Question

In Star wars: Empire Strikes Back, Luke travels from the icy planet of Hoth to the swamp planet Dagobah in search of Yoda. Let's say the hyperdrive is busted, so Luke has to use his subspace engines. In lore, the distance between Hoth and Dagobah is approximately 4500 parsecs (1pc = 3.26 light years). The size of a T-65 series X-wing fighter is about 12.5m, which is similar to a modern day fighter jet. Let us assume that the X-wing holds 10 tons of propellant, and the maximum mass flow rate of the four engines combined is 1kg/s.

-The life support in a X-wing fighter usually lasts about 2 weeks. How much Isp does the X-wing need to have in order to let Luke make his travel without perishing? (2pts)

-The highest Isp currently achievable (in the real world) is about 10,000 s. How long will it take Luke to reach Dagobah in this case? (2pts)

Of course the numbers will be ridiculous, but I want to see if you approach the problem correctly and can formulate the equations. And also have a little fun!

- Edit: Assume the initial mass of the X-wing is 13 tons. Also ignore any special relativity effects.

Answer 1

Using the ideal rocket equation:

We can assume the spacecraft starts from rest and rapidly reaches a constant speed, then:

Where:

If he uses the ship from the real world: