FirstPrinciplesa Physoly project
EN-11energytrap · Energy vs. momentum misuse

Bound orbits have negative total energy

  1. 01

    The tempting model

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

  2. 02

    Why it feels right

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

  3. 03

    Where it breaks · how to catch it

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

  4. 04

    The correct model

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

  5. 05

    Repair · see it, then test it

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

    Tempting move

    Positive, equal to K.

    Correct move

    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?

    Make a fresh prediction before referring to the worked example.

    Then practise it on the ladder

    R30Orbit energy bridgeadds: Bound gravitational orbits have negative total energy.