Friction in space as approaching light speed

[Jackslap]

I was talking with a guy at work about relativity. I have VERY limited knowledge in the area of physics ( one college level class on radiation physics, and read a few books and essays on my own) but he has absolutely none. He watched a show on Nova or Discovery that blew his mind about light speed and time travel etc.

I was explaining to him a little bit about some things I had read when this OTHER guy comes up a starts pontificating a little bit. He's kind of a know-it-all jerk who likes to show off. Granted he has more education than the rest of us (degree in engineering of some sort), but he always tries to lord himself over everyone else. No one was arguing with him, he just started volunteering a bunch of information to everyone. He said one thing that caught my interest and I want to know if it is correct. It sounds like it probably is but I just want to make sure.

I am not looking to prove him wrong, just verify what he said.

He said that there is still friction in space due to small particles floating around (dust?) and also miniscule amounts of gas like hydrogen and helium. He said that those elements however are so very little like 1 atom per cubit meter, that they don't really have an effect on objects ( spacecraft ). But he said that as you approach the speed of light, they DO start to have an effect because now said object is traveling through MUCH more area than it was a slower speeds, so the amount of hydrogen, helium, and dust affecting the object is now a factor. A direct relationship between speed and the amount of friction being created.

Is that true? This is my first post so I'm sorry if I went too long or whatever. I have an interest in this stuff, but am only starting to realize it at an adult age. Too bad I didn't care enough when I was in high school, perhaps my whole life would be different.

 

[Nabeshin]

There was a thread similar to this not too long ago where I derived a general equation for the temperature of a spaceship as a function of time.:

https://www.physicsforums.com/showthread.php?t=291975

You can play with it if you want and see how hot it will get as .5c, .9c, etc, but at such speeds it probably doesn't work too well because I didn't take into account relativity.

 

[Jackslap]

O.k. What I did was post an incomplete question. I don't know enough about physics to start using your formula my friend.

The guy was saying that there is friction in space, and that friction in space becomes a factor as something approaches the speed of light.

So I guess if I had to come up with a hypothetical situation I'd ask:

If I were traveling at a much slower speed, like the space shuttle, could I turn off the engines and keep traveling infinitely if I ignore gravity or slamming into another object.

BUT, if I were now traveling at the speed of light to begin with, would I be able to continue at THAT speed, or would friction become such a huge factor that I would not be able to maintain and start slowing down to a speed in which friction is no longer a factor.

Remember, it was that dude that said that hydrogen, helium, and dust particles are what causes faster moving things to slow down and that at slower speeds those particles do not become a factor.

I hope I am coming across clear.

 

[Nabeshin]

O.k. What I did was post an incomplete question. I don't know enough about physics to start using your formula my friend.

The guy was saying that there is friction in space, and that friction in space becomes a factor as something approaches the speed of light.

So I guess if I had to come up with a hypothetical situation I'd ask:

If I were traveling at a much slower speed, like the space shuttle, could I turn off the engines and keep traveling infinitely if I ignore gravity or slamming into another object.

BUT, if I were now traveling at the speed of light to begin with, would I be able to continue at THAT speed, or would friction become such a huge factor that I would not be able to maintain and start slowing down to a speed in which friction is no longer a factor.

Remember, it was that dude that said that hydrogen, helium, and dust particles are what causes faster moving things to slow down and that at slower speeds those particles do not become a factor.

I hope I am coming across clear.

Friction is ALWAYS a factor. There is no magical speed at which friction no longer slows your craft -- the effect just becomes minimal with respect to small velocities. A space shuttle would eventually come to a halt, just as a craft traveling at .9999c would.

As you can see from my example, kinetic energy loss is on the order of .001J/s. So even at .1c the change in speed from ISM collisions is really minimal.

 

[Jackslap]

Awesome man, you rule. I'm am no where close to being able to understand all that math that you posted in your other threads. I'm very new to all this. I don't understand the formulas, but I'm finding out that I like the theories and real life applications for all this physics stuff.

So, to press my luck...

He (the guy that I work with) also said that it is impossible for any object to approach light speed because of this whole friction thing. He said that as you go faster, you go through more area, and therefore more of that space particulae will affect you and serve to slow you down.

Now, I remember hearing something about approaching light speed is impossible because as you do so something happens to the mass of the object and the amount of energy it takes to keep up light speed approaches infinity. So you could never get going that fast. Is that correct? If it is, leave that aside for another discussion.

