If Earth Fell Straight Into the Sun

If Earth Fell Straight Into the Sun

Earth would take roughly six months to plunge into the Sun if its orbital motion vanished, a result set by orbital mechanics and gravitational dynamics.

Orbital mechanics delivers a counterintuitive result: if Earth suddenly lost its sideways orbital motion and began falling radially toward the Sun, the plunge would last about as long as half a current orbit, roughly six months.

The key lies in how gravitational potential energy and kinetic energy are coupled in a bound two‑body system. As long as Earth moves on a nearly circular path, centripetal acceleration supplied by gravity matches the required orbital speed. Remove that tangential velocity and the same inverse‑square gravitational field now drives a purely radial infall. Solving Newton’s equation for this special case shows that the free‑fall time from the present orbital radius to the central mass equals half the orbital period of an ideal elliptical trajectory with the same semimajor axis.

This is a manifestation of Kepler’s laws and the conservation of mechanical energy, not an arbitrary coincidence. The motion can be treated as an extremely eccentric ellipse whose aphelion coincides with Earth’s current distance and whose pericenter lies at the Sun’s center. In that formulation, the crash corresponds to reaching the extreme of that ellipse after half a period. The same gravitational parameter that sets Earth’s current angular momentum and period therefore also fixes the timescale of its hypothetical terminal descent.

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