  Recent observations of black hole shadows have revolutionized our ability to
probe gravity in extreme environments. This manuscript presents a novel
analytic method to calculate, in leading-order terms, the key parameters of
photon sphere and shadow radius. This method offers advantages for complex
metrics where traditional approaches are cumbersome. We further explore the
impact of black hole mass on the photon sphere radius, providing insights into
black hole interactions with their surroundings. Our findings contribute
significantly to black hole physics and gravity under extreme conditions. By
leveraging future advancements in observations, such as the next-generation
Event Horizon Telescope (ngEHT), this work paves the way for even more precise
tests of gravity near black holes.
