What Speed Of Gravity Is Used In Space Probe Trajectory Calculations.

[spartan45]

What speed of gravity is used in space probe trajectory calculations?

It is now believed that gravitational force travels with the speed of light. Thus if the gravitational force between the Sun and Earth were suddenly to disappear by the vanishing of the Sun, it would take about 8 minutes for the effect to be experienced on the Earth. The Earth would then fly off along a tangent to its original curved path. This being the case, the answer to the question seems clear, but it is not so.

When an object like the Earth is moving around the Sun, the attraction of the Earth is toward the instantaneous position of the Sun and not where the Sun had been if its position was retarded using the relative velocity (this retardation actually does happen with the optical position of the Sun, and is called annual solar aberration). If the pull of gravity was toward the optical and not the actual position of the Sun, it would cause a pull ahead of the Earth, which would cause the orbit of the Earth to spiral outward. No such thing has been observed, and the Earth’s orbit is stable.

Any change in a gravity field must propagate at the speed of light, but once a gravity field is established, (as in the case of the entire visible universe), the effect of this field on an orbiting object is instant wherever it is, following Newtonian law of gravitational force that gravity is directed along the line joining the instantaneous positions of objects, like the Earth and the Sun. Einstein improved Newtonian law of gravitational force with his theory of relativity showing, amongst other things, that even electromagnetic radiation (e.g. light) despite having no mass, is affected by gravity because spacetime is warped by gravity. Objects in free fall follow geodesic paths in spacetime and general relativity also takes into account the extremely small effect caused by an objects velocity. https://en.wikipedia.org/wiki/Geodesics_in_general_relativity

The solar eclipse of 21^st Aug 2017 would be a good opportunity to use a gravimeter to show the direction of largest gravitational force occurs when the actual position of Sun, Moon and Earth are in a straight line, so that after about 8 minutes 19 seconds when the light retarded position of the Sun, Moon and Earth are in a straight line the gravimeter  should  have shifted about 5.7x10^-3 degrees east of the visible Sun’s position, as it still points towards the actual position of the Sun and the total gravitational force weakened slightly. The 5.7x10^-3 deg. figure was calculated using Earth’s orbital velocity of 29.78 km/s multiplied by 499 seconds giving 14,860km divided by the Earth/Sun distance of 149,600,000 km to give Tan 9.933x10^-5 which is the 5.7x10^-3 degree gravimeter easterly shift that should be expected if this experiment was performed. See diagram.

Conclusion: Newtonian law of gravitational force is used in space probe trajectory calculations because the only way space probe trajectory calculations work is to use the actual (instantaneous) position of the gravity source and not it’s light retarded position.