I've been thinking about this an awful lot lately but I can't seem to get my head around something.

Velocity is how fast an object moves. On Earth if you were travelling 600kmph that means you would cover 600km of distance over the Earth's surface in one hour's time. That much makes sense (if it didn't I'd really be ******ed). But if you look at the Earth in isolation of other celestial bodies (as in, only looking at objects travelling over the Earth's surface) it can be seen as a constant, a fixed surface area around which one can travel. But I've been thinking about how you calculate velocity in space. It seems different because you're travelling through a medium between points. Is speed only relative to objects around you? For example, if you were on a space ship travelling from Earth to Jupiter your velocity could only be determined as how fast you are travelling toward or away from something, as in you were travelling 600kmph away from Earth or 600kmph towards Jupiter. But, consider that objects in space move, and Jupiter is not always the same distance away from Earth at all times. For example, you're in a space ship and your destination is a comet. If you were travelling 600kmph away from Earth in the direction of the comet and the comet was travelling 600kmph away from Earth, would you not then be travelling 600kmph away from Earth but 0kmph towards the comet? Would you not need to travel 1200kmph away from Earth in order to travel 600kmph towards the comet?

So, in my mind, velocity can only be calculated by measuring the distance you're travelling to or from an object, but even then you could be travelling at two different velocities depending on which objects you're using. So what about the speed of light? If you had two ships capable of travelling half the speed of light flying away from each other at that speed, would that not mean that each ship is travelling the speed of light in relation to the other?

I'm using 600kmph as the velocity just to keep things simple. I realize that in space 600kmph is a relatively slow speed.

**edit: Tried to explain how I see it in my mind it a little clearer in light of Jux's comment.

 

The point you're standing on is not a constant, fixed place. It's moving through space. Relative to a point on Earth, you may be moving x mph, but relative to another point, say, the flag on the moon, you could be moving y mph. But in your example, both ships may be departing from one another at the speed of light, but neither is breaking the light barrier.

There's a good episode of "The Universe" on the History Channel regarding the speed of light.

 

What I meant by the Earth being fixed is kind of like viewing travelling across the surface of the Earth as though it existed in a bubble. For example, Mt. Cook isn't moving in relation to me (well, not moving at any rate really all that significant due to continetal drift for the purpose of this explanation). I am the only object travelling towards or away from it. I was looking at it on a smaller scale, at Earth in isolation and a single human travelling towards a relatively fixed point on the surface.

 

Ok. I'm a bit confused ... seems like a relatively simple concept but worded a bit more difficult, so I'm not sure I'm getting the full idea. So the comet thing. If you're traveling 600 kph away from Earth, towards a comet also moving 600 kph away from earth, then you're correct that you're not gaining any ground on the comment. Relative to the comet, assuming speeds were identical, you're not moving. You're both maintaining a constant speed in the same direction, maintaining the same distance from each other but leaving Earth. It's like two cars leaving a city - the car 500 yards in front of you is going 75 mph, and so are you, but you're not gaining any ground. To catch the comet, you could simply go 601 kph, and eventually catch it, or go faster to get their quicker. Your speed from Earth would still be 601 kph or whatever, but you now have a closing speed on the comet. So to your final point, if you want to have a closing speed of 600 kph towards the comet, you would need to travel a total of 1200 kph - you match the speed of the comet, and then accelerate to find the desired closing speed.

Does that mean speed is only relative to the objects around you? Well, a frame of reference is needed in some cases, but I don't think the objects around you change the speed you're traveling (aside from gravitational forces, etc). You need those objects if you want to say "relative to the earth, I'm moving away from it at 600 kph" and you take into how fast you're moving away from it and how fast it's moving away or towards you, but in terms of simply how fast you're going, I don't think that really changes (assuming no outside forces).

 

*holding head in hands*OW!, OW!, OW!, OW!

too much math.

 

Yeah, basically what I'm getting at is that any individual object's speed is relative to every other object in the universe. Thus, it how fast an object travels can only be determined in how fast it moves towards or away from other objects.


**edit: afterthought, an object can only be said to move if there's another object it can move in relation to (towards, away, around, what have you). In a universe consisting of only one object, that object cannot move because it has nowhere to go.

BTW, I have a BA in English. This is all coming out of the dark and frightening place that is between my ears. I don't profess to have any extensive knowlege of physics.  

 

The speed of light through a vacuum is a known constant. It doesn't have to pass a planet or be relative to any certain object to justify that. Certain mediums, like water, can slow it, but in a vacuum it will always be the same. Your universe of one object seems more philosophical; if a tree falls type of stuff. The question is what are the boundaries of the universe? It can still travel within that universe, even as the only object.

In your example, I think you have to take into account the motion of the planet because it seems like you're doing it halfway. You can use vectors to illustrate it.

Example:

<------(comet@600kph) (earth)
Let's say comet is moving 600 kph from stationary earth. That is comet's speed, assuming no gravitational effect. But, if we include consideration of the earth's movement, and say it's going 600 kph the other way:

<------(comet@600kph) (earth@600kph)------>
Now they are moving away from each other at 1200 kph and the comet would appear that fast to a bystander on earth but that does not change the comet's speed of 600 kph. The comet is still traveling at 600 kph, but relative to the earth it's moving away from the planet at 1200kph.

