Circular Orbital Velocity, Escape Velocity & Kepler Period Calculator

Compute LEO/MEO/GEO satellite speed and orbital period in minutes.

Circular Orbital Velocity
7.67 km/s
Keplerian Orbital Period 92.48 minutes
Local Escape Velocity 10.84 km/s
Orbits Completed per 24 Hours 15.57 orbits/day
Inputs
km
Planet mean radius in kilometers (6,371 km for Earth).
km
Satellite altitude above the surface in kilometers (e.g., 400 km ISS).
m/s²
Surface gravitational acceleration in m/s².
Results & Graph
Circular Orbital Velocity
7.67 km/s
Keplerian Orbital Period
92.48 minutes
Local Escape Velocity
10.84 km/s
Orbits Completed per 24 Hours
15.57 orbits/day

Circular Orbital Velocity

Graph 1 • Central Body Radius Km Sensitivity Recalculates the domain equation across 50% to 150% of the primary input while holding other parameters constant.
0 km/s 5.1 km/s 10.2 km/s 50%: 5.27 km/s 5.3 50% 75%: 6.58 km/s 6.6 75% 100%: 7.67 km/s 7.7 100% 125%: 8.62 km/s 8.6 125% 150%: 9.48 km/s 9.5 150%
Graph 2 • Primary & Supporting Metric Comparison Compares the primary output alongside supporting domain benchmarks.
Circular Orbital Velocity 7.67 km/s Keplerian Orbital Period 92.48 minutes Local Escape Velocity 10.84 km/s Orbits Completed per 24 Hours 15.57 orbits/day
Graph 3 • Exact Output Table & Units Displays each calculated output in its exact domain unit.
Circular Orbital Velocity7.67 km/sKeplerian Orbital Period92.48 minutesLocal Escape Velocity10.84 km/sOrbits Completed per 24 Hours15.57 orbits/day
Summary: At 400 km altitude (r=6771 km), circular orbital speed is 7.67 km/s, escape velocity is 10.84 km/s, and orbital period is 92.5 minutes.
Summary: At 400 km altitude (r=6771 km), circular orbital speed is 7.67 km/s, escape velocity is 10.84 km/s, and orbital period is 92.5 minutes.
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Formula & Mathematical Methodology: Orbital & Escape Velocity Physics & Engineering Equation

vorbit = G·M / r
vescape = 2·G·M / r
Torbit = 2π·r / vorbit
v_orbit = √(G·M / r); v_escape = √(2·G·M / r); T_orbit = 2π·r / v_orbit
  • centralBodyRadiusKm: Central Body Radius Km (km)
  • orbitalAltitudeKm: Orbital Altitude Km (km)
  • surfaceGravityMps2: Surface Gravity Mps2 (m/s²)

Rounding: Physical constants follow CODATA/NIST values; output quantities display to 2 decimal places.

Worked Example: Physics & Engineering Benchmark: Orbital & Escape Velocity

Compute LEO/MEO/GEO satellite speed and orbital period in minutes.

  1. Enter the physical dimensions, electrical parameters, or thermodynamic state variables.
  2. Apply the governing equation: v_orbit = √(G·M / r); v_escape = √(2·G·M / r); T_orbit = 2π·r / v_orbit.
  3. Inspect the primary SI output, derived quantities, and 3 visual SVG graphs.
Result: Computes Orbital & Escape Velocity via v_orbit = √(G·M / r); v_escape = √(2·G·M / r); T_orbit = 2π·r / v_orbit.

Frequently Asked Questions

What equation powers the Circular Orbital Velocity, Escape Velocity & Kepler Period Calculator?

It evaluates v_orbit = √(G·M / r); v_escape = √(2·G·M / r); T_orbit = 2π·r / v_orbit using IEEE-754 double precision and renders three synchronized SVG plots.

Can I test parameter sensitivity across multiple values?

Yes. Graph 1 automatically plots a 50%–150% parameter response curve, and you can pin up to 3 custom scenarios.

Are all units consistent with SI standards?

Yes. Each input field specifies its exact SI or engineering unit and converts internally where needed.

Science & Engineering · Classical Mechanics & Kinematics

Circular Orbital Velocity, Escape Velocity & Kepler Period Calculator: inputs, method, and how to read the result

Compute LEO/MEO/GEO satellite speed and orbital period in minutes.

Choose inputs for the case you are checking

The defaults are illustrative. Replace them with values for your case and keep the units shown beside each field.

  • Central Body Radius Km: Planet mean radius in kilometers (6,371 km for Earth).
  • Orbital Altitude Km: Satellite altitude above the surface in kilometers (e.g., 400 km ISS).
  • Surface Gravity Mps2: Surface gravitational acceleration in m/s².

What the calculation includes

With the default values shown, Circular Orbital Velocity is 7.67 km/s. The calculation follows Orbital & Escape Velocity Physics & Engineering Equation; the formula and variable definitions above show how the inputs combine.

One-input check: With the other defaults held constant, changing Central Body Radius Km from 6,371 km to 7,008 km changes Circular Orbital Velocity from 7.67 km/s to 8.06 km/s. This is a comparison inside the calculator's stated model, not a prediction.

Where to use caution

  • Uses standard SI physical constants (g = 9.80665 m/s², c = 299,792,458 m/s, σ = 5.670374×10⁻⁸ W·m⁻²·K⁻⁴).
  • Engineering reference model; apply appropriate safety factors and empirical calibration for critical hardware designs.

Scope: SI / NIST Physics & Engineering Standard Check the assumptions and limitations against your situation before relying on the estimate.

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