Two boosts. A slower final orbit.
Start in a 2,000 km circular orbit with a transfer burn already previewed. Fire it, coast and hold at apoapsis, plan circularization there, and fire again. Compare your final speed with the initial 6.900 km/s.
FIELD NOTE 15 / ORBIT MANOEUVRES
One burn. A different orbit.
Change your velocity here. Discover what happens around the rest of the orbit.
0 h 00 min · 4 model minutes per real second
Current pathIf you fire nowTarget circleBefore last burn
P = periapsis, A = apoapsis; gold primes mark the preview. White arrow: velocity. Gold arrow: proposed Δv. Arrow lengths use separate scales; the vector diagram below uses one speed scale. Very large paths continue beyond the view.
Your spacecraft begins in a circular orbit, 2,000 km above Earth. The gold path previews a 500 m/s prograde burn.
- Altitude above the surface
- 2,000 km
- Current speed
- 6.900 km/s
- Total engine Δv used
- 0 m/s
BEFORE YOU FIRE
Preview the consequences.
The spacecraft stays at the same position during an ideal instantaneous burn. Its velocity changes, and a different orbit passes through that point.
| Orbital property | Current | After planned burn |
|---|---|---|
| Periapsis altitude | — | — |
| Apoapsis altitude | — | — |
| Orbital period | — | — |
| Eccentricity | — | — |
| Specific energy | — | — |
An engine burn changes orbital energy and can change angular momentum.
Speed changes along the way.
The trace records the actual flight. Speed jumps at an ideal burn and changes smoothly under gravity while you coast.
Follow the energy.
KineticPotentialTotal
Total orbital energy stays constant between burns. These plots retain the last six model hours.
Your burn history.
No burns yet. Preview a manoeuvre, then fire when you’re ready.
The spacecraft is coasting. Controls update the preview while the flight continues.
Make a prediction. Change one thing. See what happens.
Model notes & references ↗FOLLOW THE SCIENCE
An engine changes the orbit.
Gravity carries you through it.
A coasting spacecraft keeps falling under gravity. Its current position and velocity determine its unpowered path. A brief engine burn changes velocity, so the spacecraft begins following a different path through the same location.
From a circular orbit, a small prograde burn turns the burn location into the low point of a larger ellipse. The spacecraft climbs toward the opposite side, losing speed as it gains gravitational potential energy. A retrograde burn lowers the opposite side instead. NASA: changing orbits and transfer trajectories ↗
THREE FLIGHTS TO TRY
Let your intuition make a prediction.
Two braking burns. A faster final orbit.
Begin at 12,000 km and target 2,000 km. Fire the previewed retrograde transfer burn, coast and hold at periapsis, then plan and fire circularization. What happened to speed during the long fall between burns?
Where does a burn buy more energy?
Begin at periapsis of a 2,000 × 12,000 km ellipse. Preview 500 m/s prograde and note the energy gain. Coast to apoapsis without firing. Compare the same burn there. The Δv is equal; is the energy change?
Trial buttons deliberately restart the flight. Ordinary burn, target and view controls preserve time and motion. The eccentric trial supplies its starting orbit as an initial condition, so its Δv counter begins at zero.
One burn changes the far side first.
FROM A CIRCULAR ORBIT · PROGRADE
Speed up here. Climb away.
An ideal burn cannot instantly move you higher. It adds velocity at the same location. For a moderate prograde burn, that point becomes periapsis—the closest point—and apoapsis rises on the opposite side.
FROM A CIRCULAR ORBIT · RETROGRADE
Slow down here. Fall inward.
A moderate retrograde burn makes the burn location apoapsis. The new periapsis lies lower on the opposite side. The spacecraft then gains speed while falling toward it. Too much braking can make the path intersect Earth.
These simple opposite-side rules apply to tangent burns from a circle, or suitably sized tangent burns at an ellipse’s apsides. At other locations, radial motion matters: both apsis distances and the direction of the ellipse can change. Try the radial burn buttons and watch the preview.
Reaching the height is not the same as joining the circle.
A Hohmann transfer connects two coplanar circular orbits with a tangent ellipse. The first burn enters that ellipse. After half of the transfer orbit, the second burn matches the circular speed at the destination radius. Without it, the spacecraft follows the ellipse back again.
For an outward transfer, both burns are prograde. Yet the final circular speed is lower than the initial circular speed, because circular speed decreases with radius. The long coast between burns is part of the speed history. The raising trial here goes from 6.900 km/s at 2,000 km altitude to 4.658 km/s at 12,000 km altitude, using about 2,160 m/s total engine Δv. Bryan Weber: the Hohmann transfer ↗
Circular speed: vc = √(μ/r)
Transfer semimajor axis: at = (r₁ + r₂)/2
Coast time: t = π√(at³/μ)
Transfer semimajor axis: at = (r₁ + r₂)/2
Coast time: t = π√(at³/μ)
Speed changes. Unpowered orbital energy does not.
As the spacecraft falls, gravitational potential energy becomes kinetic energy. As it climbs, the exchange runs the other way. Between burns, the sum stays constant in this two-body model. Engine burns create steps in the spacecraft’s orbital-energy trace.
Specific orbital energy: ε = v²/2 − μ/r
Vis-viva: v² = μ(2/r − 1/a)
Bound-orbit period: T = 2π√(a³/μ)
Vis-viva: v² = μ(2/r − 1/a)
Bound-orbit period: T = 2π√(a³/μ)
Specific energy means energy per unit spacecraft mass. Negative total energy corresponds to a bound orbit. Zero is the parabolic escape threshold; positive energy gives a hyperbolic escape path. An open trajectory has no repeating orbital period or finite apoapsis. A bound mathematical ellipse can still intersect Earth; being bound does not make it a safe orbit.
The same Δv can change the energy by different amounts.
For an instantaneous burn, position and gravitational potential energy stay fixed. Expanding the kinetic-energy difference gives:
Δε = v⃗ · Δv⃗ + ½|Δv⃗|²
The dot product makes direction important. It also shows why an equal prograde Δv adds more orbital energy when the spacecraft is already moving faster. Compare the preview at periapsis and apoapsis of the eccentric trial. This is the core of the Oberth effect; it concerns orbital energy gained per velocity increment.
Δv is an engine budget, not your final speed minus your initial speed.
The counter adds the magnitudes of all fired velocity changes. Gravity also changes speed during coasting. Actual propellant mass depends on the engine’s effective exhaust speed and the spacecraft’s changing mass; this experiment does not assign kilograms of fuel.
A radial burn changes the shape in a different way.
Radial out and radial in point along the line between Earth and the spacecraft. At that instant they leave specific angular momentum unchanged, because r⃗ × Δv⃗ = 0. They generally change orbital energy and reshape the path. Prograde, by contrast, follows the full velocity vector, which need not be perpendicular to the radial direction on an ellipse.
The mathematics, assumptions & references
States, impulses and orbit geometry
The spacecraft is a massless test particle in a fixed, spherical Earth gravity field, with μ = 398,600.4418 km³/s² and R = 6,371 km. All motion is confined to one plane. Internal units are kilometres, seconds and kilometres per second. Burn controls and the Δv budget display metres per second. Altitudes subtract R; equations use centre-to-centre distances.
r⃗after = r⃗before
v⃗after = v⃗before + Δv⃗
h = x vy − y vx
e⃗ = [(v² − μ/r)r⃗ − (r⃗ · v⃗)v⃗]/μ
p = h²/μ · rp = p/(1 + e)
ra = a(1 + e), for bound ellipses
v⃗after = v⃗before + Δv⃗
h = x vy − y vx
e⃗ = [(v² − μ/r)r⃗ − (r⃗ · v⃗)v⃗]/μ
p = h²/μ · rp = p/(1 + e)
ra = a(1 + e), for bound ellipses
The current and previewed orbits are recomputed from those states. P and A denote the current periapsis and apoapsis; primes denote the planned orbit. A nearly circular orbit has no meaningful unique apsis direction, so apsis shortcuts are disabled there. Retrograde means opposite the current velocity, even if a previous large burn has reversed the direction of travel. Circularization removes radial velocity and sets √(μ/r) in the existing direction of angular momentum; the zero-angular-momentum limiting case uses counterclockwise motion. Bryan Weber: state vectors and orbital elements ↗
Transfer calculations
Δv₁ = √[μ(2/r₁ − 1/at)] − √(μ/r₁)
Δv₂ = √(μ/r₂) − √[μ(2/r₂ − 1/at)]
Budget = |Δv₁| + |Δv₂|
Δv₂ = √(μ/r₂) − √[μ(2/r₂ − 1/at)]
Budget = |Δv₁| + |Δv₂|
These signed tangent increments are positive for raising and negative for lowering a circular orbit. The transfer-planning button is available only while the current orbit is circular. It plans the first increment from the current radius to the selected target radius. It does not fire either burn. Circularization is a separate vector calculation at the current position; to complete the intended transfer, first coast to the opposite apsis.
The target is a circular reference path, not another spacecraft. The model does not solve rendezvous timing, plane changes, launch trajectories, finite-thrust steering, propulsion efficiency, Earth oblateness, atmospheric drag, lunar or solar perturbations, or navigation uncertainty.
Time, intersections and numerical method
Coasting uses universal-variable Kepler propagation, with Stumpff functions and a bracketed Newton solution. Each coast segment is evaluated from the state immediately after its latest burn, avoiding accumulated integration drift. The same formulation covers ellipses, near-parabolic motion and hyperbolas. Surface-intersection time is found before propagation so the spacecraft stops at its first future crossing of r = R, including after a high-altitude coast. Radial limiting trajectories use their time-of-flight relations.
Coast & hold shortcuts advance the same flight to the next apsis and explicitly pause there, stopping earlier if the surface is reached. They consume no Δv. Pressing Play continues from that exact point. Regular controls only alter the preview or reference circle. Explicit restarts clear time, history and the Δv budget. The manual burn amount returns to zero after firing to make the completed action clear. Reduced-motion preferences start playback paused; hidden tabs freeze model time.
Flight plots sample every 30 model seconds and retain six hours. Both sides of each impulse are recorded at the same time, so speed and energy jumps remain vertical. The log shows the most recent burns while the accumulated Δv includes every burn since restart. Distances share one geometric scale; spacecraft and markers are enlarged. Fit paths limits the view to an 85,000 km centre-to-edge radius; very large or open trajectories are clipped, with a direction marker when the spacecraft is outside the view.