How do migratory birds use the Sun as a compass?

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A herd of wildebeest, including calves, moves across a dusty savanna in Africa with scattered trees visible in the background. — Migration A herd of common wildebeest (*Connochaetes taurinus*) migrating across a dusty savanna in Africa. The animal is a keystone species (i.e., a species with a disproportionately large effect on its biological community) in plains and acacia savanna ecosystems from southeastern Africa to central Kenya.

Migratory birds utilize the Sun as a compass by integrating celestial observations with an internal clock to compensate for the Sun's movement across the sky throughout the day.1

There are two primary theories regarding this mechanism:

Sun Compass Theory: This suggests birds determine direction by measuring the horizontal angle from the Sun’s projection on the horizon. By compensating for the Sun's changing position, they maintain a constant heading.1
Matthews' Theory: Proposed by G.V.T. Matthews, this theory posits that birds observe the Sun’s arc. By measuring the Sun's maximum altitude (the angle relative to the horizon) and comparing it to their familiar habitat, birds can determine their latitude. Furthermore, by using their internal clock to compare the Sun's current position to its expected highest point at noon, they can derive information regarding their longitude.1

While these mechanisms explain how birds maintain direction, they are part of a broader system of celestial navigation that allows birds to establish a navigational "grid" for orientation and goal-directed flight.1