Answer to Question #162980 in Astronomy | Astrophysics for Joe Biden

Question

The star of a distant solar system explodes as a supernova. At the moment of the explosion, an resting exploration spaceship is 15 AU away from the shock wave. The shock wave of the explosion travels with 25000 km/s towards the spaceship. To save the crew, the spacecraft makes use of a special booster that uniformly accelerates at 150 m/s2 in the opposite direction. Determine if the crew manages to escape from the shock wave. (Neglect relativistic effects.)

Answer 1

Calculate the time it takes for the spaceship to reach 25000 km/s:

$$t=\frac{v}{a}=166667\text{ s}.$$

Calculate what distance the shockwave will cover during t:

$$d=v_st=4.167·10^{12}\text{ m},$$

or 27.85 AU.

So, only 27.85-15=12.85 AU left for the spaceship to develop the speed of 25000 km/s. Is it possible? Find the distance required for the ship to accelerate from rest to 25 000 000 m/s with acceleration of 150 m/s²:

$$d=\frac{v^2}{2a}=2.08·10^{12}\text{ m},$$

or 13.9 AU.

Therefore, when the shockwave will travel 27.85 AU from the star at 25 000 km/s, the speed of the spaceship will be lower than 25 000 km/s. They cannot escape.