I Spacetime Curvature: Eliptical Orbital Paths & Keppler Laws

Osvaldo
Messages
27
Reaction score
1
Though it is hard not to believe in the spacetime curvature that cause planets to follow curved path arround massive objects, I wander how come these paths are eliptical, the object change velocity when moving arround the massive object and what is more obeys the Keppler laws. If there is not such a gravitational force (as said byexperienced physics) which would really caused these conditions, how come these orbital movements do not belong to a central force? Can somebody give a clear explanation?
 
Physics news on Phys.org
Kepler laws or eliptic orbit of planets is derivied from Newton's inverse square law of universal gravitation.
I understand this Newton's inverse square law of central force is a fairy good approximation of GR theory or curved spacetime around the Sun, a massive body.
 
Osvaldo said:
I wander how come these paths are eliptical
They are actually not quite elliptical. GR explains both why they are almost elliptical and also correctly predicts how much they deviate from being completely elliptical.
 
Osvaldo said:
Though it is hard not to believe in the spacetime curvature that cause planets to follow curved path arround massive objects, I wander how come these paths are eliptical, the object change velocity when moving arround the massive object and what is more obeys the Keppler laws. If there is not such a gravitational force (as said byexperienced physics) which would really caused these conditions, how come these orbital movements do not belong to a central force? Can somebody give a clear explanation?
Locally and for weak fields the space-time geometry just reproduces the same effect Newton's force would have, and would also result in an elliptical orbit:



But globally you get an additional effect from space curvature, so the orbit is not closed:
http://demoweb.physics.ucla.edu/content/10-curved-spacetime (Figure 2)
 
  • Like
Likes Dale
A.T. said:
Locally and for weak fields the space-time geometry just reproduces the same effect Newton's force would have, and would also result in an elliptical orbit:



But globally you get an additional effect from space curvature, so the orbit is not closed:
http://demoweb.physics.ucla.edu/content/10-curved-spacetime (Figure 2)
 
Wonderful demonstration. Never saw it like the one in the video. Thanks a lot
 
In this video I can see a person walking around lines of curvature on a sphere with an arrow strapped to his waist. His task is to keep the arrow pointed in the same direction How does he do this ? Does he use a reference point like the stars? (that only move very slowly) If that is how he keeps the arrow pointing in the same direction, is that equivalent to saying that he orients the arrow wrt the 3d space that the sphere is embedded in? So ,although one refers to intrinsic curvature...
ASSUMPTIONS 1. Two identical clocks A and B in the same inertial frame are stationary relative to each other a fixed distance L apart. Time passes at the same rate for both. 2. Both clocks are able to send/receive light signals and to write/read the send/receive times into signals. 3. The speed of light is anisotropic. METHOD 1. At time t[A1] and time t[B1], clock A sends a light signal to clock B. The clock B time is unknown to A. 2. Clock B receives the signal from A at time t[B2] and...
So, to calculate a proper time of a worldline in SR using an inertial frame is quite easy. But I struggled a bit using a "rotating frame metric" and now I'm not sure whether I'll do it right. Couls someone point me in the right direction? "What have you tried?" Well, trying to help truly absolute layppl with some variation of a "Circular Twin Paradox" not using an inertial frame of reference for whatevere reason. I thought it would be a bit of a challenge so I made a derivation or...

Similar threads

Back
Top