The planets react to the instantaneous position of other planets even though the time for light to travel between them may be hours, days, weeks or months. If there was a lag in the reaction because of the light speed, many planet orbits would fly apart in spirals. Funny, nobody make a fuss about this because it has always been this way.
Listen to you guys and we can't even protect a sweet woman from being executed by judge and you're talking about zapping around at the speed of light--blahblahblahblah...
No, there was an experiment done a couple years ago using the same methodology determining the speed of light - Jupiter and mistimed calculations due to speed of light error.
Jupiter was to pass by a loud radio source, and it was determined when and how the gravity would alter the signal given speed of light values, or instantaneous values.
The speed of the influence of gravitational effects is the speed of light. This means if the sun were to spontaneously vanish from the center of the solar system, it would take 8 minutes for the earth to fly off in a straight line.
Actually, according to Einstein, gravity travels at exactly the speed of light. If ths sun were to disappear or explode right now, we wouldn't know or feel anything for a full 8 minutes.