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Escape Velocity Power Budget Planner

The Escape Velocity Power Budget Planner estimates the average propulsion power associated with accelerating a specified mass to an ideal escape-speed scale over a chosen burn duration. It calculates escape velocity from body mass and radius, converts that speed into kinetic energy, adjusts for propulsion efficiency, and applies a design margin to produce an average input-power figure.

This is most meaningful as an energy-and-power thought experiment for propulsion concepts where input power is a useful design quantity, such as electric or beamed-energy systems. It is not a chemical-rocket power model and does not represent a real ascent trajectory. The calculation ignores gravitational potential during a finite climb, propellant kinetic energy, exhaust dynamics, changing vehicle mass, thrust limits, atmospheric loss, and the actual time history of acceleration.

Mission inputs

×10²⁴ kg
km
kg
min
%
%
Result
—
Calculated result
Escape velocity—
Kinetic energy target—
Input energy before margin—
Average input power—

1. Enter body mass and radius
These inputs set the ideal escape-speed target used by the energy calculation.

2. Set the accelerated mass
Use the mass whose kinetic energy you want to raise to the escape-speed scale.

3. Choose an acceleration duration
The same energy delivered over a shorter time requires more average power.

4. Enter energy-conversion efficiency
Efficiency converts useful kinetic-energy demand into upstream input energy.

5. Apply a power margin
Add an explicit margin after efficiency losses.

6. Interpret the result carefully
Use the output for conceptual power comparison, not as a launch-vehicle sizing result.

The planner converts ideal escape speed into kinetic energy and then into average input power:

v_escape = √(2GM / r) Kinetic energy = ½ m v_escape² Input energy = kinetic energy / efficiency Average input power = input energy / acceleration time Design power = average input power × (1 + margin)

Mass is in kilograms, speed in m/s, energy in joules, and time in seconds. Efficiency and margin are converted from percentages to decimals. The physics is deliberately simplified: an object at surface escape speed has kinetic energy equal to the magnitude of its gravitational binding energy per unit mass, but a real propulsion system does not generally deliver that requirement as a simple constant-power kinetic-energy transfer.

What the result means

The main result is average upstream power needed to supply the idealized kinetic-energy target within the selected duration after efficiency loss and margin.

Do not use this result as a chemical-rocket engine power rating; propulsion architectures require their own thrust, mass-flow, exhaust, and trajectory models.

Given

  • Earth-like mass and radius
  • Accelerated mass: 1,000 kg
  • Acceleration duration: 60 min
  • Energy conversion efficiency: 60%
  • Power margin: 15%

Calculation
Escape speed ≈ 11,186 m/s. Kinetic energy = 0.5 × 1,000 × 11,186² ≈ 62.56 GJ. Input energy = 62.56 / 0.60 ≈ 104.27 GJ. Base average power = 104.27 GJ / 3,600 s ≈ 28.96 MW. Design power = 28.96 × 1.15 ≈ 33.30 MW.

Result
Average design input power ≈ 33.3 MW.

The number is an idealized energy-delivery comparison for the chosen mass and duration, not a full propulsion-system requirement.

Is this the power output of a rocket engine?

Not generally. Chemical rockets are better characterized through thrust, mass flow, exhaust velocity, chamber conditions, and trajectory performance. This page treats escape-speed kinetic energy as an input-power thought experiment.

Why does burn duration change power but not energy?

The ideal kinetic-energy target is set by mass and speed. Delivering the same energy over less time raises average power; spreading it over more time lowers average power.

What does conversion efficiency include?

Use it as a lumped fraction of upstream energy that becomes the modeled useful kinetic energy. Real propulsion systems may require a more specific efficiency definition.

Does the model include changing spacecraft mass?

No. The accelerated mass is constant. Propellant consumption, exhaust energy, staging, and vehicle mass change are outside this simplified model.

When is this calculator most useful?

It is most useful for conceptual electric, beamed-energy, or general energy-scale comparisons where average input power is meaningful. Use a propulsion-specific model for engineering design.