 9
• Detecting Planet 9 via Hawking radiation
• A candidate location for Planet Nine from an interstellar meteoroid: The messenger hypothesis
• The Brute-Force Search for Planet Nine
• What if planet 9 has satellites?
• Prospects for localising Planet 9 with a future Uranus mission
• Is the recently proposed Mars-sized perturber at $65-80\text{AU}$ ruled out by the Cassini ranging data?
• Motion of a testing particle in gravitational field of a ring