Powered by OpenAIRE graph
Found an issue? Give us feedback
image/svg+xml art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos Open Access logo, converted into svg, designed by PLoS. This version with transparent background. http://commons.wikimedia.org/wiki/File:Open_Access_logo_PLoS_white.svg art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos http://www.plos.org/ ZENODOarrow_drop_down
image/svg+xml art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos Open Access logo, converted into svg, designed by PLoS. This version with transparent background. http://commons.wikimedia.org/wiki/File:Open_Access_logo_PLoS_white.svg art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos http://www.plos.org/
ZENODO
Other literature type . 2025
License: CC BY
Data sources: ZENODO
image/svg+xml art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos Open Access logo, converted into svg, designed by PLoS. This version with transparent background. http://commons.wikimedia.org/wiki/File:Open_Access_logo_PLoS_white.svg art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos http://www.plos.org/
ZENODO
Other literature type . 2025
License: CC BY
Data sources: ZENODO
ZENODO
Other literature type . 2025
License: CC BY
Data sources: Datacite
ZENODO
Other literature type . 2025
License: CC BY
Data sources: Datacite
ZENODO
Other literature type . 2025
License: CC BY
Data sources: Datacite
ZENODO
Other literature type . 2025
License: CC BY
Data sources: Datacite
versions View all 5 versions
addClaim

Momentum Ledger Π∞: Improving Spacecraft Navigation and Propellant Performance A Technical White Paper for SpaceX Flight Dynamics and GNC

Authors: Cromwell, Tami Marie Tammy Marie Stomberg;

Momentum Ledger Π∞: Improving Spacecraft Navigation and Propellant Performance A Technical White Paper for SpaceX Flight Dynamics and GNC

Abstract

This technical white paper presents the Momentum Ledger (Π∞), a global momentum-flux framework derived from the integral form of energy–momentum conservation, ∇aTab=0,\nabla_a T^{ab} = 0,∇aTab=0, extended to a spacecraft control volume and its boundary at null infinity. Π∞ provides a unified method for modeling all untracked momentum leaving a space vehicle through thermal radiation, radio-beam recoil, ion-thruster plume asymmetry, reflectivity imbalance, outgassing, and other small but cumulative effects. These effects—typically of order mm/s in flybys and 10−10 m/s210^{-10}\ \mathrm{m/s^2}10−10 m/s2 in deep-space cruise—become mission-relevant for long-arc navigation, Mars transfers, solar-sail operations, high-power communications, and electric-propulsion architectures. This white paper focuses on practical engineering implementation for flight dynamics and GNC systems, including: real-time thermal and RF recoil modeling plume asymmetry estimation solar-photon imbalance detection integration of Π∞ into EKF and batch-least-squares navigation filters case studies relevant to SpaceX Starship interplanetary missions, EDL timing, and deep-space operations All equations and schematics are rendered natively in LaTeX/TikZ for clarity and reproducibility.This document is intended to accompany Module D: Boundary Momentum Flux in Radiative and Low-Thrust Dynamics (Zenodo DOI: 10.5281/zenodo.17624470), which contains the full mathematical derivation of Π∞.

Keywords

Solar physics, momentum flux Π∞ spacecraft navigation GNC thermal recoil radio-beam recoil plume asymmetry solar photon pressure boundary flux conservation laws deep space dynamics Starship SpaceX spacecraft force modeling, Heat (physics), Physics, boundary flux momentum conservation spacecraft dynamics radiation pressure thermal recoil solar sail Pioneer anomaly flyby anomaly Deep Space Network Zero Infinity Project Pi_infinity, Physics/education, Quantum physics, Nuclear physics, Particle physics, Physics/standards, Physics/instrumentation, Atomic physics, Plasma physics, boundary flux momentum conservation spacecraft dynamics radiation pressure thermal recoil solar sail Pioneer anomaly flyby anomaly Deep Space Network Zero Infinity Project Pi_infinity, Laser physics, Transport (physics), Mathematical physics, Space travel, Physics/methods, Mesoscopic physics, spacex, Space Research, momentum flux Π∞ spacecraft navigation GNC thermal recoil radio-beam recoil plume asymmetry solar photon pressure boundary flux conservation laws deep space dynamics Starship SpaceX spacecraft force modeling, Theoretical physics, Health Physics

  • BIP!
    Impact byBIP!
    selected citations
    These citations are derived from selected sources.
    This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
    0
    popularity
    This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
    Average
    influence
    This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
    Average
    impulse
    This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
    Average
Powered by OpenAIRE graph
Found an issue? Give us feedback
selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
0
Average
Average
Average
Green