# Could a rocket come close to the speed of light?

• Pauru
In summary, the conversation discusses the possibility of a rocket reaching 99% the speed of light with unlimited fuel and a constant acceleration. Some argue that this is not possible due to the increase in mass as velocity increases, while others argue that this concept is outdated. The rocket would never stop accelerating and there is no limit to how close it could get to the speed of light given enough time and space. The discussion also touches on the fuels that could potentially allow a rocket to reach such high speeds, such as antimatter and advanced fusion engines, but it is noted that these are currently only theoretical. Overall, the conversation delves into the theoretical possibilities of a rocket reaching extremely high speeds in space.
Pauru
Hey everyone!

So a guy at work today said "if you have a rocket with unlimited fuel(hypothetically speaking of coarse) at a constant accelleration, and was in space. It's velocity could reach like 99% the speed of light" I argued that it was not possible, as it approached the speed of light it's mass would increase and you would require more energy to increase the velocity. I realize the question is flawed already with the fuel at an inflate amount.

Anyway I then looked at liner velocity equations v=v1 + adt... So let's just use some numbers v= ? v1= 0 a= 9.8 and dt = infinite. After I look at this equation it made me think he was right.

So I have a few questions. First is it possible for a rocket to achieve this? At what velocity would the rocket stop accelerating? did I use the right equations? Is there a better equation to use? And what equation takes into account for the increase in mass as velocity increase?

I'm sorry if these questions are annoying you guys probably run into them a lot.

Anyway thanks for your time and help

-Pauru

Welcome to PF Pauru. Taking out the problems of blue shifting oncoming radiation, maintaining the ship etc there is no limit to how close to the speed of light a rocket can get given enough time and space.

The rocket would never stop accelerating. From the perspective of the crew the rocket accelerates at a constant level always.

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You argued that it's impossible to reach 99% the speed of light. This is incorrect. It's not possible for a rocket to reach 100% the speed of light, but it IS possible for it to reach 99%. There is a HUGE distinction there.

Even 99.999999999999999999% is possible (theoretically).

If you were measuring the speed of this magical rocket from earth, it need not stop accelerating. However, it's acceleration would slow down more and more as it approached the speed of light...but it never need reach 0. It's kind of like walking across a room by halving the distance to the wall. You will never reach the wall, but you can keep getting closer.

As ryan_m_b mentioned, from the astronauts' perspective the rocket can keep a constant acceleration. The discrepancy is due to relativity.

Pauru,

Since it's impossible to have an unlimited supply of fuel, any discussions of achieveable speeds of a rocket with infinite mass is moot. That being said, the discussion then moved to 'What fuels could get me close to the speed of light?' The answers for on-board fuels (which excludes schemes like external fixed lasers pushing you along, or solar sails) comes down to antimatter, or advanced fusion engines. Top speeds depend on the overall design and fuel, but can be perhaps 10% to 50% of light speed. Now, could a Gigaton of antimatter get you to 99% of c? Perhaps, but I wouldn't want to be in the same solar system when they test it! All this is future tech though...

Yes, whether in practice you could do this feat with a rocket is a different discussion altogether. In theory, however, even a simple chemical rocket could reach close to the speed of light. It would probably need to be bigger than the earth, but that's another story...

Well, no. A chemical rocket the size of the Earth would need to accelerate it's own mass. Chemical rockets of any size won't get anywhere near 'c'.

RocketSci5KN said:
Chemical rockets of any size won't get anywhere near 'c'.

This is simply not true. There is no reason why a chemical rocket of any size won't get anywhere near c. Yes the more massive it is the more it has to accelerate but we can just add more fuel (with a bit more to counteract that fuel etc). It may be huge and would never be built but to say it's not technically possible is just plain false.

Lsos said:
Even 99.999999999999999999% is possible (theoretically).

If you mean infinitely many 9's, then it's not possible because 0.9999999... (infinite 9's) = 1.

