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

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Discussion Overview

The discussion revolves around the concept of how the Earth's mass might change if it were to move at a significantly higher velocity, specifically 1000 km/s faster than its current speed. Participants explore the implications of this scenario through the lens of relativity, examining definitions of mass, energy, and the relationship between velocity and mass in both theoretical and practical contexts.

Discussion Character

  • Debate/contested
  • Technical explanation
  • Conceptual clarification
  • Mathematical reasoning

Main Points Raised

  • Some participants argue that the mass of the Earth is independent of its relative speed to an observer.
  • Others clarify that in relativity, there are different definitions of mass, including invariant mass and relativistic mass, with the latter increasing with speed.
  • One participant suggests using kinetic energy calculations to determine changes in mass due to velocity, referencing the Newtonian formula for kinetic energy.
  • Another participant questions the relationship between acceleration, velocity, and mass, expressing confusion about how these concepts interrelate.
  • Some participants assert that energy is required to accelerate an object, which relates to the concept of mass-energy equivalence.
  • There is a discussion about whether the increase in mass due to velocity can be explained or understood, with some expressing skepticism about the definitions and implications of mass in relativity.
  • One participant emphasizes that the increase in kinetic energy does not imply a change in mass according to the definition of invariant mass.
  • Another participant raises concerns about the practical implications of these concepts, particularly in the context of an object like a bomb moving at high velocity.

Areas of Agreement / Disagreement

Participants express multiple competing views regarding the definitions of mass in relativity and whether mass changes with velocity. There is no consensus on the implications of these definitions or the relationship between mass, energy, and velocity.

Contextual Notes

Participants highlight the complexity of definitions in relativity, particularly the distinction between invariant mass and relativistic mass. There are unresolved questions about the nature of mass and energy conversion, as well as the assumptions underlying the calculations discussed.

  • #31
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?
 
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  • #32
Let me see if i am of any help. :wink:

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.
 
  • #33
Bjarne said:
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
 
  • #34
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.
 
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  • #35
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.
 
  • #36
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)
 
  • #37
it does require energy to bend space. To increase velocity and hence mass, we supply energy which then bends space as it moves. :)
 
  • #38
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 ?
 
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  • #39
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.
 
  • #40
The speeds do not increase as they are supposed to, it requires extra energy.
Agree
 
  • #41
vin300 said:
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.
 
  • #42
Doc Al said:
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
 
  • #43
vin300 said:
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.
 

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