BUG: Flight.potential_energy has the wrong sign (decreases with altitude)

[yu010101]

Describe the bug

Flight.potential_energy becomes more negative as the rocket climbs. The implementation computes

standard_gravitational_parameter * total_mass * (1 / (self.z + self.env.earth_radius) - 1 / self.env.earth_radius)

which is negative for z > 0. The gravitational potential energy relative to sea level should be mu * m * (1 / R - 1 / (R + z)), which is positive and increases with z. Flight.total_energy inherits the sign error. The trajectory itself is not affected; only the potential_energy and total_energy outputs.

To Reproduce

Standard atmosphere, tabulated thrust, no data files. Between burn-out and apogee the mass is constant, so the change in potential energy should match m·g·Δz:

"""Minimal reproduction: Flight.potential_energy has the wrong sign (decreases as altitude increases).
Uses only the standard atmosphere and a tabulated thrust curve (no data files, no network)."""
import warnings; warnings.filterwarnings("ignore")
from rocketpy import Environment, SolidMotor, Rocket, Flight

env = Environment(latitude=32.990254, longitude=-106.974998, elevation=1400)
env.set_atmospheric_model(type="standard_atmosphere")
motor = SolidMotor(thrust_source=[[0, 0], [0.1, 1800], [1, 1700], [3, 1500], [3.8, 1400], [3.9, 0]],
                   dry_mass=1.815, dry_inertia=(0.125, 0.125, 0.002), nozzle_radius=0.033, grain_number=5,
                   grain_density=1815, grain_outer_radius=0.033, grain_initial_inner_radius=0.015,
                   grain_initial_height=0.12, grain_separation=0.005, grains_center_of_mass_position=0.397,
                   center_of_dry_mass_position=0.317, nozzle_position=0, throat_radius=0.011,
                   coordinate_system_orientation="nozzle_to_combustion_chamber")
rocket = Rocket(radius=0.0635, mass=14.426, inertia=(6.321, 6.321, 0.034), power_off_drag=0.5, power_on_drag=0.5,
                center_of_mass_without_motor=0, coordinate_system_orientation="tail_to_nose")
rocket.add_motor(motor, position=-1.255)
rocket.set_rail_buttons(0.0818, -0.618, 45)
rocket.add_nose(length=0.55829, kind="von karman", position=1.278)
rocket.add_trapezoidal_fins(n=4, root_chord=0.12, tip_chord=0.06, span=0.11, position=-1.04956)
flight = Flight(rocket=rocket, environment=env, rail_length=5.2, inclination=85, heading=0, terminate_on_apogee=True)

tb, ta = motor.burn_out_time, flight.apogee_time          # after burn-out the mass is constant
zb, za = flight.z(tb), flight.z(ta)
dpe = flight.potential_energy(ta) - flight.potential_energy(tb)
m = flight.rocket.total_mass(ta)
print(f"z: {zb:.1f} m -> {za:.1f} m (rising), constant mass {m:.3f} kg")
print(f"Delta potential energy reported: {dpe:+.1f} J")
print(f"m*g*dz (g=9.80665):              {m*9.80665*(za-zb):+.1f} J")
print("SIGN BUG" if dpe < 0 < za - zb else "ok")

Output on RocketPy 1.13.0:

z: 1981.8 m -> 4485.2 m (rising), constant mass 16.241 kg
Delta potential energy reported: -398754.6 J
m*g*dz (g=9.80665):              +398711.0 J
SIGN BUG

Expected behavior

With the two terms swapped, the same script gives +398754.6 J, within 0.01 % of m·g·Δz (the residual is consistent with g decreasing with altitude).

Screenshots

N/A

Additional context

• Same behaviour on RocketPy 1.10.0 (Python 3.9) and 1.13.0 (Python 3.14). The formula is unchanged on develop (a50d07d, 2026-09-14).
• Proposed fix in Flight.potential_energy: mu * total_mass * (1 / self.env.earth_radius - 1 / (self.z + self.env.earth_radius)). Happy to open a PR with a regression test, e.g. potential_energy(apogee) - potential_energy(burn_out) > 0.
• I searched issues and PRs for "potential energy", "potential_energy", "total_energy" and "mechanical energy" and found no report of this.