Recent content by rocky

Yes, those numbers came from the book. The full capacity fuel mass is 2,000,000kg. The dry mass of the ship is described as "around 100,000kg", but it would need to be about 20 times lighter for the mass ratio to work. The acceleration for the ship on the outbound journey might actually be 15...

Does this account for the need to slow down? Don’t we need to use the square root of the mass ratio?

That looks like the Tsiolkovsky rocket equation, which becomes the equation I posted above for a photon rocket when you account for relativity: https://en.wikipedia.org/wiki/Tsiolkovsky_rocket_equation Anyways, thanks everyone for sharing your thoughts. I wanted to see if I was missing...

Sorry, I wasn't clear there. That's meant to be the mass ratio for the outbound trip, I just wanted to clarify that it includes acceleration and deceleration. Am I using the wrong formula? The return trip would have a reduced mass ratio: 1,333,333kg fuel for a 100,000kg ship, although the ship...

Outbound trip. So to recap: ship mass 100,000kg, fuel 2,000,000 kg. Constant acceleration/deceleration at 15m/s^2 over a distance of 11.9 light years. It's supposed to take just under 4 years of proper time (which checks out for that acceleration and distance), but from what I can tell that...

Yes, sorry I didn’t clarify. R being the mass ratio required for each burn, so R^2 is the mass ratio for the whole trip.

I’m not sure I understand the question. Doesn’t that equation give the max speed that can be attained with a given mass ratio, accounting for the need to slow down? The ship refuels after the journey, it doesn’t carry fuel to make a return trip.

After reviewing the book a bit, I found the mass of the ship, but now I'm even more confused. The ship weighs 100,000kg, and carries 2,000,000kg of fuel. With a perfect fuel efficiency, that mass ratio can only get up to 0.91c if it needs to slow down as well...

Thanks! I couldn't think of any constraint that made sense in the book. I don't believe engine efficiency was mentioned. The way the engine works in the book is essentially by converting mass to light energy and shining that behind the ship. I was just hoping to confirm that my math made sense...

My proposed plan assumes it can reach the same rapidity as the calculated plan. Basically, I’m wondering why the author proposed a plan with a lower acceleration. It kind of seems like a plot hole, since the ship is capable of higher acceleration, and the fuel constraint doesn’t seem to increase...

Apologies, here is the content of the attachment: Relevant equations: Proper time to travel a given distance at constant acceleration: ##\tau = \frac{c}{a}\cosh^{-1}\left(1 + \frac{a D}{c^2}\right)## Rapidity: ##\phi = \frac{a \tau}{c}## Velocity at a given rapidity: ##v = c \tanh{\phi}##...

My image got compressed beyond readability, so here is the PDF version

Warning: Minor spoilers for the book Project Hail Mary ahead. A ship has travelled to Tau Ceti (11.9 light years from Earth). The ship uses light as propulsion, and effectively converts the fuel mass into light energy. It carries 2,000,000 kg of fuel. During the journey it underwent a constant...