How To Calculate Circularization Ksp Kos

Estimate apoapsis circularization delta-v, burn time, and orbital speeds for Kerbal Space Program using the same core physics your kOS script will rely on.

What this calculator solves

• Current orbital speed at apoapsis or periapsis
• Target circular speed at the chosen altitude
• Required prograde or retrograde delta-v
• Estimated burn time from thrust, mass, and Isp

Core equations used

Vis-viva equation for local orbital velocity and Tsiolkovsky rocket equation for propellant-driven burn duration estimates.

These are the same concepts behind robust kOS maneuver automation.

Quick kOS workflow

• Read body mu and radius from the game environment
• Measure apoapsis and periapsis from the current orbit
• Compute desired circular velocity at burn radius
• Compute current local velocity from the transfer ellipse
• Schedule the burn centered on node or apsis passage

Expert Guide: How to Calculate Circularization in KSP with kOS

If you want reliable autonomous launches and orbit insertion in Kerbal Space Program, you need more than a rough feel for when to burn. You need a repeatable way to calculate circularization delta-v, understand where the number comes from, and convert that delta-v into a practical burn plan your kOS script can execute. The goal of circularization is simple: turn an elliptical orbit into a circular one by changing your orbital velocity at a chosen point, usually at apoapsis after launch or periapsis after a transfer. The execution, however, depends on orbital mechanics, unit conversions, and staging constraints.

In KSP and kOS, the most common scenario is a launch to a parking orbit around Kerbin. During ascent, your spacecraft rises until it reaches a planned apoapsis, perhaps 75 km to 100 km. If your periapsis is still below the atmosphere or even below the surface, your orbit is not stable. Circularization is the burn that raises periapsis to match apoapsis, creating a roughly circular parking orbit. This is where a maneuver node helps manually, but kOS shines because it can perform the same calculation every time and execute with precision.

What Circularization Actually Means

An orbit is circular when the orbital radius remains constant. In practical terms, that means apoapsis altitude and periapsis altitude are equal. If they are different, the orbit is elliptical. To circularize, you change your velocity at one of the apsides:

• Burn prograde at apoapsis to raise periapsis and create a circular orbit at apoapsis altitude.
• Burn retrograde at periapsis to lower apoapsis and create a circular orbit at periapsis altitude.

For ascent to low orbit, the first case is overwhelmingly the standard one. Your rocket reaches apoapsis with insufficient horizontal speed for a stable orbit, so you accelerate prograde until your local velocity matches the circular velocity required at that radius.

Circular speed at radius r: v_circular = sqrt(mu / r) Speed in the current ellipse at radius r: v_ellipse = sqrt(mu * (2 / r – 1 / a)) Semi-major axis: a = (r_apoapsis + r_periapsis) / 2 Circularization delta-v: delta_v = v_circular – v_ellipse

Here, mu is the body’s standard gravitational parameter, r is the orbital radius from the center of the body, and a is the semi-major axis of the current orbit. In KSP, altitude is shown above sea level, but the equations require radius from the body center. That means your script or calculator must add body radius to the displayed altitude.

Why kOS Players Need the Math, Not Just the Node

The stock maneuver node system can estimate circularization interactively, but kOS automation needs explicit numbers. A good script should know:

1. The current body radius and gravitational parameter.
2. The craft’s apoapsis and periapsis altitudes.
3. The current burn point, usually apoapsis.
4. The target circular velocity at that altitude.
5. The difference between current speed and target speed.

Once you know delta-v, you can estimate burn time using the rocket equation. Burn time matters because long burns should be centered around apoapsis rather than started exactly at it. If your burn takes 30 seconds, the ideal start time is around 15 seconds before apoapsis. More advanced scripts compensate for changing thrust-to-weight ratio, steering losses, and finite burn duration, but the simple centered-burn rule works very well for most ascent stages.

Effective exhaust velocity: ve = Isp * g0 Mass after burn: m1 = m0 / exp(delta_v / ve) Mass flow: mdot = thrust / ve Burn time: t = (m0 – m1) / mdot

In these equations, Isp is specific impulse in seconds, g0 is standard gravity at 9.80665 m/s², m0 is initial mass, and thrust must be in newtons. Since KSP displays thrust in kilonewtons and vessel mass often in tons, your script must convert units properly: 1 kN = 1000 N, and 1 t = 1000 kg.

Worked Example Around Kerbin

Suppose your ascent reaches an 80 km apoapsis while periapsis is still 30 km. You want to circularize at apoapsis around Kerbin. Kerbin’s radius is 600,000 m and its gravitational parameter is 3.5316 × 10¹² m³/s². Convert altitudes into orbital radii:

• Apoapsis radius = 600,000 + 80,000 = 680,000 m
• Periapsis radius = 600,000 + 30,000 = 630,000 m
• Semi-major axis = (680,000 + 630,000) / 2 = 655,000 m

Now compute the current velocity at apoapsis from the elliptical orbit and compare it with the circular velocity at the same radius. The resulting difference is the exact ideal impulsive delta-v needed to circularize. In a typical Kerbin ascent, the answer is often around 70 to 120 m/s depending on your profile. That range feels familiar to experienced players because launch guidance usually does most of the work before the final top-off burn.

The closer your periapsis already is to apoapsis, the smaller the circularization burn. A smooth gravity turn reduces insertion delta-v because it builds horizontal velocity earlier.

Reference Body Statistics for Common KSP Circularization Scenarios

The table below includes standard values used in many KSP calculators and scripting references. These numbers are useful when sanity-checking your script output.

Body	Radius (m)	Gravitational Parameter mu (m³/s²)	Example Low Circular Orbit	Approx. Circular Speed There (m/s)
Kerbin	600,000	3,531,600,000,000	80 km	2,279
Mun	200,000	65,138,398,640	15 km	550
Minmus	60,000	1,765,800,000	15 km	162
Duna	320,000	301,363,210,000	60 km	914
Eve	700,000	8,171,730,000,000	100 km	3,194
Jool	6,000,000	282,528,000,000,000	220 km	6,709

Notice how strongly circular speed depends on both body mass and orbital radius. Around Kerbin, low orbit speeds are over 2.2 km/s, while around Minmus they are only a small fraction of that. A kOS script that works beautifully around Kerbin can still fail elsewhere if body parameters are hard-coded or if atmosphere assumptions are not generalized.

Common Circularization Errors in kOS Scripts

Most circularization bugs come from one of a few predictable mistakes:

• Using altitude instead of radius. Orbital equations need radius from body center.
• Mixing units. kN versus N and tons versus kilograms are common traps.
• Ignoring finite burn time. Starting at apoapsis instead of centering the burn leads to overshoot.
• Using surface velocity instead of orbital velocity. Near atmosphere and rotation effects, that distinction matters.
• Burning too late. Long upper-stage burns can pass apoapsis before enough horizontal velocity is added.

When debugging a kOS circularization routine, print each intermediate value: current radius, semi-major axis, local orbital velocity, target circular velocity, and computed delta-v. If the final answer looks wildly wrong, the issue is usually visible in one of those terms.

Comparison Table: Typical Kerbin Parking Orbit Insertion Cases

The next table shows realistic examples for Kerbin circularization at apoapsis with different periapsis values. This is useful for intuition and mission planning.

Apoapsis Altitude	Periapsis Altitude Before Burn	Burn Point	Approx. Circularization Delta-v	Interpretation
80 km	-50 km	Apoapsis	About 320 to 360 m/s	Very vertical ascent, poor gravity turn, large insertion cost
80 km	10 km	Apoapsis	About 140 to 170 m/s	Usable ascent but not very efficient
80 km	30 km	Apoapsis	About 85 to 95 m/s	Typical clean launch profile
80 km	60 km	Apoapsis	About 30 to 40 m/s	Excellent gravity turn and upper stage timing

How This Connects to a Real kOS Script

In kOS, you can automate circularization by reading orbital data from the vessel and body. The calculator on this page mirrors that process. A practical script typically performs these steps:

1. Wait until a desired apoapsis is reached during ascent.
2. Coast until the vessel approaches apoapsis.
3. Compute circularization delta-v using body mu and current orbital geometry.
4. Compute expected burn time from current stage thrust, mass, and Isp.
5. Start the burn half the burn time before apoapsis.
6. Stop thrust when target periapsis or target orbital velocity is achieved.

A high-quality implementation also watches for staging changes. If your circularization burn spans a decoupler event, then mass, thrust, and Isp can all change. In that case, a single precomputed burn time may not stay accurate. The best scripts recalculate during flight or use a guidance loop that monitors remaining delta-v and orbital state in real time.

Manual Flight Versus Scripted Flight

Manual players often eyeball the navball and estimate insertion by watching periapsis rise. That approach is intuitive and fun, but scripting demands deterministic logic. Once your kOS routine is based on vis-viva and the rocket equation, it becomes transferable across launch vehicles and destinations. You can re-use the same control logic for Kerbin ascent, Mun orbit insertion, Duna parking orbits, or even periapsis circularization after aerobraking adjustments.

Authoritative Orbital Mechanics References

If you want to validate the physics behind your KSP calculations, these public references are excellent:

• NASA Glenn Research Center: Specific Impulse
• NASA JPL Solar System Dynamics: Astronomical and Physical Parameters
• MIT: Orbital Energy and Velocity Concepts

Even though KSP uses a scaled solar system, the same mathematical framework applies. That is why players who learn orbital mechanics through KSP often find real aerospace references surprisingly readable. The main difference is just the planetary constants.

Best Practices for Better Circularization Performance

• Launch with a smooth gravity turn so less delta-v is needed at apoapsis.
• Use upper stages with good vacuum Isp for orbital insertion burns.
• Center the burn on the apsis, especially when thrust is low.
• Recompute after staging if vessel mass or thrust changes materially.
• Keep your parking orbit high enough to avoid atmospheric drag on bodies with atmospheres.
• Prefer direct body parameter reads over hard-coded values when scripting.

Final Takeaway

To calculate circularization in KSP with kOS, you need two pieces of math: vis-viva to determine how fast you are moving at the burn point and the circular orbit formula to determine how fast you should be moving there. The difference is your required delta-v. Once you have delta-v, the rocket equation gives you a practical burn-time estimate. That pair of calculations is the foundation of a professional-grade autopilot script. Learn them once, implement them cleanly, and you will have a reusable orbit insertion method for nearly every mission profile in the game.

The calculator above gives you a fast mission-planning estimate, but it also doubles as a debugging tool for your automation. Compare your kOS output against it, verify your units, and tune your burn timing. Once the numbers agree, your script will stop guessing and start flying like it understands orbital mechanics.