Spherical geometry explores shapes and measurements that lie on the curved surface of a sphere. This sets it apart from Euclidean geometry, which studies objects on a plane.

Compared to Euclidian geometry, properties of objects like spherical triangles and great circles also differ. For instance, in spherical triangles, the angles add up to more than $180^{\circ }$ because of the curved surface.

Additionally, measurements of side lengths and angles follow arcs of great circles instead of straight lines, resulting in different relationships between angles and sides.

Spherical geometry has various applications in fields such as astronomy and cartography. It is especially useful in navigation systems because it helps in determining the shortest routes between points on the Earth's surface and calculating the positions of stars.