Using Modified Newtonian Dynamics to Calculate the Anomalous Acceleration of Oumuamua and Partially Predict the Additional Acceleration of 3I/ATLAS

Abstract

For any interstellar celestial body whose trajectory can be calculated using Newton's gravitational equation, there corresponds a unique trajectory corrected by kinematic gravitational effect. The parameters for calculating this corrected trajectory are derived from its simulated trajectory, substituting these parameters into the Modified Newtonian Dynamics equations will yield the uniquely corresponding corrected trajectory. Here using Modified Newtonian Dynamics (MOND) extended by Kinematic gravitational effect (KGE) calculated the anomalous acceleration of 1I/2017 U1'Oumuamua and made a partial prediction for the additional acceleration of 3I/ATLAS. Under the premise of excluding the gravitational influence of the planets in the solar system, during the period from Oct 19, 2017 to Jan 2, 2018, relative to the predicted trajectory position solely by the Sun's gravity, kinematic gravitational acceleration will lead to an extra trajectory deviation about 40,732 km in Oumuamua's trajectory, close to the 40,000 km given by astronomical observations. On Oct 25, 2017 12:00 at 1.36 AU the comparable acceleration caused by KGE is 2.68*10-6 m/s-2, which is very close to the value in orbital fits in 2018 that A1=2.7*10-6 m/s-2 the margin of error between them is less than 2%. Similarly, Atacama Large Millimeter Array (ALMA) indicated that 3I/ATLAS was 4 arcseconds away in Right Ascension from where it was supposed to be on October 29, 2025 if its trajectory was dictated by gravity. At perihelion, the observed non-gravitational acceleration A1 is about 134.26 km/day-2 radially, A2 is about 57.35 km/day-2 transversely. This equals an acceleration 146.00 km/day-2 or 0.0196 millimeter/s2 at moving direction, which is close to the MOND predicted comparable accelerations Ac1.36 and Akc1.36 of 139.97 km/day-2 or 0.01875 millimeter/s2 at moving direction, the margin of error is near 4%.