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Imagine I have a generation ship that is heading to a nearby star system say 10 light years away, the average lifespan for the crew is 150 years on Earth and is expected to increase by about 5 years with each generation. No cryonic suspension due to the ban on any form of suspended animation on human by law and many policies are in place to ensure the population demography on board is healthy across every generation, so we can now laser focus on the economic and science aspects of this one way trip.

I believe delta v is important when planning trips within the solar system since as the name suggests it is the changes in velocity when jumping between orbits, what about jumping between star systems? Are we going to factor delta v for all interstellar flights regardless? if so why?

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  • $\begingroup$ Are you strictly limiting the concept of Delta V to purely reactionary mass? Or is it also the energy source on board (fusion mass, fuel, quantity of anti-matter) that gets consumed (converted to energy)? What about the 'Delta V' from gravitational boosts that is currently commonly used in interplanetary travel, that does not have to be pre-loaded on the ship in any form at the start that needs to be 'used up'? Or for instance in Alcubierre-type drives, where Delta V (even at velocities below FTL) is purely based on energy? Or is the 'energy source' some form of Delta V 'reactionary mass? $\endgroup$ Nov 30 '21 at 16:01
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Physics is physics everywhere.

  1. Your generation ship is coasting between start and arrival point: this means that it will be slowed down or accelerated by the attraction of the body whose Hill's sphere it's passing in at any moment. This influences the delta v. See the plot of the heliocentric velocity of Voyager 2 for a reference, and notice how it keeps decreasing, albeit slowly enter image description here

  2. Assuming your generation ship wants to land on a planet or orbit it and not just smack on it at several tens of km/s, it will need to slow down during the approach. Once again, this is delta v.

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  • $\begingroup$ Comments are not for extended discussion; this conversation has been moved to chat. $\endgroup$
    – L.Dutch
    Dec 1 '21 at 16:11
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Yes, it's relevant. For a few reasons:

  1. If your delta v is 0, you're not going anywhere. Sure this is a degenerate case, but if it were truly irrelevant it wouldn't matter. More practically, your delta v is going to need to be at least your star's escape velocity (barring exotic scenarios such as an extremely close approach by your target star.)
  2. Stars are not at rest with respect to one another. So at a minimum, you will require at least the delta v of the relative speeds of your origin and destination systems.
  3. Even in generational ships, time to destination matters. Realistically speaking, half your delta v is basically your cruising speed (ok, this doesn't hold as you get up into the really relativistic speeds, but in that case we're probably not talking generational ships.) So delta v will directly relate to how long your journey will take.
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  • $\begingroup$ So the voyager spacecraft, with no 'Delta V' left, is not going anywhere? $\endgroup$ Dec 1 '21 at 15:11
  • $\begingroup$ @JustinThymetheSecond Sure, magically construct your generational ship already at cruising speed and you won't need any delta v to get to your destination. Still might want some if you're planning on stopping though... $\endgroup$
    – Gene
    Dec 2 '21 at 7:48
  • $\begingroup$ Your quote "If your delta v is 0, you're not going anywhere. " You do not need delta v to go somewhere, but you Do need delta v to change directions. Basic Newtons Laws. 'Aim and shoot' works perfectly fine. $\endgroup$ Dec 2 '21 at 15:23
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For interstellar journeys at sub light speeds the size of the DV is largely irrelevant in terms of the time it takes to complete the journey.

Using your example and assuming an upper velocity (which is not mentioned in your question btw) of .10C the journey is going to take approx 100 years with the acceleration & deceleration phases added on.

From the perspective of the crew it doesn't really matter if the ship takes 3 years to reach its 'cruising' velocity or just 3 weeks. With latter you end up with a 100 year (plus 6 weeks) long journey. With the former it takes 106 years. For all intents an purposes putting the 'pedal to the metal' only shaves a measly approx 6% off the total travel time. Hardly a huge saving for a generation ship. And of course the time saving only worsens with increases the distance. Double the distance the ship has to travel to 20 LY and at the high DV your only saving approx 3% on travel time over the lower DV. And on it goes.

Plus a lower DV is an easier engineering challenge which you want wherever possible. Everything on a generation ship has to be engineered to last because if breaks down and cant be repaired with what you have on board you screwed.

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    $\begingroup$ I think you fundamentally misunderstand what delta v is. You seem to confuse it with maximum acceleration. Delta v is about you ability to change you velocity by a certain amount. How fast you do it isn't relevant. In fact, designers often have to trade delta v for acceleration and vice versa. So, given that you can roughly expand half the delta v accelerating, this is your cruise speed. Roughly as solarsystems and planets do move through space at velocities and on different vectors, so a few dozen km/s will go into correcting that. $\endgroup$ Nov 30 '21 at 9:08
  • $\begingroup$ No I understand it refers the rate of change in velocity. My point, however poorly expressed is that the shortest time required for any journey between two points is set by the maximum possible velocity and the time it takes to reach that velocity. The question was centered about issues with aging and the generations needed to make the trip. In that context Delta V is largely irrelevant. It is relevant of course in terms of the engineering limitations/drive type and astro-navigation etc but not really the length of the journey. $\endgroup$
    – Mon
    Nov 30 '21 at 21:35
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    $\begingroup$ Rate of change in velocity is dv/dt (aka acceleration.) dv/dt != dv. $\endgroup$
    – Gene
    Nov 30 '21 at 22:55
  • $\begingroup$ @Mon Keep in mind that "maximum possible velocity" is actually the speed of light. Not 0.1c. If a ship can accelerate to 0.1c in half the time, it can in theory reach 0.2c in the same time (all other factors being equal). Which is a substantially more useful difference since you turn your hundred year journey into fifty.. Of course, that's not factoring in the Rocket Equation. but if I have twice the delta-V, that means functionally half the flight-time assuming the same acceleration curves. $\endgroup$
    – Ruadhan
    Dec 1 '21 at 15:21
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    $\begingroup$ No one here seems to agree with what Delta V is (noun or term), but they all insist that what you said is not it. Go figure. 'Delta V' is needed to REACH a particular velocity, but it is not needed to SUSTAIN a particular velocity unless a negative 'Delta V' (resistance, friction, or gravity for instance) is applied (basic Newtons' Law). 'Acceleration' is the RATE of change between two velocities (time dependent), the term 'delta-v' is the magnitude of the change, the noun 'Delta V' is what 'powers' or 'produces' that change. $\endgroup$ Dec 1 '21 at 15:25

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