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Live Orbital Velocity Calculator
Calculate circular and escape speeds around any primary celestial body:
CIRCULAR SPEED (v_orb)
6.67 km/s
ESCAPE SPEED (v_esc)
9.43 km/s
01.
Newton's Law of Universal Gravitation
Every particle of matter attracts every other particle with a force proportional to the product of their masses and inversely proportional to the square of the distance between their centers:
F = G · (m₁ · m₂) / r²
In Gravity Pulse, an $\epsilon$ softening factor is applied ($r² + \epsilon²$) to prevent infinite force singularities when two bodies make close flybys.
02.
Kepler's Laws of Planetary Motion
1. Law of Ellipses: The orbit of a planet is an ellipse with the Sun located at one of the two focal points.
2. Law of Equal Areas: A line segment joining a planet and the Sun sweeps out equal areas during equal intervals of time (bodies speed up near perihelion!).
3. Harmonic Law: The square of the orbital period $T$ is directly proportional to the cube of the semi-major axis $a$ ($T² \propto a³$).
03.
Orbital & Escape Velocity
To achieve a stable circular orbit around mass $M$ at radius $r$, the gravitational pull must perfectly balance the centripetal acceleration ($m v² / r = G M m / r²$):
v_orbit = √(G·M / r) | v_escape = √(2·G·M / r)
If a body exceeds the escape velocity ($\sqrt{2} \approx 1.414$ times the orbital speed), its trajectory opens from an ellipse into an unbounded parabolic or hyperbolic escape path.
04.
The Three-Body Problem & Chaos
While the two-body problem has an exact closed-form analytical solution, three or more mutually attracting bodies produce chaotic, non-integrable trajectories first proved by Henri Poincaré in 1890.
Remarkably, periodic choreographic solutions exist, such as the Chenciner-Montgomery Figure-8 orbit featured in the presets, where three equal masses trace a single closed loop without colliding!
05.
Black Holes & Singularities
When matter collapses within its Schwarzschild radius ($r_s = 2GM/c²$), not even light can escape the gravitational event horizon. In Gravity Pulse, singularities absorb colliding matter, conserving total momentum and devouring entire asteroid swarms.