Estimate standard gravitational parameter using flexible scientific inputs. Switch methods, convert units, and inspect formulas. Built for careful physics analysis, teaching, and orbital studies.
This chart compares standard gravitational parameters for common bodies and your current result when available.
| Body | Mass (kg) | Radius (m) | Surface Gravity (m/s²) | μ (m³/s²) |
|---|---|---|---|---|
| Moon | 7.34767309e22 | 1.7374e6 | 1.62 | 4.9048695e12 |
| Earth | 5.9722e24 | 6.371e6 | 9.81 | 3.986004418e14 |
| Mars | 6.4171e23 | 3.3895e6 | 3.71 | 4.282837e13 |
| Jupiter | 1.89813e27 | 6.9911e7 | 24.79 | 1.26686534e17 |
1) Mass Method: μ = G × M
2) Surface Gravity Method: μ = g × r²
3) Orbital Method: μ = 4π²a³ / T²
The standard gravitational parameter combines the gravitational constant and body mass into one value. It is useful in orbital mechanics because many motion equations depend on μ directly rather than on G and M separately.
Use the mass method when body mass is known, the surface method when radius and surface gravity are available, and the orbital method when semi-major axis and orbital period are measured from an orbit.
It is the product of the gravitational constant and mass. Physicists write it as μ = GM. It simplifies many orbital and gravitational calculations because one combined quantity is often enough for motion analysis.
Many orbital formulas depend on GM rather than mass by itself. Using μ reduces repeated multiplication, improves clarity, and matches how spacecraft navigation and celestial mechanics problems are usually written.
The SI result is m³/s². Space and orbital references also often use km³/s² because those values are easier to read for planets, moons, and spacecraft trajectory calculations.
Use it when you know surface gravity and body radius, but not mass directly. This happens in practical astronomy, geophysics, and educational problems where surface measurements are easier to obtain.
Use it when an orbit is observed. If you know semi-major axis and orbital period, Kepler-based motion lets you estimate μ without entering mass or surface gravity values.
Yes. It converts supported mass, radius, length, acceleration, and time units into SI values before calculating. That keeps formulas consistent and helps prevent unit mismatch errors.
Yes. The calculator works for planets, moons, stars, asteroids, and custom bodies. It is also useful for satellite orbit exercises when orbital period and semi-major axis are known.
Because μ may be very large, small mistakes in mass, radius, period, or units can create major result differences. Always verify units and scientific notation before interpreting the output.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.