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Since GR assumes that gravity waves travel at speed c, we expect we would be able to some day detect an aberration effect similar the that of light. Of course, gravity waves are so tiny in magnitude, we haven't yet unambiguously detected them, so aberration measurements aren't yet possible. However, planetary orbits appear to behave as if gravity waves have "infinite" speeds, since they aren't seemingly affected by the finite time between where a planet is currently located and the time lapse from Sun's force.

Can someone explain why planetary orbits behave as if gravity waves have Newtonian-like "infinite" velocities? I'd appreciate a response that doesn't resort to tensor notation.

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Similar lack of simple 'delay' happens with electromagnetic fields. When you have a point charge moving with constant velocity, the field does not work as if it had some lag. You can play with this applet to get the idea: http://www.cco.caltech.edu/~phys1/java/phys1/MovingCharge/MovingCharge.html

In electromagnetic field, the past motion of the field source makes the field at distance be as if the motion was continued at same velocity to the present time and then the field was propagated at infinite speed.

Note that this does not happen due to some extra rule; that's what the field equations naturally work out to.

With the general relativity, AFAIK, that sort of 'extrapolation' works not only for speed but also for the acceleration, so that if you have an object moving with constant acceleration, you won't be able to distinguish GR from instantaneous propagation. The delay effects in GR are, consequently, very small.

Here is an article about this strange phenomena: http://math.ucr.edu/home/baez/physics/Relativity/GR/grav_speed.html

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Right now the Earth is responding to the curvature of space in it's immediate vicinity. If something drastic were to happen to the Sun the curvature in the vicinity of the Earth wouldn't be affected for eight minutes or so, until the gravitational waves generated by whatever happened to the Sun arrived at the Earth and changed the curvature in it's vicinity. So planetary orbits don't behave as if gravity waves have an infinite velocity

It isn't correct to think of the Earth being "held" by the Sun's gravition with gravity waves and/or gravitons flashing to and fro to do the holding. All the matter in the Solar System generates a curvature and all the matter then responds to the local curvature, so no infinite speed transmission is necessary. Any changes in the curvature do propagate at the speed of light.

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Can someone explain why planetary orbits behave as if gravity waves have Newtonian-like "infinite" velocities?

Here's a simple (maybe a little oversimplified, but good enough to start) explanation: the gravitational center of the solar system can be considered to be fixed in place in a nearly inertial reference frame. If you consider the gravitational center fixed, you can't tell whether the planets are orbiting where the center is now (infinite speed of gravity) or where it was some number of minutes ago (finite speed of gravity), because they are the same place. It may look like the former case, but in reality it is the latter.

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