Calculating Earth's Increased Mass with Velocity Change: A Scientific Analysis

[Bjarne]

How much more mass would the Earth have when it was moving let’s say 1000km/s faster than now. And how can it be calculated?

 

[Civilized]

The mass of the Earth is independent of its relative speed to an observer.

 

[DrGreg]

In relativity there is more than one definition of mass.

According to the definition that almost all physicists use nowadays, the rest mass or invariant mass of an object doesn't change due to speed.

According to an older definition that is still used in some coffee-table books and maybe even in some schools, the relativistic mass or inertial mass of an object increases as it goes faster relative to the observer. The increase is due to counting the object's kinetic energy (KE) as part of its mass, via E = mc².

Strictly speaking, we should use the correct relativistic equation for KE, but 1000 km/s is still fairly slow, relativistically speaking, so the Newtonian formula mv²/2 isn't far wrong.

So this is what you do. Find the Earth's mass in kg and its speed in m/s. Calculate the KE by the formula above and divide by c², where c is the speed of light in m/s. What answer do you get?

 

[infomax]

The definition of mass in physics is
M=F/A
when the force is applied to body , a part of energy is used to increase of mass and rest contribute to increase in velocity
lets go by mathematical sense
when you apply force to body and the body seems not to accelerate as much is it has to then you feel the bodies mass has increased(because we conclude acceleration is inversely proportional to mass)
so there is no change in mass in our Earth frame but it is for the rest frame that anybody is there

 

[Bjarne]

How much velocity is converted to mass, when the Earth would move let’s say 1000km/s faster (than now)? How can it be calculated?

 

[DrGreg]

How much velocity is converted to mass, when the Earth would move let’s say 1000km/s faster (than now)? How can it be calculated?

I gave an answer in post #3. If you don't understand what I said, you will need to give me a clue: which bit did you not understand?

 

[Bjarne]

I understand how to calculate how much mass would increase due to velocity, but not to calculate how much velocity to “pay” for that extra mass.

 

[Naty1]

You original question uses a change in velocity of 1000 km/sec...that is used in DrGregs equation in post #3 to calculate the change in energy/mass as you requested.

If you are implying the increase in mass slows the velocity a bit, that's a separate question and a separate problem requiring different assumptions. The answer depends on your question assumptions.

 

[DrGreg]

I understand how to calculate how much mass would increase due to velocity, but not to calculate how much velocity to “pay” for that extra mass.

Now I understand your question.

The short answer is "none".

It's not as if you have a choice between velocity or kinetic energy (= extra relativistic mass). You can't convert velocity into energy, i.e. reduce the velocity to increase the energy. Both increases occur at the same time and are two different ways of measuring the same thing.

Your question is a bit like asking "how much velocity to pay for doppler shift", or even "how much velocity to pay for speed".

 

[Bjarne]

But when velocity is converted to mass, - velocity is converted to energy.
Where does that energy come from?
Energy is never "free"

 

[Doc Al]

But when velocity is converted to mass, - velocity is converted to energy.

Velocity isn't "converted" to mass or energy.

Where does that energy come from?
Energy is never "free"

The energy comes from whatever sped the object up. It requires work--energy--to accelerate an object.

 

[Bjarne]

The energy comes from whatever sped the object up. It requires work--energy--to accelerate an object.

Sorry, this really sounds strange to me.

I mean to speed up an object can happens in many different way. The result is acceleration.
But what have acceleration and more mass with each other to do. – Do we know what really happens in this process?

So fare I understand we general don’t know how mass is created, - right?

Let say a-bomb is circling the Earth with huge velocity.
This bomb has now more mass compared to when it was on the Earth.
When it explodes and the energy (mass) is released, the force would be greater compared to when the explosion toke place on the Earth.

But where is the “connection” (cause-effect) between on the one hand: acceleration/velocity and on the other hand the result: more mass.

Maybe this sounds stupid to you, but I really want to understand what is going on here.

 

[Dale]

First, the idea of "relativistic mass" (the kind of "mass" that increases with velocity) is deprecated by most modern physicsts. The reason is that it is just another name for total energy. So, if an object is at rest it has KE = 0, but by E=mc² it still has a lot of energy. If you do work on that object then its KE will increase. The total energy then has increased from the rest energy to the rest energy + the KE, and since "relativistic mass" is just the total energy then it also has increased. There is no big mystery here, work increases KE which increases total energy which is "relativistic mass".

 

[Bjarne]

First, the idea of "relativistic mass" (the kind of "mass" that increases with velocity) is deprecated by most modern physicsts.

So we are not sure whether this is a fact or not ?

There is no big mystery here, work increases KE

The mystery to me is:
1.) Either we have more mass (due to velocity) or we have not.
2.) If we really have more mass (due top velocity) we also should also be able to explain how is this possible, at least hypothetical..

