Orbital Decay and Atmospheric Re-entry

Atmospheric drag is the resistance experienced by an orbiting object when it collides with the extremely thin gases of the upper atmosphere. In low Earth orbit, this drag continuously removes orbital energy and angular momentum, causing the orbit to shrink until sustained atmospheric re-entry occurs.

How drag changes an orbit

Drag acts opposite to the object's velocity relative to the atmosphere. Its approximate magnitude is given by F = 1/2 rho Cd A v², where rho is atmospheric density, Cd is the drag coefficient, A is cross-sectional area and v is relative speed.

• A drag-induced reduction in speed makes the object fall toward a lower orbit rather than remain at its original altitude.
• For an eccentric orbit, drag is usually strongest near perigee, where atmospheric density and speed are greatest; repeated passages progressively reduce the orbit, especially its apogee.
• Although a stable lower circular orbit has a higher orbital speed, reaching it requires loss of total mechanical energy. This resolves the apparent paradox that drag slows an object but orbital speed later increases as it descends.

Why orbital decay accelerates

Atmospheric density increases sharply as altitude falls, so each lower passage generally produces more drag. This creates a positive feedback: energy loss lowers the orbit, the denser atmosphere increases drag, and subsequent energy loss becomes faster.

• Objects with a larger area relative to mass generally decay faster; resistance to deceleration is represented by the ballistic coefficient, commonly expressed as m divided by CdA.
• Solar ultraviolet heating and geomagnetic activity can expand the upper atmosphere, increasing density at orbital altitudes and shortening orbital lifetime.
• Decay rates also vary with altitude, atmospheric conditions, shape and orientation, so re-entry time cannot be predicted from altitude alone.

Transition to atmospheric re-entry

Once the orbit penetrates sufficiently dense atmosphere, drag overwhelms continued orbital motion and the descent becomes rapid and irreversible. Orbital kinetic energy is transferred mainly to the atmosphere, while intense aerodynamic heating and mechanical loads can cause ablation, melting and fragmentation.

• Small or low-melting-point components often burn up, while some compact, heat-resistant fragments may survive to the surface.
• Controlled re-entry targets a chosen region, whereas uncontrolled re-entry leaves the time and location dependent on uncertain decay conditions.

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