Calculator Inputs
Example Data Table
| Scenario | Body 1 Mass | Body 2 Mass | Distance | Relative Speed | Radial Speed |
|---|---|---|---|---|---|
| Earth-Moon reference | 5.9722e24 kg | 7.34767309e22 kg | 384,400 km | 1.022 km/s | 0 km/s |
| Sun-Earth circular estimate | 1 solar mass | 1 Earth mass | 1 AU | 29.78 km/s | 0 km/s |
| Binary stars test case | 1.2 solar masses | 0.9 solar masses | 0.25 AU | 88 km/s | 3 km/s |
These examples help verify unit handling and show how orbit class changes with distance and speed.
Formula Used
This tool treats the system as two point masses interacting only through gravity. It works best for isolated systems where outside forces, drag, and third-body effects are negligible.
1) Gravitational force
F = G m₁ m₂ / r²
2) Reduced mass
μ = (m₁ m₂) / (m₁ + m₂)
3) Relative-frame kinetic energy
K = 0.5 μ v²
4) Gravitational potential energy
U = -G m₁ m₂ / r
5) Total mechanical energy
E = K + U
6) Specific orbital energy
ε = v² / 2 - G(m₁ + m₂) / r
7) Tangential speed and angular momentum
vₜ = √(v² - vᵣ²), h = r vₜ
8) Eccentricity
e = √[1 + (2 ε h²) / (G² (m₁ + m₂)²)]
9) Semi-major axis for non-parabolic motion
a = -G(m₁ + m₂) / (2 ε)
10) Period for bound elliptical motion
T = 2π √(a³ / G(m₁ + m₂))
How to Use This Calculator
- Enter masses for both bodies and choose their units.
- Provide the current separation distance between the bodies.
- Enter the total relative speed of one body with respect to the other.
- Enter the radial speed component. Use negative values for inward motion.
- Pick the desired decimal precision, then press Calculate.
- Review orbit type, energies, barycenter distances, and period results.
- Use the CSV or PDF buttons to save the calculated output.
Frequently Asked Questions
1) What does this calculator solve?
It evaluates an ideal two-body gravitational system. It estimates force, energy, barycenter position, orbit type, semi-major axis, and orbital period from masses, distance, and relative motion.
2) What is radial speed?
Radial speed is the velocity component along the line joining the two bodies. Positive values mean moving apart, while negative values mean approaching each other.
3) Why can the orbit be elliptical or hyperbolic?
The orbit class depends on total energy and eccentricity. Lower speeds at the same distance often produce bound ellipses, while higher speeds can create open escape trajectories.
4) What is the barycenter?
The barycenter is the system’s center of mass. Both bodies orbit this point, and its location depends on the mass ratio and their separation distance.
5) Does this include real-world perturbations?
No. It ignores drag, non-spherical gravity, tidal effects, relativity, and third-body perturbations. Use higher-fidelity numerical models for mission design or precise astrophysical studies.
6) When is orbital period shown?
Orbital period is defined only for bound elliptical motion. Open trajectories such as parabolic or hyperbolic paths do not have a repeating closed period.
7) Can I use solar masses and AU together?
Yes. The calculator converts all supported mass, distance, and speed units into SI units internally, then computes results consistently from those converted values.
8) Why must radial speed not exceed total speed?
Because total relative speed already includes all velocity components. If radial speed exceeds it, the tangential component becomes imaginary, which is physically invalid.