So is the effect between the passing planets different whether they encounter in the same or opposite direction in their orbits with the same relative speed difference?
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1$\begingroup$ Do you know the equation (even Newtonian) for gravitational forces? $\endgroup$– Carl WitthoftCommented Mar 3, 2017 at 14:39
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$\begingroup$ @CarlWitthoft perturbation effects depend on more than $-Gm_1m_2/r^2$. There are significant differences in orbital perturbations in the two cases. One way to look at this would be to look at the inclination of the perturber as being either 0 or 180 degrees. The question is reasonable. $\endgroup$– uhohCommented Mar 11, 2017 at 1:51
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$\begingroup$ @Marijn The effect is different yes. You use "effect" in your title, but in the body of your question you mention the "force or velocity". Well they will certainly be different - if you plot force versus time, you'll see a narrower "bump" or impulse, and of course the relative velocity will be higher, but I think you should include the word "effect" in the body of your question to match the title. That seems to me to be what you are really after, the result. $\endgroup$– uhohCommented Mar 11, 2017 at 1:59
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$\begingroup$ @uhoh thanks for you understanding, I've changed it. But you say that the relative velocity is higher, perhaps, but in my question the relative speed is the same in both direction. $\endgroup$– MarijnCommented Mar 11, 2017 at 9:54
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$\begingroup$ If you choose a particular star, let's say the Sun for example, and assume circular orbits, the speed of an orbit is determined by the radius of the orbit. If you want to keep two orbits the same distances from the sun, then their speeds will be the same. If they orbit in the same direction, the relative speed between the two planets will be lower. If they orbit at the same speeds and distances but opposite direction, the relative speeds between the two planets will be greater. $\endgroup$– uhohCommented Mar 11, 2017 at 13:23
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1 Answer
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From the any of the planet's point of view, the encounter is exactly the same regardless of direction if the relative speed and force is equal. This should be pretty clear for symmetry reasons. For any encounter, the law is $v_{in} = v_{out}$. However, if the encounter takes a long time, you would also have to consider the influence of the central body of the system. The problem then becomes a three-body problem and this case is not restricted enough for an analytical solutions. We can make a few observations though: As the velocity vectors of both objects before the encounter have no radial component, both orbits are going to get a higher eccentricity. Any other information depends on knowing the distance of the encounter and the relative masses.
answered Mar 5, 2017 at 19:57
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1$\begingroup$ The question is not about the instantaneous force at minimum distance, it is about the effect. The effects will be very different, and some generalizations may apply. As I've said above, there are significant differences in orbital perturbations in the two cases. One way to look at this would be to look at the inclination of the perturber as being either 0 or 180 degrees. The question is reasonable. I have a strong hunch there is a better answer than this. The problem is that the question-closers may kill the question before it can be generated. $\endgroup$– uhohCommented Mar 11, 2017 at 1:51