 

[Dale]

So we are not sure whether this is a fact or not ?

It is not a question of fact, it is a question of definition. If you define "mass" to mean "relativistic mass" then mass increases with velocity. If you define "mass" to mean "invariant mass" then mass does not increase with velocity.

 

[DrGreg]

So we are not sure whether this is a fact or not ?

The mystery to me is:
1.) Either we have more mass (due to velocity) or we have not.
2.) If we really have more mass (due top velocity) we also should also be able to explain how is this possible, at least hypothetical..

As I explained in post #3, there is more than one definition of "mass" in relativity. According to the definition most physicists prefer, mass does not increase. According to another definition, it does. The difference is whether you decide to count kinetic energy as part of the mass or not. Either way, everyone agrees the kinetic energy increases, even in Newtonian (non-relativistic) physics.

Sorry, this really sounds strange to me.

I mean to speed up an object can happens in many different way. The result is acceleration.
But what have acceleration and more mass with each other to do. – Do we know what really happens in this process?

So fare I understand we general don’t know how mass is created, - right?

Let say a-bomb is circling the Earth with huge velocity.
This bomb has now more mass compared to when it was on the Earth.
When it explodes and the energy (mass) is released, the force would be greater compared to when the explosion toke place on the Earth.

But where is the “connection” (cause-effect) between on the one hand: acceleration/velocity and on the other hand the result: more mass.

Maybe this sounds stupid to you, but I really want to understand what is going on here.

The energy comes from the rockets that you use to accelerate the bomb. As the rockets fire, they put extra kinetic energy into the bomb, and when it explodes, that extra energy is released and makes the explosion a little greater.

For more information see Mass–energy equivalence.

 

[Doc Al]

The mystery to me is:
1.) Either we have more mass (due to velocity) or we have not.

As explained, it depends on the definition of mass that one is using. (Using the more standard definition of invariant mass, one would say there is no mass increase.) Don't confuse an increase in relativistic mass with an increase in "matter".

2.) If we really have more mass (due top velocity) we also should also be able to explain how is this possible, at least hypothetical..

Again, it depends on what you mean by "explain". If you understand the definition of relativistic mass, then there is no mystery. (You must be reading more into this than there is. It's kind of like asking, how is it possible for an object to have zero speed in one frame yet have kinetic energy in another.)

A more productive question to ask is: Why does it take more and more energy to get a smaller and smaller increase in speed? (That can be viewed as a purely kinematic effect derived from the basic principles of special relativity.)

 

[Bjarne]

Is it any resistance by traveling in space, except gravity and collision with particles (cosmic dust)?

 

[Alewhey]

Is it any resistance by traveling in space, except gravity and collision with particles (cosmic dust)?

I'm not sure if you think that question is somehow related to your previous ones, but anyway: photons carry momentum and as such can also decelerate matter traveling through space. But there is no 'intrinsic' resistance to motion in free space. For such resistance to exist we would have to define some priviledged frame of reference as being 'stationary', which I believe is in violation of relativity.

 

[Bjarne]

Why does it take more and more energy to get a smaller and smaller increase in speed?

Yes this is the correct question.
Both:
1.) Why
2.) And how can we calculate it?
3.) For instance how much force does it take to accelerate the Earth up to + 100 km/s
4.) And how much to plus + 1000 km/s
5.) And let’s say we reach + 1000 km/s. - Does it require force to maintain that extra speed. (If we ignore gravity and collision with cosmic dust.) I guess no. (?)

 

[Doc Al]

Yes this is the correct question.
Both:
1.) Why
2.) And how can we calculate it?

The relativistic formula for the kinetic energy of a moving body is:
KE = (γ - 1)mc², where γ = 1/√(1 - v²/c²)

For speeds small compared to the speed of light (c), the KE equals 1/2mv². But as speed approaches c, the kinetic energy approaches infinity.

As to "why", you'll have to study special relativity.

3.) For instance how much force does it take to accelerate the Earth up to + 100 km/s
4.) And how much to plus + 1000 km/s

Asking how much force is required is the wrong question. (Any amount of force will work; a smaller force just requires more time.) The right question is how much energy is required to attain some speed. Calculate the energy using the above formula. Since the speed of light is 3 x 10⁸ m/s, a speed of 1000 km/s is too small to worry about relativistic effects.

5.) And let’s say we reach + 1000 km/s. - Does it require force to maintain that extra speed. (If we ignore gravity and collision with cosmic dust.) I guess no.

No force is required to maintain an object's speed (as long as nothing acts to slow it down).

 

[Bjarne]

Light photons have mass, - due to velocity.
Are there a simple way to explain why?

