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Radiation pressure refers to pressure exerted by electromagnetic radiation (EMR). Electromagnetic radiation has a momentum associated with the energy it carries, i.e., the EMR's energy divided by its speed (the speed of light (c)). Pressure on an object results when it absorbs, reflects, or emits radiation, the amount being such that the total momentum is conserved, the change in the object's momentum balanced by that of the incoming and/or outgoing EMR. EMR is typically in equilibrium only within a sufficiently large opaque body, so in other cases, there is generally a direction to the pressure. For example if all EMR present is moving in a single direction, it applies no pressure perpendicular to that direction. On the other hand, the pressure we feel from gas (i.e., the atmosphere) is generally within or close to equilibrium (when the air is still), applying pressure in every direction.
Radiation pressure is small enough to be negligible in everyday life, but can be significant when it is steady over long intervals, e.g., it is a factor in the navigation of interplanetary travel. It is also a factor in the dynamics of circumstellar disks. Small particles have a greater the ratio of cross-section-to-mass and react more to the push, which organizes the dust particles by size, the smaller ones out further in the disk. The pressure affects planet formation within those stages in which the solids are small, but the pressure's effects are too small to have much effect on subsequent planetary migration.
When radiation pressure is extreme, such as within or at the surface of a star, within a supernova, or surrounding an active galactic nucleus (AGN), it can definitely be a significant factor.