Gravity and FTL

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  • #1
jgravatt

Main Question or Discussion Point

The earth has a gravitational pull that attracts things to it correct? If we launced a rocket from Earth and said rocket was
traveling from the ground to space at, oh let's say, 100 miles per hour (or kilometers - it really doesn't matter). Given the slow speed of the rocket, it would never leave orbit correct? If that is the case, can we say that the gravitational influence of the earth negatively exceeds the speed of the rocket, or in other words, exceeds the speed of the rocket in the opposite direction? Obviously, the Earth's gravitational influence is not as great as something larger (such as the Sun) or something physically different (such as a black hole). Using the same idea, light being the rocket and a black hole being the Earth, can it be said that the black hole's gravitational influence negatively exceeds the velocity of light? I'm sure it's not that simple, but what I would like to know is if the speed of gravitational influence (given a large enough object) would be considered FTL?

Jeremy
 

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  • #2
turin
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I would (caveat: rather ignorantly) say no. I have heard that it is believed that the speed of gravitation is c. I have heard that the supporting evidence is the upper limit on the mass of the graviton, but I have also heard that the graviton has not yet been observed, so I don't know what that would mean. At any rate, the reason I say no, is that, in the case of a BH, space-time still looks like it always does in geodesic coordinates. And that's what it comes down to: the choice of coordinates. Just because something looks wierd in a particular coordinate system (i.e. light cannot escape) doesn't mean that it is a good representation, or even true. It is just that, near a BH, space-time gets so messed up that you can't extend your flat coordinate system out very far and you realize the curved-ness more easily.
 
  • #3
chroot
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I don't know what you mean by "negatively exceeds." I also don't know what you mean about a 100 mph rocket that would "never leave orbit" -- a 100 mph rocket would never reach orbit.

- Warren
 
  • #4
jgravatt
By negatively exceeds, I mean exceed the speed of the rocket in the opposite direction. Example: If a rocket is traveling east at 100 miles per hour and the gravitational influence (or just gravitation pull) of some object keeps it from continuing east or better yet, pulls it back west, could you say that the gravitational influence of that object exceeds the speed of the rocket - slowing it down to the point where the rocket stops and begins traveling in the opposite direction.

I used the 100 mile per hour rocket as an example because it would not leave earth and never reach orbit. In other words, would the earth's gravitational influence appear to be greater than the speed of the rocket? Sorry, I probably should have clarified that.

Thanks for responding.

Jeremy
 
  • #5
chroot
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Yes, general relativity predicts that gravitational disturbances travel at the speed of light. Recent experiments seem to confirm this prediction, but the case has by no means been totally closed on the issue.

In any event, the Newtonian idea that gravitational disturbances propagate everywhere instantaneously is at odds with quite a bit of modern, experimentally-supported physics and is almost assuredly incorrect.

- Warren
 
  • #6
russ_watters
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Originally posted by chroot
I don't know what you mean by "negatively exceeds." I also don't know what you mean about a 100 mph rocket that would "never leave orbit" -- a 100 mph rocket would never reach orbit.

- Warren
However, with a source of thrust able to provide a steady 100mph speed perpendicular to the surface, it would leave earth's gravitational influence eventually.
 
  • #7
chroot
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Originally posted by russ_watters
However, with a source of thrust able to provide a steady 100mph speed perpendicular to the surface, it would leave earth's gravitational influence eventually.
That's true, but that's a pretty degenerate "orbit."

- Warren
 
  • #8
turin
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Originally posted by russ_watters
However, with a source of thrust able to provide a steady 100mph speed perpendicular to the surface, it would leave earth's gravitational influence eventually.
I was just thinking about this. Good point. If the rocket goes 100 mph, then it goes 100 mph (I'm assuming at sea level?). As it rises higher and higher, with the same amount of thrust, it will actually increase its speed (I'm of course assuming that all of this discussion is wrt the earth's surface). Maybe jgravatt can clarify what is meant by this 100 mph rocket, specifically why it couldn't escape the earth's gravity if it continued at 100 mph (wrt the surface of the earth).
 
  • #9
jgravatt
Sorry about the confusion. I was ignorantly thinking that something traveling at such a slow speed would never break the earth gravitational pull. Is there an equation that I could use to determine what minimum velocity would be required to break free of an objects gravitational influence?

Jeremy
 
  • #10
chroot
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Originally posted by jgravatt
Sorry about the confusion. I was ignorantly thinking that something traveling at such a slow speed would never break the earth gravitational pull. Is there an equation that I could use to determine what minimum velocity would be required to break free of an objects gravitational influence?

Jeremy
To leave the Earth completely (and be able to turn off the engine and not immediately fall back), a spacecraft would have to reach escape velocity, defined here:

http://hyperphysics.phy-astr.gsu.edu/hbase/vesc.html

At the surface of the Earth, escape velocity is ~11 km/sec.

At a distance of 100,000 Earth radii, 637 810 000 000 m (4.26 AU), escape velocity is only ~35 m/s.

If the craft travelled at 100 mph (44.7 m/s) for about 450 years, it would be free of the Earth's gravitational influence.

(back of the envelope calculation)

- Warren
 
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  • #11
chroot
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Update: more precision. At 100 mph, the craft would be free at a distance of 2.66 AU. It would take the craft 283 years.

- Warren
 
  • #12
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Originally posted by chroot
Update: more precision. At 100 mph, the craft would be free at a distance of 2.66 AU. It would take the craft 283 years.

- Warren
Dang! There goes my super-charged Chevy experiment. Too much gas for the tank
 
  • #13
russ_watters
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Originally posted by chroot
That's true, but that's a pretty degenerate "orbit."

- Warren
Yeah, I'm not saying its a good idea or anything.

And thanks for the escape velocity calculation - I was thinking about it, but you know about me and math and the restraining order thing...

Today I was talking on the phone with a contractor and I subtracted 2.9 from 10 and got 6.1.
 

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