Harness Newton's law of universal gravitation (F = G·M·m / r²), Keplerian orbits, and hyperbolic slingshots. Drag to slingshot your scientific probe across living solar systems, steal momentum from giant planets, time precision Hohmann transfer burns, and dock with orbital stations across 6 progressive astronomical campaign missions.
Earth-Moon Relay & Direct Orbit Transfer
Master the art of space navigation through intuitive tactile controls. No equations required to launch, but understanding orbital mechanics turns near-misses into surgical dockings.
Your scientific mission is to launch research spacecraft across multi-body gravitational fields, execute planetary slingshots and Hohmann transfers, and achieve precision orbital rendezvous with target space stations.
Orbit Slinger offers three synchronized ways to control your spacecraft on desktop, laptop, and mobile touchscreens.
Follow this sequential flight protocol on every launch to guarantee rendezvous success.
Drag your probe backward on the canvas or dial in exact degrees and thrust on the control panel. Check the cyan forward vector arrow pointing towards your departure trajectory.
The dotted predictive curve shows your flight path across all gravitational fields. If it turns golden-orange, your spacecraft is entering a high-velocity gravity assist slingshot!
Orbital stations continuously travel around their parent planets. Do not aim where the station is now—aim where it will be when your craft arrives (calculate the lead angle).
Glide into the station's glowing capture collar at ≤ 22.0 km/s. If you are travelling too fast, fire a quick Retrograde burn (-Δv) just before arrival to prevent a high-speed collision crash.
From basic lunar transfers to high-relativity black hole slingshots, each mission introduces authentic celestial mechanics, unique gravitational challenges, and strict launch budgets.
Launch probe from Low Earth Orbit to dock with the Lunar Gateway station orbiting our Moon. ⚠️ DOCKING PROTOCOL: You must shoot down all 5 micrometeorites using point-defense lasers [Space / Click Canvas] to unlock the Gateway docking bay, then enter collar at safe speed (≤ 22 km/s).
A hyperbolic flyby craft will escape into deep space unless decelerated! ⚠️ DOCKING PROTOCOL: You must shoot down all 4 stray debris boulders using lasers [Space / Click Canvas] to unlock Lunar Polar Station, then execute a Retrograde braking burn [S] at perilune to capture into closed orbit and dock at ≤ 22 km/s.
Outer station "Europa Outpost" is far out of direct engine range! Whip your probe around massive Jupiter in a close parabolic flyby to steal orbital momentum. ⚠️ DOCKING PROTOCOL: Secure or shoot all 3 scientific data beacons to unlock the Europa Outpost docking bay, then dock safely.
Execute a classic Hohmann transfer orbit from Earth around the Sun to rendezvous with Ares Research Station orbiting Mars. ⚠️ DOCKING PROTOCOL: Eliminate all 3 rogue Martian sentry drones to clear the airspace before the Ares docking collar will open.
Navigate the shifting, chaotic gravity of a co-orbiting Binary Star pair. ⚠️ DOCKING PROTOCOL: Intercept and destroy both hostile Gunships to protect Archimedes Station shields; the Lagrange L4 docking collar unlocks once the threat is neutralized.
Final relativistic challenge! Thread your probe past the photon sphere of Gargantua. ⚠️ DOCKING PROTOCOL: Destroy all 3 Quantum Shield Generators and annihilate the Rogue Singularity Core to unlock the Interstellar Ark docking bay.
Every arc, slingshot, and orbital insertion in the game is governed by the exact differential equations of classical astrodynamics.
Fg: Gravitational Attraction Force between primary and probe [Newtons, N = kg·m/s²]G: Universal Gravitational Constant (6.6743 × 10−11) [m³/(kg·s²)]M: Mass of Primary Body (Earth, Sol, Mars, Jupiter) [Kilograms, kg]m: Mass of Spacecraft Probe (1,000 kg scientific payload) [Kilograms, kg]r: Radial Separation Distance between centers of mass [Meters, m or km]a: Gravitational Acceleration on probe (a = Fg / m) [m/s²]In-Game Meaning: The gravitational pull decays with the square of distance. Halving your distance to Jupiter quadruples the attraction force, pulling your spacecraft into an intense hyperbolic curve.
v: Instantaneous Orbital Velocity along trajectory [Meters per second, m/s (or km/s)]μ: Standard Gravitational Parameter of host (μ = G · M) [m³/s² (or km³/s²)]r: Current Radial Distance from host center to spacecraft [Meters, m (or km)]a: Semi-Major Axis of orbit conic (ellipse > 0, hyperbola < 0) [Meters, m (or km)]ε: Specific Mechanical Energy (ε = ½v² − μ/r = −μ/2a) [Joules per kg, J/kg (or MJ/kg)]In-Game Meaning: Connects speed v, distance r, and orbital semi-major axis a. At periapsis (closest approach), potential energy drops to minimum and kinetic energy peaks, making your spacecraft scream past at maximum velocity.
