1
vote
1answer
176 views

Pursuit curves and arc length question

I am studying pursuit curves where a fast pirate ship which pursues a heavily laden treasure ship which tracks along a straight line. The ratio of the speeds of the ships is r > 1 (which is fixed) and ...
3
votes
1answer
147 views

Realizing polar function via Newtonian gravitation

Let $r=f(\theta)$ be a smooth, $2\pi$-periodic function, representing a curve star-shaped with respect to the origin. Maybe something like this:           ...
8
votes
2answers
583 views

Fireworks under inverse-cube gravity

What is the path of a projectile under an inverse-cube gravity law? Imagine that the law of gravity was changed overnight from $F(r) = G m_1 m_2 / r^2$ to $F(r) = G' m_1 m_2 / r^3$. To be ...