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Curved Spacetime and Gravity

  1. Mar 26, 2009 #1
    Hi,
    If gravity is result of curved spacetime;
    1.why are there eliptical orbits around spherical bodies?
    2.Why don't I stop accellerating when I reach the lowest point of the curvature, ie, on surface of earth I am at lowest point of curvature I should stop accellerating (maybe fall back up) ?
     
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  3. Mar 27, 2009 #2

    mathman

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    For questions like these, Newtonian mechanics works just fine.
    1. The shape really doesn't matter. Gravity of spherically symmetric bodies is the same as for a point with the same mass at the center. The possible orbits are conic sections.
    2. You stop moving when you hit the ground because the ground is in the way. The acceleration is still there. That's indicated by the fact that you weigh something when you step on a scale. Your weight is a measure of force.
     
  4. Mar 28, 2009 #3
    If you have a non rotating body, let's say, a long stick, (to start off with), and this body is heading towards a large gravity source, like, the earth. It is a long stick, but not that massive, so our theoretical stick will be captured, and fall into an orbit around the earth.

    It's a thought question, so as to how that can happen isn't the important part, it is about curved spacetime and gravity. We can add thrusters to slow it down, whatever. But only to get to the point where gravity will cause an orbit. We want no thrust at the point where things start to curve.

    What I'm wondering about, is will our stick, (which starts out passing by with the long axis pointing past the earth), will gravity (or curved spacetime) actually cause the stick to continue it's course, but curve around the earth?

    Does gravity, in relativity, does it actually cause the path of objects to curve, and to them, they are still going "straight"? Does an observer on the stick (OK we could call it a long thin spaceship I guess) feel like nothing has happened, assuming there is no acceleration, to get into orbit?

    Or if the stickship simply passes by, and is curved into a new trajectory, does an observer on the stickship feel and change? Like when a car goes around a corner? Or is it all free fall to them?

    I'm trying to imagine what happens to an object when it is curving. Like light, they say that when it "bends" due to a massive gravity field, the photons don't actually bend, the light thinks it is still going straight, spacetime bends. Curves.

    Is this true for objects as well?
     
  5. Mar 28, 2009 #4
    Wow. That sounds terrible. Let me try and clean that up.

    1) Does an object in orbit travel through curved spacetime?

    2} Does the object experience any acceleration as it orbits? The kind that an observer onboard can detect?

    3) Is it all free fall? Or can you feel a change when a gravity source changes your trajectory?

    4) Will a long rod, whose long axis is at right angles to a gravity source, will it maintain a right angle as it curves around the planet? Or will it point in the same direction? In other words, if the rod is "pointed" towards a star, as it starts to orbit, does it rotate away from the star?

    5) Will pictures help explain this?
     
  6. Mar 28, 2009 #5

    A.T.

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    Yes
    No

    Yes

    That depends. But let's say both ends of the rod have the same distance to the source of gravity, and the oribit is a circle. In that case the rod will maintain a right angle to the line between its center an the source of gravity
     
  7. Mar 30, 2009 #6
    Thanks. I thought that was the case, but wasn't sure.

    So an object in "free fall" is actually falling in curved spacetime? Is that correct?
     
  8. Mar 31, 2009 #7

    A.T.

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    I don't know what "falling in spacetime" would mean. I would rather say:
    An object in "free fall" is advancing on a straight path in spacetime:
    http://www.relativitet.se/spacetime1.html
     
  9. Mar 31, 2009 #8
    Forgive me if I'm wrong, but don't objects in orbit experience centripetal acceleration? The observer wouldn't necessarily "feel" it, but that doesn't mean it would not exist.
     
  10. Mar 31, 2009 #9

    A.T.

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    Depends on the definitinon of acceleration. In GR acceleration means the proper acceleration that you can "feel" (measure with a accelerometer). Unlike the coordinate acceleration (velocity derivate) proper acceleration is absolute (independent of the frame of reference).
     
  11. Apr 10, 2009 #10
    Here's the thing then. If an object gets captured by another object, so that it goes into orbit around the much larger object, it isn't experiencing acceleration, like an object that is falling towards an object. Instead it is moving at a constant velocity (hence the free fall or weightlessness experience, like the ISS), in a straight line, which seems curved because of the warped space time.

    Is that even close?
     
  12. Apr 11, 2009 #11

    A.T.

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    Almost. The key is: straight line in space-time = no acceleration. But it does not mean a constant velocity in space. Unlike in flat space-time, a straight line in curved space-time doesn't imply a constant velocity in space.

    The velocity in space we observe is changing, so in a flat space-time the path of the object would be curved, which means acceleration. The idea is to warp space-time in a way that makes the path of every free faller straight, so they aren't accelerated anymore.
     
    Last edited: Apr 11, 2009
  13. Apr 21, 2009 #12
    I'm confused.

    1) Is an object in orbit accelerating?

    If so ..

    1.a) In what reference frame?
    1.b) Can the acceleration be measured?

    2) Is an object on the surface of the earth accelerating?

    3) If you say no, what about a tall tower on the earth, say, 22,500 miles high, is the top of that accelerating?

    4) Is a geosynch satellite at the same height accelerating?
     
  14. Apr 21, 2009 #13
    And what relationship to warped spacetime do any of those objects have?
     
  15. Apr 22, 2009 #14

    A.T.

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    1) Is an object in orbit accelerating?

    Proper accerleration: no
    Coordinate acceleration: depends on the reference frame

    1.a) In what reference frame?

    Proper accerleration: is the same in every reference frame (absolute)
    Coordinate acceleration: see above

    1.b) Can the acceleration be measured?

    Proper accerleration: yes, with an accelerometer
    Coordinate acceleration: yes, as the derivate of velocity

    2) Is an object on the surface of the earth accelerating?

    Proper accerleration: yes
    Coordinate acceleration: depends on the reference frame.

    3) If you say no, what about a tall tower on the earth, say, 22,500 miles high, is the top of that accelerating?
    4) Is a geosynch satellite at the same height accelerating?

    If you omit the mass of the rest of the tower, both cases are the same.
    Proper accerleration: no
    Coordinate acceleration: depends on the reference frame.

    And what relationship to warped spacetime do any of those objects have?

    If proper accerleration = 0 they advance straight ahead in warped spacetime.
     
  16. Apr 22, 2009 #15
    inre:
    "2} Does the object experience any acceleration as it orbits? The kind that an observer onboard can detect?

    No"

    AT, sorry, but you are incorrect here. the observer would surely be able to detect that the direction his ship is traveling is constantly changing. acceleration is a change in velocity - since velocity is a vector, this can mean a change in speed, or a change in direction.
     
  17. Apr 22, 2009 #16

    A.T.

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    I assumed that "experience any acceleration" meant proper acceleration. The object doesn't experience proper acceleration.

    You are referring to coordinate acceleration, which is frame dependent (as is velocity). In the objects own frame (where the object is a rest) coordinate acceleration is zero as well. Coordinate acceleration would be not zero in a frame attached to the earths center for example. But that is not what I understood by "what the object experiences".
     
  18. Apr 22, 2009 #17

    Mentz114

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    Have you seen film of people in the space stations ? They are in free fall (in orbit) and do not experience any proper acceleration.
     
  19. Apr 22, 2009 #18
    that question did not specify proper acceleration. my answer is correct.
     
  20. Apr 22, 2009 #19

    A.T.

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    Nor did it specify coordinate acceleration, which you assume
    Not in general. Your answer assumes a certain frame in which the velocity of the object is changing (coordinate acceleration.). But the onboard observer could just as well pick a frame, where he has no coordinate acceleration.
     
  21. Apr 23, 2009 #20
    Thanks for all the input.
     
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