Newton's Law of Universal Gravitation
Newton's law of universal gravitation says every point mass attracts every other point mass with a force along the line joining them. It is the only force in the simulator, and it is enough to reproduce Kepler's three laws.
Inverse-square law
The gravitational force between two masses m₁ and m₂ separated by a distance r has magnitude G·m₁·m₂/r², where G ≈ 6.674 × 10⁻¹¹ N·m²·kg⁻². Doubling the distance reduces the force by a factor of four. The force is always attractive and acts along the straight line connecting the two centres of mass.
Standard gravitational parameter
For orbital problems the product μ = G·M of the gravitational constant and the central body's mass appears so often that it is given its own symbol, μ (the standard gravitational parameter). For Earth, μ ≈ 3.986 × 10¹⁴ m³·s⁻². Using μ removes the need to know G and M separately and makes the orbit equations much cleaner.
Why orbits are conic sections
When a body moves under an inverse-square central force, its trajectory is always a conic section: an ellipse, parabola, or hyperbola, with the central body at one focus. Bound orbits (closed paths) are ellipses; the circle is the special case of zero eccentricity. This result, derived from Newton's laws, is the mathematical foundation of every closed trajectory you can draw in the simulator.
Einstein's refinement
General relativity (1915) replaces the idea of a force at a distance with curvature of spacetime produced by mass and energy. For weak fields and low speeds, which covers every satellite around Earth, the predictions agree with Newton's law to extraordinary precision. The simulator uses the simpler Newtonian form.
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