My new question is, does the friction thing also become such a factor as you approach light speed that is serves to prevent you from getting there? Meaning, if I had the fuel and the thrust to approach light speed, could I do it or would friction prevent me?

Look at me talking like a Star Trek nerd, HA! I'm only asking all of this to satisfy my curiosity and to figure out if I should be giving this guy I work with more credit.

 

[ImAnEngineer]

It is theoretically possible to approach the speed of light (usually denoted as c), but not to reach it. Because the mass goes to infinity as the speed of your spacecraft goes to c. So when you approach c, the amount of energy put into get an extra velocity dv gets bigger and bigger. Therefore it is impossible to actually reach c with a finite amount of energy regardless of the friction.

 

[HallsofIvy]

I was talking with a guy at work about relativity. I have VERY limited knowledge in the area of physics ( one college level class on radiation physics, and read a few books and essays on my own) but he has absolutely none. He watched a show on Nova or Discovery that blew his mind about light speed and time travel etc.

I was explaining to him a little bit about some things I had read when this OTHER guy comes up a starts pontificating a little bit. He's kind of a know-it-all jerk who likes to show off.

Don't you just hate it when people start pontificating and showing off, interupting YOUR pontificating and showing off!

Granted he has more education than the rest of us (degree in engineering of some sort), but he always tries to lord himself over everyone else. No one was arguing with him, he just started volunteering a bunch of information to everyone. He said one thing that caught my interest and I want to know if it is correct. It sounds like it probably is but I just want to make sure.

I am not looking to prove him wrong, just verify what he said.

He said that there is still friction in space due to small particles floating around (dust?) and also miniscule amounts of gas like hydrogen and helium. He said that those elements however are so very little like 1 atom per cubit meter, that they don't really have an effect on objects ( spacecraft ). But he said that as you approach the speed of light, they DO start to have an effect because now said object is traveling through MUCH more area than it was a slower speeds, so the amount of hydrogen, helium, and dust affecting the object is now a factor. A direct relationship between speed and the amount of friction being created.

Is that true? This is my first post so I'm sorry if I went too long or whatever. I have an interest in this stuff, but am only starting to realize it at an adult age. Too bad I didn't care enough when I was in high school, perhaps my whole life would be different.

 

[Jackslap]

Ha! I hope it didn't really come off that way. I wasn't pontificating so to speak. Just commiserating a little bit with my fellow worker about how little both of us really knew about the subject. I had just happened to be able to clarify a certain thing he was questioning. As I said before my knowledge is quite limited. I didn't even know that the speed of light is represented as c. So thank you engineer for your post.

Anyway, if you knew the other guy, the pontificator (not a word I think), you'd understand. He's very socially awkward and he's the type of guy that thinks breaking the ice with someone is insulting them and then talking about all of his wonderful experience as an engineer. He pretty much dominates every conversation that he's a part of, doesn't listen or accept things that other people say. He's always got an experience that was bigger, better, faster, or in some other way superior to yours. You've met the type I'm sure.

It sounds like his statements were correct though, which I suspected, so I will have to keep my mouth shut on this one and accept the fact that he really does know somethings I don't (which isn't hard because I don't know much about physics as I have said). I hope I've made it quite clear that I'm not looking to argue with anyone. In fact I never disputed what he was saying as he said it. I merely sought council elsewhere to verify the info he gave.

 

[LURCH]

So, to press my luck...

He (the guy that I work with) also said that it is impossible for any object to approach light speed because of this whole friction thing. He said that as you go faster, you go through more area, and therefore more of that space particulae will affect you and serve to slow you down.

Now, I remember hearing something about approaching light speed is impossible because as you do so something happens to the mass of the object and the amount of energy it takes to keep up light speed approaches infinity. So you could never get going that fast. Is that correct? If it is, leave that aside for another discussion.

My new question is, does the friction thing also become such a factor as you approach light speed that is serves to prevent you from getting there? Meaning, if I had the fuel and the thrust to approach light speed, could I do it or would friction prevent me?

This is the kind of question from which one can learn a great deal. Truth is, it's two very different questions and the difference between them is absolutely crucial.

So, short answer; yes, friction could become a factor at very high speeds, even in space. And even that would depend on the region of space through which one travels. Just as jets can achieve higher speeds by traveling through the thinner air at high altitudes, a spacecraft traveling through intergalactic space would experience a lot less drag than one moving between stars within a galaxy.

