Phase Angle KSP Transfer Calculator

Calculator

Transfer type

Origin orbit radius

Target orbit radius

Gravitational parameter

Current origin angle, degrees

Current target angle, degrees

Phase tolerance, degrees

Parking altitude adjustment

Delta v correction percent

Example Data Table

Mission example	Origin radius	Target radius	Parent body parameter	Use case
Kerbin to Duna style transfer	13,599,840,256	20,726,155,264	1.1723328e18	Outer transfer phase check
Duna to Kerbin style transfer	20,726,155,264	13,599,840,256	1.1723328e18	Inner transfer phase check
Low orbit to moon style transfer	680,000	12,000,000	3.5316e12	Local parent transfer

Formula Used

The calculator uses a circular, coplanar Hohmann transfer model.

Transfer semi-major axis:

a_t = (r₁ + r₂) / 2

Transfer time:

t_t = π √(a_t³ / μ)

Orbital period:

T = 2π √(r³ / μ)

Angular speed:

n = 360 / T

Required phase angle:

φ = 180° - n_target × t_t

Current phase angle:

φ_current = θ_target - θ_origin

Synodic period:

S = 360 / |n_target - n_origin|

Velocity estimates:

v = √(μ / r)

v_transfer = √(μ(2 / r - 1 / a_t))

How to Use This Calculator

Enter the origin orbit radius.
Enter the target orbit radius.
Enter the parent body gravitational parameter.
Enter current origin and target angles.
Add phase tolerance for a planning range.
Add parking altitude when needed.
Add a correction percent for practical delta v margin.
Press calculate to view the result above the form.
Use CSV or PDF buttons to save your result.

Understanding Phase Angle Planning

A phase angle is the angular gap between two orbiting bodies. In transfer planning, it tells where the target should be before the departure burn. The calculator uses orbital radius, gravitational parameter, and current positions to estimate that gap. It is useful for KSP style mission design, problems, and transfer checks.

Why Phase Angle Matters

A craft does not fly directly to a planet in most efficient transfers. It follows an ellipse. During that transfer, the target keeps moving around the parent body. The required phase angle places the target where the craft will arrive. If the target starts too far ahead or behind, the craft reaches empty space. Good timing saves fuel. It also reduces correction burns.

Core Orbit Ideas

The tool assumes circular, coplanar orbits. This keeps the mathematics clear. The transfer ellipse has a semi major axis equal to the average of the two orbital radii. Its travel time is half of that ellipse period. The target motion during this time is subtracted from one hundred eighty degrees. That gives the required starting angle. A positive signed value means the target leads the origin. A negative value means it trails.

Reading the Results

The current phase is measured from the origin body to the target body. The phase error shows how much the current setup differs from the ideal setup. The waiting time estimates when the same phase will occur again. The synodic period shows the full repeat cycle between both orbits. The delta v values are optional planning estimates. They use ideal Hohmann equations and ignore losses.

Practical Use

Use consistent units. If radius is in meters, use the gravitational parameter in cubic meters per second squared. The output time will be in seconds. Larger radii and smaller gravity create longer transfers. Small angle errors can still matter on long routes. Use the tolerance value to set a safe planning band.

Limits and Accuracy

Real missions can involve eccentric orbits, inclination changes, atmosphere, and manual steering. KSP maneuvers may also include patched conics and encounter tuning. Treat the result as a strong first estimate. Then refine the burn with map view, maneuver nodes, and correction burns near the middle of the transfer.

FAQs

What is a phase angle?

It is the angular separation between the origin body and the target body. For transfer planning, it tells where the target should be before departure.

Does this calculator work for inner and outer transfers?

Yes. Enter both orbit radii. The calculator identifies the direction from the radius values and applies the same transfer timing logic.

What units should I use?

Use consistent units. If radii are in meters, use the gravitational parameter in cubic meters per second squared. The time output will be seconds.

What does a negative phase angle mean?

A negative signed phase means the target trails the origin. A positive signed phase means the target leads the origin.

Why is my wait time large?

The wait time depends on relative angular speed. Similar orbital periods make the phase repeat slowly, so the next window can be far away.

Is the delta v exact?

No. It is an ideal Hohmann estimate. Real burns can need extra margin because of steering, atmosphere, inclination, and encounter corrections.

Can I use this for eccentric orbits?

This page assumes circular, coplanar orbits. Eccentric or inclined paths need more advanced orbital methods and manual verification.

Why add a tolerance value?

Tolerance creates a practical angle band. It helps you decide whether the current phase is close enough for planning or testing.