Tool 8 · Maneuver & Mission Design

Phasing Maneuver Calculator

Design a simple two-impulse phasing maneuver for catch-up or separation problems. Enter a circular reference orbit, the required phase angle change, and the number of phasing revolutions to estimate the phasing orbit period, semi-major axis, altitude limits, and total Δv.

What this tool computes

A phasing maneuver changes the spacecraft's orbital period so that it arrives back at the same reference point earlier or later than another object. This is useful in rendezvous, station-keeping preparation, constellation spacing, and ISS-style catch-up reasoning.

  • Reference circular orbit period
  • Required time lead or lag
  • Phasing orbit period
  • Phasing orbit semi-major axis
  • Perigee and apogee altitude estimate
  • Two-impulse Δv to enter and exit the phasing orbit

Core phasing idea

If the spacecraft needs to change its relative angular position by \(\Delta\theta\), the time offset over one reference orbit is connected to the target period by:

\[ \Delta t = \frac{\Delta\theta}{360^\circ}T_0 \]

For \(N\) phasing revolutions, the phasing orbit period is approximated as:

\[ T_p = T_0 \pm \frac{\Delta t}{N} \]

A shorter phasing period makes the spacecraft move ahead. A longer phasing period makes it fall behind.

Phasing orbit size

Once the phasing period is known, Kepler's third law gives the phasing orbit semi-major axis:

\[ a_p = \left[\mu\left(\frac{T_p}{2\pi}\right)^2\right]^{1/3} \]

This tool assumes the burn is made tangentially at the circular reference radius. The opposite apsis is then estimated using:

\[ r_{opposite}=2a_p-r_0 \]

How to interpret the result

  • Catch up / move ahead: use a shorter period phasing orbit.
  • Fall behind: use a longer period phasing orbit.
  • More phasing revolutions usually reduce the required period change and Δv.
  • Too aggressive a phase correction can drive the phasing orbit too low or physically impossible.

Educational simplification

This calculator assumes impulsive tangential burns and coplanar two-body motion. Real rendezvous planning also needs safety corridors, relative motion constraints, navigation uncertainty, and mission rules.

Interactive phasing calculator

Use positive angle magnitude. Direction is selected below.
Choose a preset, then adjust the phase angle and revolutions manually.

Results

Reference period

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Required time shift

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Phasing period

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Phasing semi-major axis

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Phasing altitude range

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Total Δv

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Interpretation

Run the calculator to estimate the phasing orbit and maneuver cost.

Reference orbit and phasing orbit
Relative phase closure

Assumptions and limitations

This tool assumes:

  • Circular reference orbit
  • Coplanar phasing orbit
  • Impulsive tangential burns
  • Two-body gravity only
  • No J2, drag, finite-burn losses, or collision-avoidance constraints
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