Why is bound orbit energy negative?

The gravitational potential energy (negative) exceeds the kinetic energy, so the total is negative and the body cannot escape.

How does energy relate to orbit shape?

Energy depends only on the semi-major axis, not eccentricity. A circle and an elongated ellipse with the same a have the same energy.

The orbit is parabolic, corresponding to escape velocity at every point.

Find the specific mechanical energy of an orbit: epsilon = -G M / (2a).

Semi-Major Axis

Central Body Mass

Specific Orbital Energy

-29,432,232 J/kg

Specific Orbital Energy vs Semi-Major Axis

epsilon = -G M / (2a)

Negative energy = bound (elliptical) orbit

Zero = parabolic escape

Positive = hyperbolic trajectory

This quantity is constant along the entire Keplerian orbit.

ISS orbit with semi-major axis a = 6 771 km around Earth.

Compute speed in a circular orbit.

Find available velocity change.

Plan a two-burn orbit transfer.