If Earth's orbital speed doubled, would its mass and gravity double?

[Scootty83]

I am not all that great at mathematics or physics or anything like that, though it does interest me a great deal and I am just trying to better understand the theories, so please bare with me here.

I have read that the closer an object gets to traveling at the speed of light its mass increases and its size decreases. Am I correct? E=mc^2 and the Lorentz Contraction.

The more mass an object has, the stronger its gravitational pull. Yes?

If Earth's speed through space doubled, I assume that its mass and gravitational pull would increase as well. Yes? Would its mass and gravitational pull be proportional to the increase of speed? In other words, would they double as well too?

Earth's orbital speed relative to the sun: 66,700mph. Doubled it's: 133,400mph

Earth's mass = 5.9742 × 10^24 kilograms. Doubled it's: 1.19484 × 10^25.

1g is equal to 9.80665 m/s^2. Doubled it's: 2g = 19.6133 m/s^2

Is this information correct?

 

[Scootty83]

I am about to unload a lot of questions, so please be patient with my ignorance.

 

[Nabeshin]

Hi and welcome to PF!

The relativistic mass you're referring to is an antiquated concept -- nobody uses it anymore. Rather, we simply refer to the mass of an object and say that the kinetic energy and momenta are given by different formula from what Newton said.

That said, unless an object is moving at a speed comparable to that of light, its energy will be completely dominated by its rest energy, i.e. just it's mc^2 energy. So the effect of the Earth's orbital speed is completely negligible, so if it doubles nobody cares.

Secondly, you cannot naively mesh special relativity and gravity by saying that if an object's relativistic mass increases then so too does its gravity. If you want to discuss gravity and special relativity, then you must discuss general relativity, which is much more complicated. If you try to use simple notions, you end up saying things like if you are in a frame where an object is moving very rapidly, it will collapse into a black hole, but in that object's own frame it obviously is not moving so no black hole. The moral of the story is, gravity would not be changed by any appreciable amount.

 

[DaveC426913]

I have read that the closer an object gets to traveling at the speed of light its mass increases and its size decreases. Am I correct? E=mc^2 and the Lorentz Contraction.

As measured from another frame of reference, yes. In it own frame of reference, nothing changes.

The more mass an object has, the stronger its gravitational pull. Yes?

Yes.

If Earth's speed through space doubled, I assume that its mass and gravitational pull would increase as well. Yes? Would its mass and gravitational pull be proportional to the increase of speed? In other words, would they double as well too?

No. It would increase by an amount so vanishingly small it would take precision instruments to measure it.

To double the mass would require it to move approximately 160,000 miles per second about 90% of the speed of light - about 5000 times faster.

Here's a relativity calculator:
http://www.1728.com/reltivty.htm?b0=80000

Input a number on the text field, press the miles per scond button. Keep increasing the number until the change factor approaches 2.

 

[daqddyo1]

Scotty83,
Your statement:1g is equal to 9.80665 m/s^2. Doubled it's: 2g = 19.6133 m/s^2 is incorrect as

1 gram is the mass if 1 cc of water and 9.8 m/s2 is a measure of acceleration of any freely falling mass very near the Earth's surface. Since these are measures of different things, they cannot be equated.
As orbital speeds, even doubled are nowhere near relativistic speeds, the effects proposed would not be observed.
However, if the orbital speed of the Earth were doubled, the Earth would move into an elliptical orbit taking it farther from the sun but returning to the distance it was when its speed doubled every "new" year.

 

[Scootty83]

Thanks all for the info. I have more questions still, but before I ask them, I'm going to see if I can answer them myself.

"Scootty" (2 o's 2 t's) is a nick name from high school... It just stuck. And I am sure you can guess the 83...

 

[ZikZak]

please bare with me here.

Not without dinner and flowers.

I have read that the closer an object gets to traveling at the speed of light its mass increases and its size decreases. Am I correct? E=mc^2 and the Lorentz Contraction.

The mass doesn't really increase. "Relativistic mass" is a concept often used to teach relativity, as a kludge to make relativistic equations look more like Newton's Laws. But the reality is that Newton was wrong about those laws near the speed of light.

The more mass an object has, the stronger its gravitational pull. Yes?