But this effect is merely friction, a somewhat "ordinary" force (one with which we all deal on a regular basis). The effects of relativity are much different. The "something" that happens to the mass of the object is a property of relativity. It can be said that the mass of the object approaches infinity as the speed approaches c, so that the last push to achieve c takes an infinite amount of force. But it could also be rephrased to say that time slows down for the object approaching c, so that the last bit of acceleration from "almost c" to "c" would take all of eternity to happen (IOW, never happens).

Now, there is a similarity between the two, in that they both increase as speed increases. But the big difference is that the friction could be overcome by brute force. If it were possible to travel at c at all (if there were no relativistic effects), then it would be possible, with a big enough thrust, to achieve c in spite of friction. Even if no such source of thrust could be developed, it could at least be imagined. It could even be calculated, simply by determining the density of "stuff" through which the vehicle will travel, the amount of drag that much stuff would cause, and the amount of thrust needed to overcome that much drag.

But overcoming relativistic effects to achieve c is not even possible in theory. When the amount of thrust required is calculated, the answer is infinite. When the amount of time it would take to get up to that speed is calculated, it is also infinite. So one could achieve c despite friction, if there were no relativistic effects; but one could never achieve c in spite of relativistic effects, even if there were no friction.

Look at me talking like a Star Trek nerd, HA! I'm only asking all of this to satisfy my curiosity...

You are among friends; that is the exact reason why (almost) every single one of us is here at PF!

 

[Jackslap]

Now, there is a similarity between the two, in that they both increase as speed increases. But the big difference is that the friction could be overcome by brute force. If it were possible to travel at c at all (if there were no relativistic effects), then it would be possible, with a big enough thrust, to achieve c in spite of friction. Even if no such source of thrust could be developed, it could at least be imagined. It could even be calculated, simply by determining the density of "stuff" through which the vehicle will travel, the amount of drag that much stuff would cause, and the amount of thrust needed to overcome that much drag.

But overcoming relativistic effects to achieve c is not even possible in theory. When the amount of thrust required is calculated, the answer is infinite. When the amount of time it would take to get up to that speed is calculated, it is also infinite. So one could achieve c despite friction, if there were no relativistic effects; but one could never achieve c in spite of relativistic effects, even if there were no friction.

WOW! Exactly what I was looking for. Thank you for explaining it so clearly. What I need to work on now for myself is understanding these "relativistic effects". I don't have enough background to fully understand what those effects are or what they mean, but I can accept the idea that it is impossible to reach light speed because of "them". I need to find an article or book that discusses this calculation that infinite energy is required to get an object up to light speed.

Through this Q&A you guys have so kindly participated in, I have realized or at least suspect that light photons can travel at c because they have no mass. Is that correct? If so, are there other mass-less particles in our universe? I'm sure these are things that I'd learn in an average physics class, but work and family life are preventing my return to college at this time.

As a bit of background for myself (if you care) I am a Radiologic Technologist. Fancy way of saying X-ray and CT tech. The only physics I ever learned in school were things like the photoelectric effect, compton interactions, differences between alpha and beta particles. Nothing much about motion and certainly nothing about astrophysics or thermodynamics.

I respect all of the knowledge you folks have, and am quite envious. Someday I suppose...

 

[Nabeshin]

I need to find an article or book that discusses this calculation that infinite energy is required to get an object up to light speed.

The derivation of this formula requires a decent knowledge of relativistic mechanics, but if you just want the formula you can easily see why it is impossible to accelerate to light speed.
The kinetic energy of an object is given by:
$$K_{e}=mc^2(\gamma-1)$$
Where $$\gamma=\frac{1}{\sqrt{1-\frac{v^2}{c^2}}}$$

Where c is the speed of light. As you can see, as v approaches c, the factor of gamma becomes arbitrarily large as the denominator approaches zero. At v=c there is a 1/0 situation, which is corresponding to an infinite amount of energy.

Through this Q&A you guys have so kindly participated in, I have realized or at least suspect that light photons can travel at c because they have no mass. Is that correct? If so, are there other mass-less particles in our universe? I'm sure these are things that I'd learn in an average physics class, but work and family life are preventing my return to college at this time.

Your hunch is correct! A particle with zero rest mass is required to travel at the speed of light!

 

[Jackslap]

The derivation of this formula requires a decent knowledge of relativistic mechanics, but if you just want the formula you can easily see why it is impossible to accelerate to light speed.
The kinetic energy of an object is given by:
$$K_{e}=mc^2(\gamma-1)$$
Where $$\gamma=\frac{1}{\sqrt{1-\frac{v^2}{c^2}}}$$

Where c is the speed of light. As you can see, as v approaches c, the factor of gamma becomes arbitrarily large as the denominator approaches zero. At v=c there is a 1/0 situation, which is corresponding to an infinite amount of energy.



