IOAA 2011, theory — Задача 7

*Short theoretical questions

Each question max 10 points*

Условие

7. A satellite orbits the Earth on a circular orbit. The initial momentum of the satellite is given by the vector $\mathbf{p}$. At a certain time, an explosive charge is set off which gives the satellite an additional impulse $\Delta\mathbf{p}$, equal in magnitude to $|\mathbf{p}|$. Let $\alpha$ be the angle between the vectors $\mathbf{p}$ and $\Delta\mathbf{p}$, and $\beta$ between the radius vector of the satellite and the vector $\Delta\mathbf{p}$. By thinking about the direction of the additional impulse $\Delta\mathbf{p}$, consider if it is possible to change the orbit to each of the cases given below. If it is possible mark YES on the answer sheet and give values of $\alpha$ and $\beta$ for which it is possible. If the orbit is not possible, mark NO.

(a) a hyperbola with perigee at the location of the explosion.

(b) a parabola with perigee at the location of the explosion.

(c) an ellipse with perigee at the location of the explosion.

(d) a circle.

(e) an ellipse with apogee at the location of the explosion.

Note that for $\alpha = 180^\circ$ and $\beta = 90^\circ$ the new orbit will be a line along which the satellite will free fall vertically towards the centre of the Earth.

Решение

Оригинал в Архива: 2011_Short_Questions.pdf