RobertT said:
If you mean infinitely many 9's, then it's not possible because 0.9999999... (infinite 9's) = 1.

now this discussion is going into maths not physics. RoberT is using calculus.

my opinion: infinite fuel(physically infinite means big big big amount)
it may be big amount but will end at at some time when speed reaches (0.999999...)*c

but the number of nine here are not infinite it is a big number say 10^10000 or more but is definitely a num (not infinity of calculus)

so 0.9999999... doesn't equals 1 here

through relativity theory it can be proved (mathematically) that no matter for how much time we apply force on a particle the particle will only reach speed of light at t=infinity

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so say the rocket is sent with INFINITE fuel( i m considering the real infinite which means fuel never ends) it will reach speed of light at infinite time...

now ifinite time is also the biggest time or in other words *the time that never comes*
this means time never comes when speed reaches 'c'

so we can see we take practically(in my last thread) or theoritically the ROCKET CAN NEVER REACH speed of light

darkxponent said:
now ifinite time is also the biggest time or in other words *the time that never comes*
this means time never comes when speed reaches 'c'

so we can see we take practically(in my last thread) or theoritically the ROCKET CAN NEVER REACH speed of light

No one was suggesting it could. The question was how close a rocket could come.

ryan_m_b said:
No one was suggesting it could. The question was how close a rocket could come.

i saw RoberT suggesting it...so i just clarified

how close rocket could come: theoritically: (1-h)*c where limit(h-->0)

practically it can't be specified in numbers as it depends on the type of technology we have...u should ask someone from NASA...we are not ones who can comment on this...maybe oneday we can reach the (1-h)*c

darkxponent said:
practically it can't be specified in numbers as it depends on the type of technology we have...u should ask someone from NASA...we are not ones who can comment on this...maybe oneday we can reach the (1-h)*c

Whilst it depends on what type of technology we have as to whether a rocket will practically reach close to the speed of light that was not the question. As for if "we" can answer the question I would advise that you refrain from trying to guess the level of expertise of the fellow people on this forum.

ryan_m_b said:
This is simply not true. There is no reason why a chemical rocket of any size won't get anywhere near c. Yes the more massive it is the more it has to accelerate but we can just add more fuel (with a bit more to counteract that fuel etc). It may be huge and would never be built but to say it's not technically possible is just plain false.

It really would be "technically" impossible because the word "technical" implies doable with technology. The energy available in a load of chemical fuel is not enough to get past a limiting velocity - which is far below c.
The only hope for really high speeds is to use things like Ion drive in which the mass which is ejected out of the back is a very small fraction of the ship's total mass and the velocity of the ejecta is a significant fraction of c relative to the ship. And you still have the problem of the total amount of energy that the ship would have to carry in the form of fuel mass.
It's a very similar problem to the one of launching from Earth; total mass vs useful payload mass. We tend to solve this with multistage rockets so as not to need to carry more mass than necessary, in the form of fuel containers / engines. Perhaps a similar multistage system could help increase the upper speed limit achievable.

There's a nice wikipedia article http://en.wikipedia.org/wiki/Relativistic_rocket" on the subject.

Note there are two scenarios. Rockets carrying their own reaction mass/energy fuel and craft propelled using external means (light-sails and such).

The most efficient theoretical self propelled rocket would use total conversion of mass to energy (if that's possible) to direct electromagnetic waves as thrust (light, microwaves, or whatever). In science fiction this is often referred to as a photon drive. Note that the thrust will be independent of the wavelength emitted, but only a function of the power = c times the force.

Such a drive will asymptotically approach c (relative to its starting frame) as it "burns" up 100% of its mass as fuel assuming perfect efficiency.

You may notice that the "starting frame" can be changed to any point later in its flight and the answer is still the same. This may seem counter intuitive but it is a reflection of the invariance of the speed of light under frame transformations in SR.

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Pauru said:
Hey everyone!

So a guy at work today said "if you have a rocket with unlimited fuel(hypothetically speaking of coarse) at a constant accelleration, and was in space. It's velocity could reach like 99% the speed of light" I argued that it was not possible, as it approached the speed of light it's mass would increase and you would require more energy to increase the velocity. I realize the question is flawed already with the fuel at an inflate amount.

Anyway I then looked at liner velocity equations v=v1 + adt... So let's just use some numbers v= ? v1= 0 a= 9.8 and dt = infinite. After I look at this equation it made me think he was right.