 

[Alewhey]

Light photons have mass, - due to velocity.
Are there a simple way to explain why?

Individual photons do NOT have mass (or more precisely, their invarient mass is zero). However they do carry energy and momentum.

 

[DrGreg]

Light photons have mass, - due to velocity.
Are there a simple way to explain why?

Individual photons do NOT have mass (or more precisely, their invarient mass is zero). However they do carry energy and momentum.

To repeat what I've said before "mass" could mean "invariant mass", which is always zero for a photon. Or it could mean "relativistic mass", which includes kinetic energy. So the simple explanation why photons have relativistic mass is because they have energy and that's how we define it.

 

[JanClaesen]

Temperature is caused by the movement of atoms, so by their kinetic energy: (1/2) mv²
v is maxed by c
Will the mass increase as well? Since apparently the increase in mass is caused by an increase in kinetic energy? If it would, this implies there isn't a maximum temperature?

 

[Doc Al]

Temperature is caused by the movement of atoms, so by their kinetic energy: (1/2) mv²
v is maxed by c

That formula for KE is only valid for small speeds. The correct expression for all speeds is given in post #21.

 

[Bjarne]

To repeat what I've said before "mass" could mean "invariant mass", which is always zero for a photon. Or it could mean "relativistic mass", which includes kinetic energy. So the simple explanation why photons have relativistic mass is because they have energy and that's how we define it.

I understand this point. But “energy” seems a bit abstract to me.
It seems we do not fully understand why “kinetic-energy” acts exactly like was it mass (mass attraction).
I mean how can kinetic energy or (motion energy) have a mass attraction property?
I guess we don’t know why kinetic energy acts like was it mass, right? – And that this expression "energy" is the end of the known road?
Sorry for keeep digging, but I want to understand...

 

[Dale]

But “energy” seems a bit abstract to me.
It seems we do not fully understand why “kinetic-energy” acts exactly like was it mass (mass attraction).
I mean how can kinetic energy or (motion energy) have a mass attraction property?

It sounds like you are suggesting that a fast-moving object should have more gravity than a slow moving object of the same rest-mass. This is incorrect in general. Remember that the source of gravity is the complete stress-energy tensor, not just mass which is only a single term.

 

[Bjarne]

Based on the equation the (contribution no. 21) KE = (γ - 1)mc², where γ = 1/√(1 - v²/c²)

The more an object tries to reach the velocity “c” the more energy it requires.
Just before reaching “c” mass will approach infinity, as well as the required energy also will?

“y” is an important proportional value both to understand the required energy as well as the increasing mass. (So far I have understood).

We can try to calculate the value of “y” when traveling 12240 m/s (as pioneer 10 did)

“y” at velocity 12240 m/s (Pioneer 10) = 8.33 × 10−10 (m/s² ??)
Pioneer probes was slowing down...… = 8.74 × 10−10 m/s²

Does that mean that the cause of the increasing requirement of energy is due to proportional increasing relativistic resistance?

According to the theory of special relativity we know what mass (an object) can not reach the speed of light. Why, what prevent it to happen?

I mean relativistic mass and energy is "real" for us.
Does it exist a real answer WHY , too ?


---------------------------------------------------------------------------------------
There must be no barriers to freedom of inquiry.
There is no place for dogma in science. The scientist is free, and must be free to ask any question, to doubt any assertion, to seek for any evidence, to correct any errors.
-- J. Robert Oppenheimer

 

[vin300]

According to the theory of special relativity we know what mass (an object) can not reach the speed of light. Why, what prevent it to happen?

You see, the factor "Y" becomes infinity at the speed and so does energy.You cannot supply infinite energy to an object.

Anybody of you got derivation of "acceleration" thread?
---------------------------------------------------------------------------------------
There must be no barriers to freedom of inquiry.
There is no place for dogma in science. The scientist is free, and must be free to ask any question, to doubt any assertion, to seek for any evidence, to correct any errors.
-- J. Robert Oppenheimer[/QUOTE]

 

[Bjarne]

You see, the factor "Y" becomes infinity at the speed and so does energy.You cannot supply infinite energy to an object.

Off course...
But why do we have some kind of "resistance”?
Why does it take more and more energy to get a smaller and smaller increase in speed?
Are there any “down to earth” explanations to that?

 

[anant25121986]

Let me see if i am of any help.

Let us start first with the concept of relativistic mass. At relativistic speeds, the mass as such remains the same. But the apparent mass increases. For all practical purposes, the mass has increased. To understand this, try to visualize a universe without any losses. Next step, think on how one can increase the speed of a spaceship (easier to explain than the earth). One will use fuel of some sort to accelerate the ship to higher speeds. Now, as the velocity increases, so does the kinetic energy. The equation for the kinetic energy is given by:

K=(\gamma - 1)*m*c^2 the value of \gamma=1/\sqrt[]{}1-v^2/c^2

Now, the total energy is given by:

T = K + E0 E0 = m*c^2
which gives,

T= \gamma*m*c^2

i.e. the mass has increased \gamma times

so u can do the calculation for the increase of the mass of the Earth using the above equation.

