USAAAO — 2025 First Round

Galileo the Tyrant has conquered the Earth. In his madness, he launched many bright satellites into space because he thought that the celestial equator should be visible from Earth, and not just be an imaginary line. These satellites all orbit around Earth 3RE from the surface, where RE is the radius of earth. However, there was a major mistake made in the plan – the satellites now orbit in a circle on Earth’s orbital plane instead of directly above the equator. Nevertheless, Galileo still forces all astronomers to use these satellites as the new Celestial Equator. They must calculate the declination for any star by finding the angle to the satellite at the same Right Ascension. What is the maximum absolute difference between the new declination and the old declination of bodies throughout the sky experienced by astronomers around the Earth? (Choose the closest value.)