Why is it that space travel takes so long? If space is (nearly) a vacuum and by Newton’s laws, the acceleration of a spacecraft would be incredibly high, wouldn’t it allow the spacecraft to reach nearby celestial bodies quickly?

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Edit: also, is it possible to approach the speed of light simply by propelling a spacecraft, assuming capacity and weight of fuel isn’t a concern?

In: Physics

Acceleration it according to F=m*a is a=f/m. So the accelerate quickly you need a powerful engine compared to the mass of the spacecraft. But a powerful engine require more fuel and you have a more mass in the spacecraft.

So it is limitation it not the max speed but the amount of fule (more exact propellant) you can carry and for how long you can use the engine that is the problem.

The amount fuel you need increase a exponentially way because initially you also need to accelerate that fuel that you have in the spacecraft. The result in the [rocket_equation](https://en.wikipedia.org/wiki/Tsiolkovsky_rocket_equation) where the limitation is the “efficiency” (specific impulse) of the rocket engine.

You can look at [https://www.youtube.com/watch?v=uWjdnvYok4I](https://www.youtube.com/watch?v=uWjdnvYok4I) for a video with a beter explanation in simple terms.

The problem is often called “tyranny of the rocket equation”

The amount of energy needed to accelerate an object increases on a curve based on it’s mass and how fast you want to go. The heavier the object, and the faster you want to travel, the more energy you need to apply to accelerate.

The problem is that Fuel is mass, so the faster you want to go, the more fuel you have to carry. This makes the rocket heavier and therefore slower.

Now with that in mind you need to realize just how vast space is.

The nearest solar system to ours is Alpha Centauri at 4.367 Light Years. This means that traveling at the speed of Light it would take you 4.367 years to get there.

By comparison Apollo 11 was traveling at 39,897 km/h, which sounds fast but the speed of light is 1,079,251,200 km/h. So Apollo 11 was traveling at .00003 PSL (Percentage Speed of Light) if I’m doing my math correctly.

We will need a revolution in propulsion technology to get up to a speed needed to reach Alpha Centauri in a lifetime.

EDIT: Another thing to consider is the G-force of acceleration. A human body is only able to sustain a few G or a few times the force of gravity for any length of time before we start getting injured. If a space craft were to accelerate too fast we would all be splattered against the bulkhead.

That acceleration has to be generated some how(fuel has mass). Once you’re on your way you would spend half your trip accelerating and the other half slowing down so you’re only really hitting your top speed for a short time. In a car you brake via the stationary road in space that’s not possible.

In Newton’s laws, Force equals Mass times acceleration, so acceleration is limited to Force divided by mass, and the mass of spacecraft plus all the fuel needed is very high.

Also, you need 9.8 m/sec^2 just to start accelerating away from earth. The bulk of your fuel is going to be spent just trying to accelerate away from earth’s gravity well. Which is why people sometimes talk of building and fueling rockets on the moon or in orbit or in the asteroid belt or any other non-earth location.

Additionally, space is fairly huge. So for New Horizons (the mission to Pluto), even though the spacecraft accelerated to 36,000 MPH, or the equivalent of 47 times the speed of sound if it were on earth, it still took almost 10 years for New Horizons to get to Pluto.

“Quickly” is relative. With constant acceleration you could reach amazingly high speeds. However, even at its closest, Mars is still about 36 MILLION miles away. Venus is about 24 million miles away but can be over 160 million miles away. Unfortunately, the energy required to maintain that acceleration and the limitations of human frailty to how quickly that acceleration can occur need to be considered as well.
Even if we found a way to accelerate an object infinitely, there must be an equal amount of slow down time to actually stop at a destination.
Half your trip would be acceleration and half would be trying to stop.