Now, if u can see, as the velocity is increased, the value of \gamma increases very rapidly. This causes a very high amount of energy required to increase the kinetic energy by a small amount. That is why as the velocity increases, more energy is required for a small further increase in velocity.

As for why this phenomena occurs, i don't think relativity can help u there. :)

Hope this helps.

 

[vin300]

Off course...
But why do we have some kind of "resistance”?
Why does it take more and more energy to get a smaller and smaller increase in speed?
Are there any “down to earth” explanations to that?

Err, because the increase is not smaller and smaller it is in fact larger and larger by y

 

[Bjarne]

anant25121986
I understand and agree to all what you wrote.

As for why this phenomena occurs, i don't think relativity can help u there.

So I guess we can conclude that some kind resistance (of unknown kind) is a possibility?

Vin3000

Err, because the increase is not smaller and smaller it is in fact larger and larger by y

Hmmm
It takes more and more energy to get a smaller and smaller increase in speed.

 

[anant25121986]

So I guess we can conclude that some kind resistance (of unknown kind) is a possibility?

I am sorry I don't understand the type of resistance you are referring to. Is it similar to a frictional force??

One more thing. I had read somewhere about speed of light being the limit. Now, one thing we need to accept is that special relativity talks only about objects and particles below the speed of light. For them, yes, the speed of light is the limit. This theory however, doesn't explicitly state that objects can not exist at the speed of light or above it. It merely fails to explain them.

 

[Bjarne]

I am sorry I don't understand the type of resistance you are referring to. Is it similar to a frictional force??

Space and matter is somehow connected.
Think about a magnetic field, or think about how matter/gravity bends space.

Mass/gravity is increasing due to higher velocity; hence space must bend proportional more due to increasing mass/velocity.

Put the same question above in a different way:
Does it require energy to bend space?
I guess we don’t know ?
-------------------------------------------
( I am a stranger if my English is not perfect just correct me)

 

[anant25121986]

it does require energy to bend space. To increase velocity and hence mass, we supply energy which then bends space as it moves. :)

 

[Bjarne]

it does require energy to bend space. To increase velocity and hence mass, we supply energy which then bends space as it moves.

Agree.
Now, - when a body moves something must happen with the space/matter connection.
I mean space bends as a result of the motion of a body right ?

But what is the "space matter connection" ?
And do we have any resistance here?
Think also of the plasma circling around the suns equator, - suddenly every 11 years, > sun storms. Is that due to the space/matter connection?
Does space resist such motion of plasma/matter ?

 

[vin300]

Vin3000

Hmmm
It takes more and more energy to get a smaller and smaller increase in speed.

when its speed is 0.7c, its proper velocity is
[1/sqrrt.(1-v^2/c^2)]v which is [1/sqrrt.(1-0.49)]0.7c = [1/sqrrt.0.51]v = (0.7/0.714)c=0.98c
when speed is 0.6c, its proper velocity is (0.6/0.8)c=0.75c
The speeds do not increase as they are supposed to, it requires extra energy.

 

[Bjarne]

The speeds do not increase as they are supposed to, it requires extra energy.

Agree

 

[Doc Al]

when its speed is 0.7c, its proper velocity is
[1/sqrrt.(1-v^2/c^2)]v which is [1/sqrrt.(1-0.49)]0.7c = [1/sqrrt.0.51]v = (0.7/0.714)c=0.98c
when speed is 0.6c, its proper velocity is (0.6/0.8)c=0.75c

Can you explain what you're doing here and what you mean by "proper velocity"?

Also folks, please use the quote feature properly so that the link to the original post is maintained and the person quoted is identified.

 

[vin300]

Can you explain what you're doing here and what you mean by "proper velocity"?

Also folks, please use the quote feature properly so that the link to the original post is maintained and the person quoted is identified.

Proper velocity is the distance measured by the stationary observer on the time elapsed on the moving observer's clock(proper time), which is gamma times v. It can also be interpreted as the velocity of the body, when it becomes equal to c by the formula becomes infinity

 

[Doc Al]

Proper velocity is the distance measured by the stationary observer on the time elapsed on the moving observer's clock(proper time), which is gamma times v. It can also be interpreted as the velocity of the body, when it becomes equal to c by the formula becomes infinity

Ah, OK. Forgot about that term since I don't use it much. Don't confuse it with the actual speed of the body as measured in some reference frame.