So I have a few questions. First is it possible for a rocket to achieve this? At what velocity would the rocket stop accelerating? did I use the right equations? Is there a better equation to use? And what equation takes into account for the increase in mass as velocity increase?

I'm sorry if these questions are annoying you guys probably run into them a lot.

Anyway thanks for your time and help

-Pauru

Let's take the rocket equation. Classically this is, I think (ignoring gravity):

v = ve ln(m0/m)

With ve = exhaust gas speed relative to the rocket, and m0 = begin mass. For m=end mass, v= end speed.

This complicates with SR, as it gets indeed increasingly more difficult to accelerate wrt the rest system. Now as I'm lazy (and with lack of time), I checked on the web and found more on that here:

http://en.wikipedia.org/wiki/Relativistic_rocket
and from there
http://math.ucr.edu/home/baez/physics/Relativity/SR/rocket.html

According to the resulting equations, it appears still to be possible - in principle! - to reach 0.99c.

Cheers,
Harald

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sophiecentaur said:
It really would be "technically" impossible because the word "technical" implies doable with technology. The energy available in a load of chemical fuel is not enough to get past a limiting velocity - which is far below c.
The only hope for really high speeds is to use things like Ion drive in which the mass which is ejected out of the back is a very small fraction of the ship's total mass and the velocity of the ejecta is a significant fraction of c relative to the ship. And you still have the problem of the total amount of energy that the ship would have to carry in the form of fuel mass.
It's a very similar problem to the one of launching from Earth; total mass vs useful payload mass. We tend to solve this with multistage rockets so as not to need to carry more mass than necessary, in the form of fuel containers / engines. Perhaps a similar multistage system could help increase the upper speed limit achievable.

My use of the word "technically" was incorrect, I meant theoretically. Here is my reasoning;

We have a chemical rocket, we add more fuel to it. This increases the mass so decreases the rate of acceleration the engines can give. However if we just keep adding mass there won't be a point where adding the mass gives no overall effect to top speed.

ryan_m_b said:
My use of the word "technically" was incorrect, I meant theoretically. Here is my reasoning;

We have a chemical rocket, we add more fuel to it. This increases the mass so decreases the rate of acceleration the engines can give. However if we just keep adding mass there won't be a point where adding the mass gives no overall effect to top speed.

OK. Except that the mass of fuel that needs to be ejected is governed by the speed at which you can eject it (momentum transfer). That's why ion drive (very low mass and high eject speed) - or, better still, photon drive, gives a higher possible final speed.

## 1. How close to the speed of light can a rocket actually travel?

The speed of light is approximately 299,792,458 meters per second, which is incredibly fast. While it is not possible for a rocket to reach the exact speed of light, it can come very close. The fastest human-made object, NASA's Juno spacecraft, has reached speeds of about 265,000 kilometers per hour, or about 0.00009% of the speed of light.

## 2. What are the main challenges in achieving such high speeds?

There are several challenges in achieving high speeds close to the speed of light. The first is the amount of energy required to accelerate an object to such high speeds. As an object approaches the speed of light, its mass increases dramatically, making it more difficult to accelerate. Additionally, there are significant challenges in designing a propulsion system that can withstand the extreme forces and temperatures involved.

## 3. Would time slow down for someone on a rocket traveling at such high speeds?

According to Einstein's theory of relativity, time is relative and can be affected by speed. As an object approaches the speed of light, time will indeed slow down for anyone on the rocket. This phenomenon, known as time dilation, has been observed in experiments with high-speed particles and is a fundamental concept in modern physics.

## 4. Is there a limit to how fast a rocket can travel in space?

There is no known limit to how fast a rocket can travel in space. However, as an object approaches the speed of light, it will require exponentially more energy to continue accelerating. Additionally, there may be other practical limitations, such as the ability to safely control and navigate a spacecraft at such high speeds.

## 5. How would traveling at close to the speed of light affect the crew on a rocket?

Traveling at such high speeds would have significant effects on the crew of a rocket. In addition to experiencing time dilation, the crew would also experience increased gravitational forces and extreme temperatures. These effects would require advanced technology and careful planning to ensure the safety and well-being of the crew during the journey.

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