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Absolutely we could, and in fact, I strongly suspect that General Relativity was never used in the Apollo program. for one thing, the on-board navigation computers were nowhere near powerful enough to perform any useful calculation with GR. on the other hand, it's possible to measure the position of the moon to within a few centimeters (much more accurate ...


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Consider that it would not be particularly difficult to do an Apollo-type landing if each of your relative velocity, range, and angular measurements were off by +/- 5%. You could simply make small iterative corrections along the way, until the absolute values were small enough to make the relative errors inconsequential. At worst you'd need to carry ...


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The Jet Propulsion Laboratory has incorporated general relativistic effects in its numerical integration of the planets since the mid to late 1960s. For example, the JPL DE19 ephemeris, released in 1967, incorporated relativistic effects in its modeling of the solar system. This didn't help much. Had they ignored relativistic effects there would have been ...


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A few sanity checks without actually computing anything: First, the error due to neglecting general relativity is so small that it didn't affect prediction of lunar eclipses and wasn't actually noticed anywhere except in Mercury's orbit (at least not until they purpose-built experiments to detect minor discrepancies). I know this doesn't give a completely ...


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The trouble with orbital mechanics is that it rapidly gets exceedingly complicated and hard to make intuitive sense of. However I think there is a reasonably straightforward way to show how little effect GR has on an Earth-Moon transfer orbit. But this takes a little preparation so bear with me while I give a short introduction. I hope everyone who reads ...


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I'll start the ball rolling on this one. My GR knowledge is probably not good enough to make this a truly satisfying answer... The gravitational acceleration for an object moving radially at non-relativistic velocities in the Schwarzschild metric is modified by a factor $(1 - r_s/r)(3[1-r_s/r] -2)$, where $r_s = 2GM/c^2 = 0.00885 m$ for the Earth. If we ...


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You only have a problem if you start without any tangential velocity and have no reflection (or you collide with a celestial body before you have a chance to evade it). Let us say you start in a stable orbit. Your ship has a bow and stern, in the direction of your velocity. If you can reflect the light towards your stern, it will accelerate you and you get ...


15

The question is about solar sails - I thought I would add this (too long for a comment) to clarify some confusion that is apparent in answers and comments. Solar sailing uses photon momentum, not the solar wind. The radiation force on a perfectly reflective sail of area $A$ is roughly $$ F_{rad} = 2\times\frac{L A}{4\pi r^2 c}$$ where $r$ is the distance ...


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Yes, but not the way you think. It's not analogous to a sail boat. A solar craft has no keel to resist movement in one direction, and I doubt that solar wind is dense enough to cause a noticeable wing effect with a sail. But stars have their own complexities you can exploit instead. Every answer thus far considers a static model where the star sits in ...


11

Yes, sort of, sometimes. As others have indicated, it is not possible for a solar sail to produce a force in the direction of the Sun. This does not, however, mean a solar sail cannot take a spacecraft to the Sun. If your spacecraft is in solar orbit, you can tilt the sail "backwards", reducing the orbital energy and lowering the orbit. The potential energy ...


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A sailboat can make headway against the wind because of the sum of force vectors due to the wind interacting with the sail and, due to the keel interacting with the water. A sailboat without a keel can not make headway into the wind. There is no "water" out there into which a solar sailer could dip its keel. http://newt.phys.unsw.edu.au/~jw/sailing.html ...


2

To answer such a question you need to set some parameters. The obvious thing to do is to ask whether, with our current technology, we could detect ourselves at the distances you suggest? The answer is no. You can find some more details in the related question Detectability of interstellar messages In summary, the most powerful radio signals we send into ...



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