Measuring Earth’s Energy Imbalance via Radiation Pressure Accelerations Experienced in Orbit: Initial simulations for “Space Balls”

The direct measurement of Earth’s radiative Energy Imbalance (EEI) from space is a challenge for state-of-the-art radiometric observing systems. EEI quantifies the fundamental rate of global heating in response to radiative forcings and feedbacks and is tightly linked to the habitability of our planet. Current spaceborne radiometers measure the individual shortwave (Solar incoming and Earth reflected solar radiation) and longwave (Earth emitted thermal radiation) components of Earth’s energy balance with unprecedented stability, but with calibration errors that are too large to determine the absolute magnitude of global mean EEI or net radiative flux, respectively, as the components’ residual. Best estimates of multi-year (2005-2020) EEI are derived from temporal changes in planetary heat content, predominantly ocean heat content, and amount to ∼0.9 Wm-2. To monitor EEI directly from space, we propose an independent approach based on accelerometry that measures non-gravitational accelerations experienced in orbit, such as induced by, e.g., radiation pressure, aerodynamic drag, and variations in spacecraft shape. The general feasibility of deriving radiative fluxes from measured radial accelerations (in Earth radius direction) experienced by a near-spherical spacecraft has been demonstrated in the 1980’s and the current accelerometer capabilities have increased by several orders of magnitude since then, which may enable a measurement of net radiative flux to within 0.1% (0.3 Wm-2). A successful mission would require one or multiple near-spherical spacecrafts to reduce the parasitic impact of aerodynamic drag and other confounding forces related to attitude variations in orbit. To provide requirements for a prospective spacecraft and mission design, we develop a simulation environment for “Space Balls” using JPL’s Mission Analysis, Operations, and Navigation Toolkit Environment (Monte) software libraries. At its current initial stage, it allows us to simulate accelerations acting on a spherical spacecraft in radial, cross- and along-track directions due to solar radiation pressure, Earth’s reflected shortwave (albedo) and emitted longwave radiation, as well as due to aerodynamic drag. We find that the magnitude of simulated radial accelerations acting on a spherical spacecraft (r=50cm, m= 50kg) due to solar, Earth albedo and thermal radiation, as well as their sensitivity to mean orbit altitude and spacecraft absorptivity agrees well with back-of the-envelope calculationsand previous simulations that assessed the role of radiation pressure accelerations for orbital drift of LAGEOS. The variability along sun-synchronous orbits during equinox aligns with expectations and the input radiation data, portraying typical diurnal and zonal variability patterns in shortwave and longwave radiation for the orbit and epoch selected. Drag- induced radial acceleration, considered a confounding effect, is negligibly small (10-11 ms-2) for a spherical satellite at mean orbit altitude of 750 km or higher. Future investigations will expand the Monte-based simulation environment with additional shape and confounding force models, and study the impact of thermal gradients across the spacecraft skin as function of satellite spin frequency. Preliminary simulations with an integrated spacecraft dynamics model suggest main confounding accelerations for a non-perfect, faceted sphere are related to Yarkovsky, drag and relativistic effects, which will have to be mitigated to facilitate a high-accuracy EEI measurement from space.