Shkadov Thruster Migration Calculator

A Shkadov thruster (sometimes called a Class A stellar engine) is a proposed way for an extremely advanced civilization to move an entire star—along with its planets—using the star’s own light. The idea is conceptually simple: place a huge, highly reflective mirror/sail so that it intercepts and reflects some fraction of the star’s radiation in one preferred direction. Because photons carry momentum, reflecting them produces a net reaction force on the star. The force is tiny, but it can act for millions to billions of years.

Introduction: What this calculator estimates

This calculator estimates:

• Thrust from anisotropic radiation pressure (newtons, N)
• Acceleration of the star (m/s²)
• Time to cover a chosen migration distance assuming constant acceleration (years)

The model is intentionally simplified so you can see the scaling with luminosity, intercepted fraction, mass, and distance.

Symbols and inputs

• L = stellar luminosity (W = J/s)
• f = mirror/interception fraction (0 to 1). Interpreted here as “fraction of total stellar power whose photon momentum is redirected to create net thrust.”
• M = stellar mass (kg)
• D = migration distance (light-years, ly) converted internally to meters
• c = speed of light (m/s)

Core physics and formulas

Light carries momentum. For a beam with power P, the momentum flux depends on how it interacts with a surface:

• Absorbing surface: force ≈ P/c
• Perfectly reflecting surface: force ≈ 2P/c (photon momentum reverses, doubling the impulse)

In the simplified Shkadov picture, a mirror causes a net anisotropy by redirecting a fraction f of the star’s luminosity. Taking ideal reflection, the thrust is:

Thrust

Once the thrust is known, the star’s acceleration is simply Newton’s second law:

Acceleration

For travel time, this calculator assumes constant acceleration from rest in a straight line. With constant a, distance is:

Distance under constant acceleration

Solving for time:

Time to cover distance D

Unit note: the input distance is in light-years; internally you convert using 1 ly ≈ 9.4607×10¹⁵ m.

Interpreting the results

• Thrust (N): Even for a Sun-like star and large f, this is typically on the order of 10¹⁸ N. That sounds huge, but stars are extremely massive.
• Acceleration (m/s²): This number is usually extremely small (often around 10⁻¹² to 10⁻⁹ m/s²). Small acceleration sustained over long times can still yield meaningful velocity changes.
• Time (years): Because the time scales as t ∝ 1/√a, doubling f or L reduces time by √2; increasing mass increases time as √M.

Worked example (Sun-like defaults)

Using the default values shown in the form (roughly Sun-like):

• L = 3.828×10²⁶ W
• f = 0.5
• M = 1.989×10³⁰ kg
• D = 1 ly

Thrust:

• F = 2 f L / c ≈ (2)(0.5)(3.828×10²⁶)/c ≈ 1.28×10¹⁸ N

Acceleration:

• a = F/M ≈ (1.28×10¹⁸)/(1.989×10³⁰) ≈ 6.4×10⁻¹³ m/s²

Time for 1 ly (D ≈ 9.46×10¹⁵ m):

• t = √(2D/a) ≈ √(2×9.46×10¹⁵ / 6.4×10⁻¹³) ≈ 5.4×10¹⁴ s ≈ 1.7×10⁷ years

So, in this idealized model, moving a Sun-like star by ~1 light-year takes on the order of tens of millions of years even with an enormous mirror that effectively redirects half the star’s output.

Scaling comparison table

The relationships below help you sanity-check outputs and understand what matters most.

Assumptions & limitations (important)

• Ideal reflectivity: Uses F = 2 f L / c, effectively assuming perfect reflection and that the intercepted fraction contributes fully to net thrust. Any real reflectivity < 1 reduces thrust.
• Geometry folded into f: In reality, the thrust depends on mirror shape, angular distribution of stellar radiation, and what portion of light is actually redirected into a useful anisotropy. Here, f is a catch-all parameter.
• Constant luminosity: Stellar luminosity changes over stellar evolution. This model keeps L constant.
• Constant mass: Ignores mass loss from stellar wind and radiation over long timescales, which would slightly change M and a.
• Constant acceleration, straight-line motion: Uses simple kinematics from rest and does not include guidance, station-keeping, or changing thrust direction.
• Neglects external gravity: Ignores the galactic gravitational potential, nearby stars, and the star’s orbital motion around the galaxy, all of which matter for real trajectory planning.
• Neglects interaction with planets: In practice you would care about how slowly changing acceleration affects orbital stability and habitability; this calculator only treats the star as a point mass being pushed.
• Non-relativistic treatment: For the kinds of accelerations here, speeds remain far below c for many scenarios, but if you were to model extremely long durations/distances you would eventually need to check relativistic regimes.
• Engineering feasibility not assessed: The calculator does not evaluate mirror size, equilibrium position, material limits, thermal loading, or control systems—only the momentum accounting and basic kinematics.

Practical tips

• If your time seems “too long,” try increasing f first (up to 1), then consider how much more luminous stars can be compared to the Sun.
• If you are exploring migration of low-mass vs high-mass stars, note that time grows with √M, so massive stars are harder to move even though they can be very luminous—there is a tradeoff.
• For very long distances, remember that the star also has an existing galactic orbital velocity; “migration” in practice may mean altering an orbit rather than traveling from rest in interstellar space.

How to use this calculator

1. Enter Star Luminosity (watts) using the unit or time period shown by the field.
2. Enter Mirror Fraction of Stellar Output (0-1) using the unit or time period shown by the field.
3. Enter Star Mass (kg) using the unit or time period shown by the field.
4. Run the calculation and compare the output with a second scenario before acting on it.