🛰️ Celestial Mechanics & Kepler's Third Law
Orbital Velocity & Kepler's Law Calculator
Compute circular orbital speed ($v_o = \sqrt{GM/r}$), orbital period ($T$), and parabolic escape velocity ($v_e = \sqrt{2GM/r}$) for satellites orbiting planetary bodies.
🛰️ ISS LEO (408 km)
📡 GPS Satellite (20,200 km)
🌐 Geostationary GEO (35,786 km)
🌕 Lunar Orbit (384,400 km)
🔴 Mars LMO (400 km)
Orbital Parameters
Circular Orbital Velocity (v₀)
7.669 km/s
Orbital Period ($T$)
92.68 mins
1.545 hours
Escape Velocity ($v_e$)
10.845 km/s
24,259 mph
Total Orbital Radius
6,779 km
r = R + h
💡 Orbital Period Equation (Kepler):
$$T = 2\pi\sqrt{\frac{r^3}{GM}} = 2\pi\sqrt{\frac{(6.779\times 10^6)^3}{3.986\times 10^{14}}} = 5,561\text{ s} = 92.7\text{ min}$$
Orbital Mechanics Formulas
By balancing gravitational attraction with centripetal force ($G \frac{Mm}{r^2} = \frac{m v^2}{r}$):
- Circular Orbital Speed: $$v_o = \sqrt{\frac{GM}{r}}$$
- Escape Velocity: $$v_e = \sqrt{\frac{2GM}{r}} = \sqrt{2} \times v_o$$
- Gravitational Parameter ($\mu = GM$): For Earth, $\mu = 3.986004418 \times 10^{14}\text{ m}^3/\text{s}^2$.
- Kepler's Third Law: $$T^2 = \frac{4\pi^2}{GM} r^3 \implies T = 2\pi\sqrt{\frac{r^3}{GM}}$$