Differential Color Refraction (DCR) effect is position error caused by the atmosphere, bending blue and red light differently.
Johnson–Cousins system (BVRI) is color system used in astronomy which measures how bright an object looks through four color filters: B = blue, V = visible (green-yellow) R = red, I = infrared
Gaia system (G, BP, RP): is the modern color system used by the Gaia space telescope. Gaia measures brightness through: G = general (broad) brightness, BP = blue photometer, RP = red photometer
Scientists converted traditional Johnson–Cousins filter data (like B and I) into Gaia’s BP–RP color through a “hidden transformation,” they achieved high precision (errors below 0.01 magnitudes). They corrected the DCR effect and improved the accuracy of the satellites’ position.
To Measure the color of a natural satellite (like Himalia or Triton) in the Gaia color system (BP − RP), they created a mathematical transformation
Fundamental Transformation Equation
This equation adjusts raw brightness measurement to make it comparable to a standard reference system. This equation tells us how to correct the raw brightness measured by a telescope for atmospheric and instrumental effects so it matches a standardized, true brightness scale like Gaia’s.
Hidden Transformation equation
m is the instrumental magnitude, X is the air mass for the observation, M denotes the standard system magnitude (e.g., V), and CI indicates the standard color index (e.g., V − R).
K’ and k’’ are the first- and second-order extinction coefficients for filter f, Tf—the transformation coefficient, and ZPf—the nightly zero point
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