And this is why "Relativistic Mass" shouldn't be used at all--- the answer to your question is "not necessarily." Newton was wrong about gravity being the attraction of masses. At low energies, that's true, but the kinetic energy of a uniformly moving mass isn't purely attractive, no.

If Earth's speed through space doubled, I assume that its mass and gravitational pull would increase as well. Yes?

No. Speed is Relative. That's where the theory gets its name from. What that means is that speed is meaningless except in relation to other bodies. In other words, aside from looking at a body and saying "that thing is traveling at 100 MPH. Therefore I must be traveling at 100 MPH relative to it," there can be no experiment you can do without reference to outside bodies whose outcome depends on the speed of the observer. If Earth's gravity, as measured by Earthlings, increased with its speed, then that would be an experiment that could be performed that would yield Earth's speed without reference to other bodies, and that cannot be. Thus the answer to your question is "no."

 

[DaveC426913]

Not without dinner and flowers.

I saw what you did there...

 

[Scootty83]

Scotty83,
Your statement:1g is equal to 9.80665 m/s^2. Doubled it's: 2g = 19.6133 m/s^2 is incorrect as

1 gram is the mass if 1 cc of water and 9.8 m/s2 is a measure of acceleration of any freely falling mass very near the Earth's surface. Since these are measures of different things, they cannot be equated.
As orbital speeds, even doubled are nowhere near relativistic speeds, the effects proposed would not be observed.
However, if the orbital speed of the Earth were doubled, the Earth would move into an elliptical orbit taking it farther from the sun but returning to the distance it was when its speed doubled every "new" year.

If I am not mistaken, "g" not only represents a gram but it is also the proper notation for g-force or gravitational force as well, which is how I was using it in this case.

Back to my question: Would these statements be accurate? 1g (or 1 g-force) is equal to 9.80665 m/s^2. Doubled it's: 2g = 19.6133 m/s^2. Can g-forces be comparable to the rate at which an object will fall towards the center of the Earth?

 

[DaveC426913]

If I am not mistaken, "g" not only represents a gram but it is also the proper notation for g-force or gravitational force as well, which is how I was using it in this case.

Is that what daqddyo1 was trying to say?

He misunderstands. You are correct.

Back to my question: Would these statements be accurate? 1g (or 1 g-force) is equal to 9.80665 m/s^2. Doubled it's: 2g = 19.6133 m/s^2. Can g-forces be comparable to the rate at which an object will fall towards the center of the Earth?

For all intents and purposes, yes.

No, an object falling towards a gravitational source cannot and will not exceed c.

 

[FtlIsAwesome]

If Earth's speed doubled, there would be a very very slight increase in relativistic mass.
An increase in relativistic mass does not mean an increase in gravity.
From Earth's perspective it would have no relativistic effects, instead other objects would.

Scotty83,
Your statement:1g is equal to 9.80665 m/s^2. Doubled it's: 2g = 19.6133 m/s^2 is incorrect as

1 gram is the mass if 1 cc of water and 9.8 m/s2 is a measure of acceleration of any freely falling mass very near the Earth's surface. Since these are measures of different things, they cannot be equated.

1 g also is a measure of Earth's gravity.

Is that what daqddyo1 was trying to say?

:rofl:

No, an object falling towards a gravitational source cannot and will not exceed c.

This is a little tricky to define. In the case of a black hole, matter never exceeds c but space itself does.

 

[DaveC426913]

This is a little tricky to define. In the case of a black hole, matter never exceeds c but space itself does.

Let's not complicate matters beyond the OP's question. He's asking about the velocity of Earth and the relativistic effect that will have on its mass and thus (albeit incorrectly) its gravity.

 

[harrylin]

I am not all that great at mathematics or physics or anything like that, though it does interest me a great deal and I am just trying to better understand the theories, so please bare with me here.

I have read that the closer an object gets to traveling at the speed of light its mass increases and its size decreases. Am I correct? E=mc^2 and the Lorentz Contraction.

The more mass an object has, the stronger its gravitational pull. Yes?

[..]

In addition to what others wrote: forces from objects at high speed, as inferred by us, are in general affected by speed. For example, the attraction between two charges that are in parallel motion reduces as a function of speed, although their charges remain the same. Thus it's wrong to think that one may extrapolate laws that are valid for objects in rest to objects in motion.

Harald

 

[FtlIsAwesome]

Let's not complicate matters beyond the OP's question.

Good point.