T: Orbital Period (time for 1 complete 360° revolution) [Seconds, s (or hours/days)]π: Mathematical Constant Pi (≈ 3.14159265) [Dimensionless ratio]μ: Standard Gravitational Parameter (μ = G · M) [m³/s²]a: Semi-Major Axis (mean orbital radius for circular orbits) [Meters, m (or km)]In-Game Meaning: Stations in distant orbits move far more slowly than inner stations. To rendezvous with an outer station, you must plan a transfer orbit whose half-period ½Ttx matches the station's orbital displacement.
h: Specific Angular Momentum (|h| = |r × v|) [m²/s (or km²/s)]r: Position Vector Length from center of primary mass [Meters, m]v: Orbital Velocity Magnitude of probe [Meters per second, m/s]v⊥: Transverse Tangential Velocity perpendicular to r [m/s]Because gravity is a strictly central force, it exerts zero torque on your spacecraft (τ = r × Fg = 0). Angular momentum h is strictly conserved, forcing speed v to increase whenever radius r decreases (Kepler's 2nd Law).
Δv: Delta-v (Velocity Change Capacity) from burn [Meters per second, m/s]Isp: Specific Impulse (thruster propellant efficiency) [Seconds, s]g0: Standard Earth Gravity Acceleration (9.80665 m/s²) [m/s²]m0: Initial Spacecraft Wet Mass before burn [Kilograms, kg]mf: Final Spacecraft Dry Mass after fuel is spent [Kilograms, kg]ln: Natural Logarithm of mass ratio (m0 / mf) [Dimensionless]Dictates how much velocity change (Δv) your spacecraft's micro-thrusters can produce from fuel mass. In spaceflight, velocity is literally currency: each prograde or retrograde burn permanently consumes from your limited Δv budget.
ΔKE: Net Kinetic Energy Gain from thruster impulse [Joules, J (or MJ)]m: Spacecraft Probe Mass[Kilograms, kg]v: Orbital Speed at the instant of burn (highest at periapsis) [m/s]Δv: Velocity Change Imparted by thruster burn [m/s]Firing your thrusters when travelling at high speed generates vastly more mechanical energy than firing at low speed. Executing a burn at periapsis deep inside a planet's gravity well provides maximum orbital leverage for your fuel!
Core mental models that transform confusing curved trajectories into predictable, repeatable flight plans.
Space is warped by mass. Think of every planet as a funnel: the closer you get, the steeper the slope (Φ = -GM/r). To leave a planet, you must generate enough kinetic energy to climb out of its potential well.
Every elliptical orbit has two defining altitudes: Periapsis (rp, closest point where velocity is highest) and Apoapsis (ra, furthest point where velocity is lowest). Firing prograde at periapsis raises your apoapsis on the opposite side.
The minimum speed required to break free from a gravitational body without further propulsion: vesc = √(2GM/r) = √2 · vcirc. Speeds below this form closed ellipses; speeds above form open hyperbolas into interstellar space.
The most fuel-efficient two-burn maneuver to transfer between two circular orbits. The spacecraft enters an elliptical transfer orbit whose periapsis touches the inner orbit and whose apoapsis touches the outer target orbit.
In the planet's rest frame, your flyby is an elastic collision (vin = vout). But in the Sun's frame, the planet is moving at vplanet. By flying behind the planet, your spacecraft steals a fraction of the planet's orbital momentum, gaining up to 2 · vplanet!
Five gravitational equilibrium points where the combined gravity of two massive bodies equals the centripetal force required to orbit with them. L4 and L5 form stable 60° equilateral triangles—cosmic parking zones explored in Mission 04!
The brilliant mathematicians, astronomers, and rocket theorists whose discoveries allow us to pilot probes across the solar system.
Analyzed Tycho Brahe's Mars observations to shatter Aristotle's 2,000-year dogma of circular orbits. Formulated the Three Laws of Planetary Motion, discovering that planetary orbits are ellipses and that planets sweep out equal areas in equal times.
Unified terrestrial falling apples and celestial planetary orbits under a single mathematical law: inverse-square universal gravitation. Proved that Kepler's empirical planetary laws were direct mathematical consequences of F = G · (M · m) / r².
Constructed the first astronomical telescope, discovering the four Galilean moons orbiting Jupiter (Io, Europa, Ganymede, Callisto). Proved that celestial bodies can orbit centers other than Earth, providing crucial proof for heliocentric astrodynamics.
Solved the restricted three-body problem, proving the existence of five stationary equilibrium points (L1–L5) where spacecraft can hover with zero propellant expenditure. Today, NASA's James Webb Space Telescope sits at Sun-Earth L2.
Derived the fundamental rocket equation relating velocity change to exhaust speed and propellant mass ratio: Δv = v_e · ln(m_0 / m_f). Envisioned multi-stage rockets, space suits, and liquid hydrogen propulsion decades before Apollo.
