Vis Viva Delta V Calculator

Calculator

Formula Used

The vis viva equation is:

v = √[ μ × (2 / r - 1 / a) ]

Here, v is orbital speed. μ is the standard gravitational parameter. r is current orbital radius. a is semi-major axis.

For a two-burn circular transfer:

a_transfer = (r1 + r2) / 2

Δv1 = |v_transfer_at_r1 - v_circular_r1|

Δv2 = |v_circular_r2 - v_transfer_at_r2|

Δv_total = Δv1 + Δv2

The optional mass estimate uses:

mass ratio = e^(Δv / Isp × g0)

How to Use This Calculator

Choose a calculation mode first. Use transfer mode for two circular orbits. Use custom mode to compare two orbit speeds at one burn point.

Select the central body. Choose custom when your mission uses another object. Enter its gravitational parameter in km³/s².

Choose whether your distances are center radii or surface altitudes. Enter departure and arrival values for transfer mode. Enter burn radius and semi-major axes for custom mode.

Add a planning margin when you want a safer budget. Add mass and specific impulse to estimate propellant needs. Press the calculate button. The result appears above the form.

Example Data Table

Understanding Vis Viva Delta V

The vis viva equation links orbital speed with position. It also links speed with orbit size. That makes it useful for burn planning. A spacecraft does not need one fixed speed. Its speed changes as it moves around an ellipse. It is faster near periapsis. It is slower near apoapsis. The equation helps estimate that speed at any radius.

What The Calculator Solves

This calculator compares two speeds at the same radius. The difference is delta v. It also estimates a two burn circular transfer. That transfer is close to a Hohmann transfer when both orbits are circular and coplanar. You can enter departure radius, arrival radius, and gravitational parameter. You can also choose a common body. Earth values are loaded by default. Custom values support mission studies around other bodies.

Why Radius Matters

Vis viva uses orbital radius from the center of the body. It does not use altitude alone. If you know altitude, add the body's mean radius first. A low Earth orbit of 400 kilometers has a radius near 6778 kilometers. Using only altitude would create a large error. Good radius data improves every speed and burn estimate.

Delta V Meaning

Delta v means the change in velocity produced by a maneuver. It is not the same as current speed. A craft may travel at 7.7 kilometers per second in low orbit. A transfer burn may need only a small fraction of that speed. The burn changes the orbit shape. The next burn often circularizes the orbit at the target radius.

Circular Transfer Logic

For a circular transfer, the tool first calculates circular speed at radius one. Then it calculates transfer speed at the same point. The first burn is the absolute difference. At radius two, it repeats the comparison. The sum gives total ideal delta v. This ignores plane changes, losses, finite burn effects, drag, and steering errors. Real missions need margins.

Custom Orbit Comparison

The custom mode compares two orbits at one radius. Enter the initial semi major axis and final semi major axis. The tool calculates both vis viva speeds. Their difference is the local impulsive burn estimate. This is helpful for orbit raising, lowering, capture checks, and classroom examples.

Mass Planning

The optional mass section uses the rocket equation. It converts total delta v into mass ratio. It also estimates propellant fraction from specific impulse. This is an ideal estimate. It assumes one effective engine value. It does not replace detailed propulsion design.

Using Results Wisely

Treat the answer as a clean physics baseline. Add safety margin for guidance, gravity losses, atmosphere, and operational limits. Check units before using exports. Keep all radii positive. Keep semi major axes physically valid. When the term inside the square root becomes negative, the selected orbit is not valid at that radius.

Before final use, compare outputs with trusted mission references. Small entry mistakes can grow quickly. Record assumptions with every saved file. Future reviews become easier and safer during later design meetings.

Export And Review

Use the CSV file for spreadsheets. Use the PDF file for quick reports. The example table shows common inputs and expected patterns. Raising from low orbit to high orbit usually needs two burns. Lowering works the same way, but signs are not shown. The calculator reports magnitudes because mission budgets use positive delta v totals.

FAQs