n-body problem

In the n-body problem, we seek to describe the interaction between a fixed number of objects under Newton's Law of Gravity. A simple equation given by Newton in 1687 describes the gravitational attraction between two objects. Using a computer, we can compute the sum of the forces acting on a fixed number of objects. Once this is known, we can deduce where the object will be in the next time step.

These images show some newly discovered periodic (repeating) orbits for 3 and 4 bodies.

Caption A: Three bodies with equal mass orbiting on a figure eight. This result was published in 2000.

Caption B: Three bodies of unequal mass. This system is similar to a planet orbiting a binary star system.

Caption C: Two pairs of bodies orbiting about each other.

Caption D: An orbit discovered in 2008 by Tiancheng Ouyang, Duokui Yan, and Skyler Simmons at BYU.

This problem is far from a mathematical curiosity. For example, NASA uses computations like these to model motions for launches of space probes and other spacecraft.

 

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The most common question students ask math teachers at every level is “When will I use math?” WeUseMath.org is a non-profit website that helps to answer this question. This website describes the importance of mathematics and many rewarding career opportunities available to students who study mathematics.


 

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20
May

Dr. Cary Oberije, a postdoctoral researcher in The Netherlands, has found that mathematical models can be used to accurately predict patients' responses to treatment. Prediction models were used to analyze lung cancer patients' likelihood of survival and...

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