Your hunch is correct! A particle with zero rest mass is required to travel at the speed of light!

Ha! That whole thing is greek to me man, but I truly appreciate all the effort you guys have put into helping me understand this little situation. I never knew this stuff could be so interesting. Kinda makes me wonder why EVERYONE isn't impressed by it. What a magnificent universe we live in, all of its mysteries...

 

[LURCH]

If you do a search on "relativistic effects" or "tmie dilatin" here in the Forums, you will find many interesting discussions on the topic.

 

[DaleSwanson]

Some more on your original question about the "dust" in space, known as the interstellar medium (ISM). There is also an intergalactic medium, which would be the dust between galaxies, and much less dense. Doing a search for both terms should give you a lot more info on them.

As for a book, Stephen Hawkins' "A Brief History of Time" is a widely available book written for a beginner. I'm sure if you start a new topic looking for book suggestions people will be able to suggest plenty.

But mainly I wanted to comment on the formulas. I know they can look quite intimidating, but really there is nothing there other than basic arithmetic. You just take your numbers put them in the right places and solve the math, and you get your answer. I've found that a lot (not all) of the formulas in physics are surprisingly easy, given what they are calculating. If you can figure out how to work out the formulas yourself it becomes much more exciting. Breaking down the formula Nabeshin gave:

$$K_{e}=mc^2(\gamma-1)$$
Where $$\gamma=\frac{1}{\sqrt{1-\frac{v^2}{c^2}}}$$

$$K_{e}$$ is kinetic energy, this is what we are solving for, to know how much energy an object has at a certain speed.

m is mass, as an example use 1000kg
c is the speed of light, 299,792,458 meter per second
$$\gamma$$ is gamma, you will find this number by first solving the second formula
v is velocity, or speed of the object, we'll use 299,000,000 as a speed right below the speed of light.

Now we just plug in the numbers and do the math:

$$\gamma=\frac{1}{\sqrt{1-\frac{299,000,000^2}{299,792,458^2}}}$$

Solve the exponents, and divide:
$$\gamma=\frac{1}{\sqrt{1-\0.9947}}$$

Subtract from 1, then find the square root:
$$\gamma=\frac{1}{0.07266}$$

Divide that by 1 to find our answer:
$$\gamma=13.7624$$

Now we have gamma, we put that in the first formula:
$$K_{e}=1000 * 299,792,458^2(13.7624-1)$$

Subtract 1, do the exponent, and multiply by 1000:
$$K_{e}=89875517873681764000(12.7624)$$

Now we just multiply these two to get our answer:
$$K_{e}=1147027309311076144873.6$$

So an object that weighs 1000kg, and is going 299,000,000m/s has an energy of 1,147,027,309,311,076,144,873.6 Joules.
For reference a nuclear bomb releases 5,020,800,000,000,000 Joules. Our spaceship has the energy of 228,455 nuclear bombs.

By looking closer at just the gamma formula you can see why traveling at the speed of light would be impossible. As v get closer to c the division of v² by c² will get closer to 1, which then gets you closer to 0 for a square root. That leaves you with 1 divided by something closer and closer to 0, which will get larger and larger. Until you actually reach 0 then you have 1/0, which is impossible.

 

[.:Endeavour:.]

Wouldn't it been much easier to to have those hugh numbers like this 5 PJ or 5,020,800 GJ? Those are big numbers and yes that is a lot of energy that a spacecraft has even more if it accidentally crashes into something then all of that energy will be released into 228,455 nuclear bombs going off altogether. But only way to be sure that these particles do act as friction is actually having a spacecraft that goes that fast which of right now is impossible to reach those speeds so we have no way of seeing that these hunches are correct if they cannot be put to the test.

 

[Nabeshin]

Wouldn't it been much easier to to have those hugh numbers like this 5 PJ or 5,020,800 GJ? Those are big numbers and yes that is a lot of energy that a spacecraft has even more if it accidentally crashes into something then all of that energy will be released into 228,455 nuclear bombs going off altogether. But only way to be sure that these particles do act as friction is actually having a spacecraft that goes that fast which of right now is impossible to reach those speeds so we have no way of seeing that these hunches are correct if they cannot be put to the test.

Hunches? These are not "hunches". They follow from scientific principles. If the scientific principles are sound (and I damn well believe in conservation of momentum), then what follows from them must also be sound.

