Orbital Mechanics Calculator
The Orbital Mechanics Calculator computes circular and elliptical orbit parameters, Hohmann transfer ΔV with transfer time, and escape velocities for any celestial body. Features interactive SVG orbit diagrams showing initial, transfer, and target orbits with ΔV annotations — free, no signup required.
Celestial Body
Orbit Altitude
Orbit Radius (from center): 6,771 km
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What is Orbital Mechanics?
Orbital mechanics (also called astrodynamics) is the branch of physics that studies the motion of objects in space under the influence of gravity. It uses Kepler's laws and Newton's law of gravitation to predict satellite orbits, plan space missions, and calculate the fuel needed for orbital maneuvers. The fundamental tool is the vis-viva equation: v² = GM(2/r − 1/a), which relates velocity to position in any orbit. Hohmann transfers — the most fuel-efficient way to move between two circular orbits — are the backbone of mission planning from LEO to interplanetary trajectories.
How to Use This Calculator
- Select a celestial body (Earth, Moon, Mars, etc.) or enter custom mass and radius
- Choose calculation mode: circular orbit, Hohmann transfer, elliptical orbit, or escape velocity
- Enter orbit altitude(s) in km above the surface
- Click Calculate to see orbital parameters and view the interactive SVG orbit diagram
- For Hohmann transfers, compare ΔV₁ and ΔV₂ burns with total transfer time
Frequently Asked Questions
What is a Hohmann transfer orbit?
A Hohmann transfer is the most fuel-efficient method to move between two circular orbits. It uses two engine burns: the first raises the orbit on one side (creating an ellipse), and the second circularizes the orbit at the target altitude. The transfer follows half of an elliptical orbit and takes longer than direct transfers, but uses minimum fuel.
Why does orbital velocity decrease at higher altitudes?
Orbital velocity follows v = √(GM/r) — as distance from the center of the body (r) increases, the required velocity decreases. This is because gravitational pull weakens with distance. At LEO (~400 km), velocity is about 7.7 km/s, while at geostationary orbit (~35,786 km), it's only about 3.1 km/s.
What is escape velocity?
Escape velocity is the minimum speed needed to break free from a celestial body's gravitational pull without further propulsion. It equals √(2GM/r) — exactly √2 times the circular orbital velocity at that altitude. For Earth's surface, escape velocity is about 11.2 km/s. It depends only on mass and distance, not on the direction of travel.
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