# As a ship accelerates to relativistic speeds, would its fuel consuption appear to speed up due to time dilation?

Given a ship under constant acceleration toward relativistic speed, for example 0.9c...

(a) Is it safe to assume the fuel consumption is constant over distance travelled? and if so...

(b) Would fuel consumption appear to the pilot to increase over time due to dilation effects?

(a) Is it safe to assume the fuel consumption is constant over distance travelled?

No. As fuel is burned, the spacecraft decreases in mass. If we're saying the spacecraft has a constant acceleration, this means that its thrust (and thus fuel consumption rate) must decrease in time to maintain a constant acceleration with a lower mass.

(b) Would fuel consumption appear to the pilot to increase over time due to dilation effects?

No. The pilot and the spaceship are in the same frame of reference, so there is no time dilation effects between the two. The fuel consumption rate the spacecraft sees is exactly what the pilot will see as long as the pilot is on the spacecraft. Time dilation only affects things moving at different speeds relative to each other.

Bonus: for an outside observer

No. Even if it were the case that fuel consumption were constant in the frame of the spacecraft, to an outside observer the time dilation effects means that the apparent passage of time on the spacecraft is slower than for the observer. Thus, fuel consumption would be observed to decrease with time due to the time dilation.

• Your answer for (b) is for an outside observer, but I was asking in regard to the pilot. Does this change your answer? (And thanks for pointing out the change in mass due to fuel consumption. That had completely slipped my mind.)
– JBH
Commented Mar 12, 2018 at 19:10
• @JBH, From the pilot's point of view, the ship is always stationary. Commented Mar 12, 2018 at 19:19
• @jameslarge, the fuel guage (so to speak) is stationary? That can't be true.
– JBH
Commented Mar 12, 2018 at 19:29
• I'm not saying that the needle on the fuel gauge never moves. I'm saying that from the POV of a person sitting in the pilot's seat, nothing in the ship is affected by time dilation because the seat is bolted to the deck. The ship does not move with respect to the seat and vice versa. Commented Mar 12, 2018 at 19:46
• @JBH, sorry for misreading the question. I have edited my answer accordingly. jameslarge is correct Commented Mar 12, 2018 at 21:41