Simple science.

 

[.:Endeavour:.]

Hunches? These are not "hunches". They follow from scientific principles. If the scientific principles are sound (and I damn well believe in conservation of momentum), then what follows from them must also be sound.

Simple science.

Ok, but do we have a spacecraft that can go at the speed of light to actually test if the matter in space does cause friction. Still, we don't have the technology that will make a spacecraft go at the speed of light; and the "hunches" that I was referring was on the theories of how friction will affect a spacecraft traveling at the speed of light.

 

[Nabeshin]

Ok, but do we have a spacecraft that can go at the speed of light to actually test if the matter in space does cause friction. Still, we don't have the technology that will make a spacecraft go at the speed of light; and the "hunches" that I was referring was on the theories of how friction will affect a spacecraft traveling at the speed of light.

We are not discussing spacecraft traveling at c, so I don't know where you got that idea. We were discussing spacecraft traveling at relativistic speeds, that is, close to c. The fact that the interstellar or interplanetary medium would cause friction is simply an extension of the principle that when objects collide things tend to heat up. Really, the problem differs very little from that of the shuttle heating when it re-enters the Earth's atmosphere. These two are the same but for two factors, velocity and particle density. That's all.

 

[DaleSwanson]

Ok, but do we have a spacecraft that can go at the speed of light to actually test if the matter in space does cause friction. Still, we don't have the technology that will make a spacecraft go at the speed of light; and the "hunches" that I was referring was on the theories of how friction will affect a spacecraft traveling at the speed of light.

One of the most important uses of science is to predict what will happen based on what we know. What good would it be if the only way we knew anything was based on what we had already done? How would we be able to try anything new without being confidant of what effects to compensate for?

As for this specifically I can't imagine what problem you have with it. As Nabeshin just said we aren't talking about friction at c, rather at speeds near it. We know friction is a factor at low speeds, why would it stop being a factor at high speeds? It's not very controversial at all. I don't know why you have a problem accepting that matter would cause friction. What specific parts do you doubt? That there is actually interstellar matter? That it is some how different from all other matter? That near c speeds would have some special effect on friction?

 

[Jackslap]

Endeavor, are you confused as to what the original topic is? I am confused by your statements, perhaps because I don't have as much knowledge as you do in this area. It seems as though you have deviated from the original question which was basically "is friction a factor in space?"

I originally didn't understand about interstellar or intergalactic matter, but these kind folks have educated me in those matters and I now understand how that matter is ALWAYS a factor, no matter the speed of an object.

It seems you have added an element to the discussion beyond my current level of understanding when you mentioned the space shuttle smashing into objects and number abbreviations.

My limited knowledge of physics (pretty much none) however does not stop me from believing Dale Swanson's calculations, even though I'm not good enough to perform the function myself. I think his numbers and his example are solid. He simply created a hypothetical situation with arbitrary numbers and plugged them into the formula. Presto...he arrives at the answer for his hypothetical question. This seems to follow a reasonably scientific process of using info you have to predict other events when given similar info.

Perhaps you are speaking on another matter entirely however. As I said, I am a bit confused by the extra information you brought up.

 

[.:Endeavour:.]

Ok, for one thing I never mentioned of the space shuttle. What I mentioned was a spacecraft colliding to an object and releasing all that energy, or most of the energy. The space shuttle was never mentioned on my first post in this subject and you can re-read it again to see that the space shuttle wasn't mention, but don't know how it was inferred to be the space shuttle. The space shuttle can be referred to a spacecraft , but I never stated that it was the space shuttle.
Maybe that was what got it out off the subject with mentioning the spacecraft traveling at the speed of light which I derived from Nabeshin mentioning the ship traveling at that speed or relative speed. Sorry for jumping into conclusions, but still science gives us the frame that we need when we create a vehicle, like the Saturn rocket, the Space Shuttle, and now the Ares I and V. Isn't how scientist came up with their laws, theories, equations, etc.? Sorry for going of topic, but I never mentioned the Space Shuttle, yet again.

 

[Nabeshin]

Isn't how scientist came up with their laws, theories, equations, etc.?

No. That's what we're trying to say. Theories are extrapolated from laws which are observed, VERY general phenomenon in our universe (conservation of energy, momentum). These theories, however, apply to a broader range of phenomenon, and yield EQUATIONS with which to describe any of these phenomenon.

