Question: Scenario: I have a generation ship moving between two star systems. Given that such a ship needs to have a completely self sufficient life cycle system to make it viable, ejecting mass continuously does not seem to me to be a very viable option for acceleration.

With this given scenario what other methods can be used to achieve acceleration and deceleration in interstellar space? 
I would like answers to be bound by the known laws of physics in our universe.

Answer: 
The best way to conserve mass is to use external energy to accelerate the ship.

[Robert L Forward](http://www.transorbital.net/Library/D001_AxA.html) had designed a multi stage lightsail which allowed ships to accelerate, and then, by detaching portions of the sail and using them to reflect laser energy back to the starship, decelerate at the target star. The disadvantage is laser driven lightsails are still quite massive, and the amount of laser energy needed to drive the starship is measured in *Terrawatts*. Building the laser launcher alone is a huge undertaking (usually described as being done by building a ring of solar power satellites and lasers in polar orbit around Mercury), gigantic focusing lenses over a thousand kilometres in diameter in the outer solar system, and then the starship itself.

[![enter image description here](https://i.stack.imgur.com/4pmW3.gif)](https://i.stack.imgur.com/4pmW3.gif)

Since a generation ship is bound to be larger than an exploration starship like the one Froward was proposing, you will need to scale things up considerably. (Realistically, if you can accelerate a ship to the sorts of speeds Forward is considering, then it isn't really a generation ship, but since it may take centuries to build colonies in the new star system, a generation ship sized construct is probably needed as a base to live and work out of until fresh colony space is created. NextBigFuture published an interesting speculation about "[Tabby's Star](http://www.nextbigfuture.com/2016/08/tabby-star-abnormalities-in-dimming-are.html)" which suggested an orbiting mirror the size of the Moons orbit around the Earth could power monster lightsails.

[![enter image description here](https://i.stack.imgur.com/3MGUY.jpg)](https://i.stack.imgur.com/3MGUY.jpg)

If a lightsail ins't your thing, then maybe a gigantic mass driver could be used to accelerate the starship. Deceleration can be handled by various means including a rocket, magsail or deploying a lightsail to use the target star's energy. Once again. we are talking about a monstrous device. Marshal Savage conceptualized something like this in his book "[The Millenial Project](http://rads.stackoverflow.com/amzn/click/0316771635)", describing a system which *stretched across the solar system*. One reason to make it so big is to keep acceleration down to a reasonable limit (3g is about the best an unprotected human can withstand, trained pilots with G suits can withstand up to 9g, for sustained acceleration beyond that limit people might have to be immersed in fluid and have all their internal spaces packed with oxygenated fluorocarbons).

Once again, using high initial accelerations allows the ship to cross the interstellar distance in decades rather than centuries, so the advantage to a large ship is as a shelter and workspace on arrival; generations of colonists might need to stay aboard the ship until a colony planet is terraformed.
Momentum of a *closed system* is always conserved unless there is external force.

Consider the mass of the rocket together with its fuel at $t\_0$ be $M\_0\,.$ Let the gas be ejected at $\dot m\,.$ Therefore, mass of the rocket along with its remnant of fuel after an infinitesimal increment $\mathrm dt$ is given as $$M(t\_0+ \mathrm dt) = M\_0 - \dot m~\mathrm dt\,.$$

Linear-momentum at time $t$ is $(M\_0-\dot m~\mathrm(t-t\_0) )\mathbf v\,.$

Applying the conservation of Linear momentum, we get \begin{align}(M-\dot m~\mathrm dt)\mathbf v\_\textrm{rocket w.r.t. ground} + (\dot m~\mathrm dt)\mathbf v\_\textrm{gas w.r.t. ground} &= \mathbf 0\\ \implies(M-\mathrm dM)(\mathbf v+ \mathrm d\mathbf v) + \mathrm dM(\mathbf v+ \mathrm d\mathbf v-\mathrm v\_\textrm{gas w.r.t. rocket}) & = \mathbf 0\\ \implies \mathrm d\mathbf v &= \frac{\mathrm dM~\mathbf u}{M-\mathrm dM}\\ \implies \dot{\mathbf v } &= \frac{\dot m\mathbf u}{M\_0-\dot m t} \,,\end{align} where $\mathbf u$ is the velocity of the gas with respect to the rocket; in the derivation, product of infinitesimal quantities have been neglected.