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diff --git a/Content/posts/2023-04-30-n-body-simulation.md b/Content/posts/2023-04-30-n-body-simulation.md index 6d6cda6..9c8e7b1 100644 --- a/Content/posts/2023-04-30-n-body-simulation.md +++ b/Content/posts/2023-04-30-n-body-simulation.md @@ -23,11 +23,11 @@ Workflow: The n-body problem is a classic puzzle in physics (and thus astrophysics) and mathematics that deals with predicting the motion of multiple celestial objects that interact with each other through gravitational forces. -Imagine you are observing a *cosmic dance* between multiple celestial bodies, all tugging on one another as they move through space. The n-body problem aims to undersand and predict the paths of these objects as they move through space. +Imagine you are observing a *cosmic dance* between multiple celestial bodies, all tugging on one another as they move through space. The n-body problem aims to understand and predict the paths of these objects as they move through space. When `n=2`, i.e we have only two objects, say the Earth and the Moon, we can easily apply Newtonian physics to predict their motion. However, when `n>2`, the problem becomes much more difficult to solve analytically.[1] This is because each object feels the gravitational pull from all other objects, and thus the equations of motion become coupled and non-linear. -As the number of objects increases, finding an exact solution becomes impossible, and we rely on analyticals approximations. +As the number of objects increases, finding an exact solution becomes impossible, and we rely on analytical approximations. ## Visualising a basic orbit @@ -717,4 +717,4 @@ function plotRandomNBodySimulation() { ## References 1. Barrow-Green, June (2008), "The Three-Body Problem", in Gowers, Timothy; Barrow-Green, June; Leader, Imre (eds.), *The Princeton Companion to Mathematics*, Princeton University Press, pp. 726–728 -2. Moore, Cristopher (1993), "Braids in classical dynamics", *Physical Review Letters*, 70 (24): 3675–3679
\ No newline at end of file +2. Moore, Cristopher (1993), "Braids in classical dynamics", *Physical Review Letters*, 70 (24): 3675–3679 |