(painstakingly typed on an iPhone so sorry for any errors)

 

You can still measure distance in space. If you where an astronaut and you where on a space walk and happened to have a meter stick and measured the emptiness there would still be a meter of emptiness. Speed isn't relative to anything it is just how much distance you cover over time.

So to answer you're question relatively yes the ships would be going the speed of light but in actuality they are doing have the speed of light.

 

The nightmarish thing is that, relative to each other, they AREN'T going to speed of light from each other, even if they're both going half the speed of light and in opposite direction. When you approach sublight speeds, basic laws of additive physics no longer apply and the equations get a lot more complicated.

Why, do you ask?

Well, with relation to you, light is always going the same speed through a vacuum, c. That means if you're going .5c, the light you observe in the same direction is still going c away from you. BUT, from an outside observation point, the light is going c, and you're going half as fast, so from THAT perspective, it's only moving .5c away from you, while from YOUR perspective, it's going c.

Think about that for a second.

It's going two different speeds, relative to the point of observation. Which is correct?

They both are!

PHYSICS! RARGH!

 

Now I know why I am NOT very good at science. Just can't get myself to understand all these Physics talk. Argh.


Edit: Meant to say not good at science. Duh.

 

Always remember you can redefine your frame of reference in order to make the math easier.

Also, a knowledge of vectors and vector geometry would probably make this a lot more clear, CdnShockwave.

Euclidean vector - Wikipedia, the free encyclopedia

So basically, if we assume that two objects are on a grid like a chessboard, and the first, say a ball, is a ways up, moving to the right at say, a square per minute (V= 1 sq/min

) . And theres another object, say a cube, starting in the bottom left corner, moving diagonally such that it is moving one square up and to the right each minute (V= 1 sq/min

+ 1 sq/min [up] = 1 sq/min [45 degrees from the intersection of the side and bottom of the board]

[** if we want to get technical, its velocity has a magnitude of sqrt(2), but just think of it as moving through the space occupied by one square].

So the two objects will intersect in d minutes, where d is the number of vertical squares between them at the start, right? Still with me (this would probably be easier with a diagram, but I'm lazy, sorry)? Since they're both moving one square to the right each minute, we can take things from the perspective of the ball, reducing the system to one axis. In this case, the cube will appear to be moving towards the ball at 1 sq/min, as the ball stands still in reference to itself (we assume there is absolutely nothing around other than the two objects). If we look at things from the cube's perspective, it too is standing still, and the ball is moving towards IT at 1 sq/min.

So if two ships were flying at eachother at 0.5c, it would appear to eachother that the gap between them was indeed closing by c. However, this would not violate any laws of physics, since neither ship would be actually going c. To answer your question, if they tried to gauge their velocity relative to a planet, or even a star, assuming that body was standing still, it would be inaccurate in absolute terms, but accurate in relation to that body. The only real way to gain an accurate, absolute measure of velocity would be to have a reference point that stands absolutely, completely still in relation to every other object in the universe. I can't think of one.

So basically, all of math and physics relies on making a ton of assumptions. In a lot of cases, it doesn't matter all that much, and the margin of error is enough that you can get away with making those assumptions. This isn't always the case though, which is why its actually a good idea to think about stuff like this from time to time. When you're an astrophysicist, at least.​

 

Get one thing straight: You cannot measure distance without a static reference point.

Speed is units, Velocity is a vector.

Try to think of your objects as a free body diagram, using on the objects in question. Remember that distance on the Earth is somewhat of an arc length. Try to think if the Earth Object initial position on Earth (p0), and its p1 after t seconds. Then try the space objects initial and final postion after the same t seconds. Then measure the distance between Space object's p1 position to Earth Objects p1 position. Make it as simple as possible by using at most 2 dimensions (Meaning the space rocket matches the Earth rotational speed) or else you will involve some heavy matrix multiplications with trigonometric functions. YouKnowWatImSayin?

 

My head as plode.

 

I talked to my student about relativity without going all out on it. It probably hurt my head even more.

 

NOOOOO!!! First it's at school now its one TFW. Ok if i find some speed and distance mathmatics crap on any of the many porn sites i visit, i will be pissed off!!

 

even if Jupiter, Earth, and you are all moving, regardless of where either point is, you are still covering distance. Just because the distance between points A and B could be increasing or decreasing doesn't mean that your velocity is going to change. it just means that it'll take you less or more time to get there.

that fact that objects are moving further apart or closer together implies distance.

 

Without speed and mathmatics crap you wouldn't have your precious VW's.

 

It's fairly simply - speed and velocity are always relative to whatever you're using as a measuring point, whether that be a blade of grass on the side of a road or the center of mass of Jupiter.

That's without getting into time/space compression which occurs near lightspeed, although that too can be very simply calculated from whatever reference point you like.

It starts getting interesting when you factor in things like curved trajectories, frame dragging, and the ability to create closed timelike curves near massive rotating flanged cylinders.

But for 99% of travel - even space travel - Newton's laws are very close to good enough.