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Circular Two-Body Orbital Velocity — result sheet
Calculate the Newtonian relative speed for two positive masses in a circular orbit at a stated center-to-center separation.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: Relative circular speed v = sqrt(G (m1 + m2) / r), using G = 6.67430e-11 N m^2/kg^2 and center-to-center separation r.
This calculator returns the relative orbital speed for an ideal Newtonian circular two-body system. It uses the sum of both masses and their center-to-center separation, so it is distinct from a one-body escape-speed calculation and does not return each body's barycentric speed.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Primary body mass — kg; Finite positive mass of the first body.; minimum 1; maximum 1.0E+31
- Secondary body mass — kg; Finite positive mass of the second body.; minimum 1; maximum 1.0E+31
- Center-to-center separation — m; Finite positive distance between body centers.; minimum 1000000; maximum 1.0E+16
Worked example
| Input | Value |
|---|---|
| Primary body mass | 1.98847E+30 |
| Secondary body mass | 5.9722E+24 |
| Center-to-center separation | 149597870700 |
The relative circular orbital speed is about 29,784.69 m/s, or 29.78469 km/s.
Assumptions and limits
- Both masses are finite positive point-mass values in kilograms and the separation is a finite positive center-to-center distance in metres.
- The orbit is circular and Newtonian, with the relative speed defined for the separation between the two bodies; the gravitational constant is fixed at the NIST CODATA value 6.67430e-11 N m^2/kg^2.
- Eccentricity, body radii, collisions, perturbing bodies, relativistic corrections, orbital period, trajectory propagation, and mission or design advice are not modeled.
Calculator note
Source and methodology
Use the official WorldCalculate methodology policy for the source, formula, precision, and boundary standards behind this calculator.
Planning estimate, not financial, medical, legal, or professional advice. © WorldCalculate — reuse with attribution. Built and curated by Hassan ALRowaie.
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