As far as the space shuttle, no one accused you of mentioning it. It is an example I used to show that we observe friction in that case and that a spaceship traveling at relativistic velocities isn't different in any salient way. It was my example, demonstrating the principle that physical laws are extrapolated to circumstances that we cannot (at the moment) directly experience. Also, I never mentioned spacecraft traveling AT the speed of light -- a feat which is clearly impossible.

 

[.:Endeavour:.]

Ok, I just started to read the recent post where the space shuttle just popped up. Before I start getting quoted from my previous post: equations are way how we understand the physical world. If science and math were taught together math would of made more scence with science been applied to it. But if the phenomenon only appears ones and never appears again, then its hard to describe the event with an equation because a one time event you can't get the whole picture by patters, if any, from another similar event. Like life. We don't have an exact equation to understand how life came to the Earth as simple organism to complex living things like ourselves.

For the light speed spacecraft or object that I got replies from, I got it while reading DaleSwanson's post. I liked how he explained the formulas (which makes it more understandable), good job. That's where I got the object going at light speed from the formulas he introduced. So, in a way I was mostly complimenting his post not everyone else. The spacecraft idea was from the 1000 kg that he mentioned as well which can be a spacecraft which is 2,204.6 pounds. There is where I got the light speed idea with the spacecraft as well from the 1000 kg that he mentioned.

(Sorry for the grammatical errors and spelling errors).

 

[Jackslap]

Ok, for one thing I never mentioned of the space shuttle. What I mentioned was a spacecraft colliding to an object and releasing all that energy, or most of the energy. The space shuttle was never mentioned on my first post in this subject and you can re-read it again to see that the space shuttle wasn't mention, but don't know how it was inferred to be the space shuttle. The space shuttle can be referred to a spacecraft , but I never stated that it was the space shuttle.
Maybe that was what got it out off the subject with mentioning the spacecraft traveling at the speed of light which I derived from Nabeshin mentioning the ship traveling at that speed or relative speed. Sorry for jumping into conclusions, but still science gives us the frame that we need when we create a vehicle, like the Saturn rocket, the Space Shuttle, and now the Ares I and V. Isn't how scientist came up with their laws, theories, equations, etc.? Sorry for going of topic, but I never mentioned the Space Shuttle, yet again.

You've caught a mistake of mine and for that I apologize. I was the one who typed space shuttle in error, it is clear you said spacecraft as you mentioned so many times in the above post. I was not trying to put words in your mouth. As I was typing that previous post I knew you said "space-something or other" I just didn't double check to make exactly sure. So it is established that you said " spacecraft ".

Now I think I might be starting to understand what happened here. You were just merely trying to make a sub-point (if it can be called such) about the whole energy being released thing. Completely unrelated to the original topic correct? That is what I have gathered from this.

Anyway, I think I see your point about how if a phenomenon only appears once it is hard to formulate with an equation how it might happen again correct? That does seem logical, however I still do not see how that is connected to Dale or Nabeshin's previous remarks. I still believe that everything they have suggested within the body of this topic is all provable. So if you were mentioning about the " spacecraft " as just a side note, a fun fact, then I understand. But if you were trying to say that something Dale or Nabeshin said is unprovable, then I don't understand.

It's nice to have adult discussions for once. I spend some time on a particular firearms website and also youtube and boy is everything in those places so childish.

 

[DaleSwanson]

For the light speed spacecraft or object that I got replies from, I got it while reading DaleSwanson's post. I liked how he explained the formulas (which makes it more understandable), good job. That's where I got the object going at light speed from the formulas he introduced. So, in a way I was mostly complimenting his post not everyone else. The spacecraft idea was from the 1000 kg that he mentioned as well which can be a spacecraft which is 2,204.6 pounds. There is where I got the light speed idea with the spacecraft as well from the 1000 kg that he mentioned.

Just to clarify I solved the formula for a speed of 299,000,000 m/s, which is about 0.997c. I picked it as a nice round number very close to (but not quite) c. 1000 kg also had no special meaning, I was going to just use 1 kg, but figured I'd use a mass that would be closer to a real spaceship or probe.

Thanks for the compliment, the sole purpose of that post was to show that the math isn't as hard as it seems at first.

 

[.:Endeavour:.]

The 1000 kg of mass is a good number because mostly the Soyuz Spacecraft's 3 part ship have a mass slightly higher than 1000 kg, but overall its much lighter than the CSM and LM as well. I've converted the 0.997c into m/s, and its good to have a whole number to calculate. Possibly Sputnik 1 was one of the satellites that weight less than 1000 kg or less than 100 kg. Math isn't hard until you get how it works and also understand its patterns.