Bound orbits have negative total energy

The mistake

Assuming a satellite in orbit has positive total mechanical energy because it is moving.

Why it feels right

Kinetic energy is positive and visually obvious; gravitational potential is negative by convention.

How to catch it

You decide escape or orbit from speed alone without total energy.

The first principle

For gravity with U = 0 at infinity, bound orbits have E = K + U < 0. Escape requires E ≥ 0.

worked mini-example

A satellite in a circular orbit has K = GMm/(2r). What is total energy?

Common wrong move

Positive, equal to K.

Correct

E = -GMm/(2r), because U = -GMm/r.

Test the repair EN-11 · transfer

Using U = 0 at infinity, which total energy corresponds to the threshold of escape from gravity?

E < 0 E = 0 E = U Any positive kinetic energy

Make a fresh prediction before referring to the worked example.