Published The Attainability of Celestial Bodies (1925), discovering that an ellipse tangent to both circular orbits represents the absolute minimum-fuel transfer trajectory between two celestial worlds.
See the exact numbers from legendary historic space missions and how they translate to Orbit Slinger's in-game telemetry readouts.
In Low Earth Orbit (r₁ = 6,563 km), Apollo 11 orbited at 7.79 km/s. The Saturn V S-IVB stage fired to raise speed to 10.84 km/s, injecting the spacecraft into an elliptical transfer to the Moon (r₂ = 384,400 km).
Voyager 1 approached Jupiter with an inbound heliocentric velocity of 14.1 km/s. Jupiter was moving at 13.1 km/s along its orbit. Flying behind Jupiter deflected the trajectory by 102°, catapulting Voyager 1 outward at 38.9 km/s.
Earth orbits at 1.0 AU (vE = 29.78 km/s); Mars orbits at 1.524 AU (vM = 24.07 km/s). The Hohmann transfer ellipse semi-major axis is atx = (1.0 + 1.524) / 2 = 1.262 AU.
Compare a circular station orbit (e = 0.0, r = 200 px) against an eccentric reconnaissance orbit (e = 0.6, a = 250 px, rp = 100 px, ra = 400 px) around a primary body (μ = 50,000):
A definitive reference table. Click [Classic Def] or [Expand All] to reveal historic Latin citations from Principia, original papers, vector formulas, and in-game mechanics.
| # | Law / Principle | Governing Formula | Pioneering Scientist | The 5-Second Plain English Summary | How It Works in Orbit Slinger | Classic Definition |
|---|---|---|---|---|---|---|
| 01 | Universal Gravitation | F_g = G · (M · m) / r² | Sir Isaac Newton (1687) | Massive bodies attract each other across space; get twice as close and the gravitational pull becomes four times stronger (1/r²). | Dictates gravitational curve strength and orbital attraction force around each celestial body. | |
| 02 | Kepler's First Law (Ellipses) | r(θ) = a(1 - e²) / (1 + e·cosθ) | Johannes Kepler (1609) | Planetary orbits are never perfect circles—they are stretched ovals (ellipses) with the heavy central body sitting off-center at one focal point. | When launching your craft, if specific orbital energy ε < 0, your probe settles into a stable Keplerian ellipse rather than drifting away into deep space. | |
| 03 | Kepler's Second Law (Equal Areas) | dA/dt = L / (2m) = Constant | Johannes Kepler (1609) | A spacecraft whips fast at its lowest altitude (periapsis) and crawls slowest at its highest point (apoapsis), sweeping out equal areas in equal times. | When slingshotting past Jupiter, your craft reaches its absolute fastest speed at closest approach, leaving a bright golden-orange velocity trail. | |
| 04 | Kepler's Third Law (Harmonic Law) | T² = (4π² / μ) · a³ | Johannes Kepler (1619) | The higher and wider an orbit is, the exponentially longer it takes to complete a single trip around the planet (distance cubed equals time squared). | Governs how much lead angle you must apply when shooting for Mars Station or Europa Outpost in their wide, slow outer orbits. | |
| 05 | Vis-Viva Orbital Energy Equation | v² = μ · (2/r - 1/a) | Gottfried Leibniz & Euler (1736) | Your flight velocity at any point is strictly locked to your distance from the central mass and the total mechanical energy of your orbit. | Determines exact arrival velocity into the target docking collar. If speed exceeds 22.0 km/s, you breach docking tolerances and crash! | |
| 06 | Hohmann Transfer Trajectory | a_tx = (r₁ + r₂) / 2 | Walter Hohmann (1925) | The absolute cheapest fuel highway between two concentric orbits is an elliptical route that gently touches both circular paths. | Executing Mission 03 requires shaping your launch ellipse so its apoapsis coincides with Mars' orbital distance. | |
| 07 | Tsiolkovsky Rocket Equation | Δv = I_sp · g₀ · ln(m₀ / m_f) | Konstantin Tsiolkovsky (1903) | In space, speed is currency: each engine burst throws propellant mass out the back to buy velocity, permanently depleting your fuel reserve. | Each micro-burn consumes exactly 20 m/s from your 100–180 m/s fuel budget. Conserving fuel yields higher star ratings at mission completion! | |
| 08 | The Oberth Effect | ΔKE = m·v·Δv + ½·m·(Δv)² | Hermann Oberth (1929) | Firing your rocket engines when already travelling at top speed delivers vastly more kinetic energy than firing when moving slowly. | When executing a hyperbolic slingshot around Jupiter, fire your prograde burn at closest periapsis to double your exit velocity boost! |
Intuitive answers to the most common puzzles in orbital mechanics and space navigation.