The Retrograde Burn That Drops Perigee into the Atmosphere

Essence: A ship in a circular orbit stays there until its energy changes. A short retrograde burn does not "point the ship down." It lowers the opposite side of the ellipse into the atmosphere, and drag does the rest.

First Principles Foundation

Specific mechanical energy and the vis-viva equation are the same laws as for insertion:

ε = v² / 2 − μ / r = −μ / (2a)

v² = μ (2/r − 1/a)

μ = 3.986004418 × 10⁵ km³/s². For a circle, a = r and v = √(μ / r).

Angular momentum sets which point is highest. A purely retrograde burn at one point on a circle reduces speed there and leaves that point as apogee. The new perigee is on the opposite side of the ellipse:

r_p = 2a − r_a

with r_a equal to the radius where the burn happened. If r_p reaches the dense atmosphere, drag is no longer a small perturbation. It removes orbital energy over the pass, or over a few passes, and the trajectory decays. That is a deorbit. It is the time-reverse of raising perigee with a prograde burn, using the same equation.

Step-by-Step Derivation

Start from the published Flight 14 altitude, approximately 275 km. With a volumetric mean Earth radius of 6371 km, r = 6646 km and the circular speed is 7.744 km/s. The period is 89.9 minutes. Three hours in that orbit is about two revolutions. SpaceX said "after 3 hours," so the revolution count is that arithmetic, not a published rev number.
Choose a perigee inside the atmosphere. An 80 km altitude is a conventional top of the dense atmosphere for this kind of estimate: r_p = 6371 + 80 = 6451 km. It is a teaching threshold, not Flight 14's targeted perigee, which has not been published as a flown number.
The burn point stays the apogee, r_a = 6646 km. The new semi-major axis is

a = (6646 + 6451) / 2 = 6548.5 km

Speed at apogee on that ellipse:

v_a = √[ 398600.4418 × (2/6646 − 1/6548.5) ] = 7.686 km/s

The retrograde Δv from the circle is

Δv = 7.744 − 7.686 = 0.058 km/s = 58 m/s

Drop the aim to a surface graze, r_p = 6371 km, and the same steps give about 82 m/s. Between a high atmospheric perigee and a ground graze, the whole family of deorbit burns from this altitude sits near 60–80 m/s.
Assumptions. Impulsive burn exactly retrograde, at a point on a circular orbit, two-body gravity, no drag until perigee. A finite burn, a non-circular starting orbit, Earth oblateness, and a lift-modulated entry all change the meters per second. They do not change the direction: retrograde lowers perigee; prograde raises it.

Application to SpaceX / xAI

SpaceX's Flight 14 plan called for a deorbit burn on a single Raptor, listed on the published timeline as about 11 seconds (T+08:52:37 to T+08:52:48), after roughly six orbits and nearly 10 hours, with splashdown in the Pacific west of Chile. The page also said the ship would not enter orbit at all unless the team was confident it could still perform that burn. The 58 m/s scale is why a single engine and a few seconds are the right order of magnitude for a ship that has already reached orbital speed. This article does not claim the flown burn lasted 11 seconds or delivered 58 m/s. Those are the plan and the textbook ellipse, respectively.

What flew was shorter in time on orbit. On September 28, 2026, SpaceX posted that flight teams would deorbit Starship to a pre-cleared Pacific area after about three hours in orbit, then that the deorbit burn was complete, then that the ship was reentering, then that splashdown was confirmed. Elon Musk called the flight the first successful orbital flight of Starship. The early end of the orbital coast — three hours against a published nearly ten — is SpaceX's own statement. Reuters attributed the shortening to an engine problem seen on the webcast. The deorbit and the splashdown are the part SpaceX confirmed directly.

Super Heavy's splashdown in the Gulf of America was a separate, earlier event. It is not this burn. The deorbit burn belongs to the ship, after the satellites were already released.

Implications and Limits

Insertion and deorbit are one budget. The prograde burn that lifts perigee out of the atmosphere has to be matched, later, by a retrograde burn that puts perigee back in. Until the second burn, the vehicle is a long-lived object. That is why orbital flight tests carry a disposal plan and why the insertion decision was gated on deorbit hardware.

A 58 m/s error does not "miss the planet." It misses the atmospheric corridor. Too little Δv leaves perigee too high and the ship stays up. Too much drives perigee into the ground or into a steeper entry than the heat shield and the attitude profile were built for. Flight 14's published entry sequence after the burn — entry, transonic, a landing flip, and a landing burn — is the controlled-splashdown version of arriving in that corridor. SpaceX confirmed the sequence happened through splashdown. It did not, in the posts used here, publish the flown Δv or the peak heating.

Drag, not the rocket, removes almost all of the 7.7 km/s. The engine's job is only to move perigee. Once the ship is in air that is thick enough, the energy leaves as heat. How that heat is survived is a different lesson.

Sources & Further Reading

SpaceX, Starship Flight 14: spacex.com/launches/starship-flight-14 (single-Raptor deorbit; published timeline near T+8:52; Pacific splashdown west of Chile on the nearly-10-hour plan; insertion gated on deorbit redundancy).
@SpaceX, September 28, 2026: deorbit after about three hours to a pre-cleared Pacific area; "Deorbit burn complete"; reentry; "Splashdown confirmed" on the first orbital flight. Separate post: Super Heavy splashed down in the Gulf of America.
@elonmusk, September 28, 2026: first orbital flight successful; all 26 Starlink V3 satellites operating nominally after deploy.
Reuters, September 28, 2026, on the mission being shortened after an engine shutdown reported from the webcast.
Vis-viva equation, two-body problem. μ = 3.986004418 × 10⁵ km³/s². The 80 km perigee used in the worked example is a conventional atmospheric threshold for the estimate, not a SpaceX target.

Independent educational fan project. Not affiliated with Space Exploration Technologies Corp. (SpaceX) or xAI Corp. All content is for educational purposes. Sources cited where applicable.