For reasons associated with a 1943 story, I am keen to find how close Earth will come to Pluto in 2024. According to https://theskylive.com/pluto-tracker today (21-May-2024), Pluto is now slowly heading away from the Sun at about 5km/s (on its eccentric 248-year orbit), however Earth is approaching Pluto at about 26km/s.
Specifically, I would like to know when (if at all) the separation will reach 5,055,434,765 km, please. As of right now (21-May-2024) the current separation is 5,164,233,302 km, so if the speed was maintained (which of course it won't be) the critical separation would be achieved about 48 days from now.
EDIT: Thanks for the speedy computation. I guess we miss the bus in July by 1% and the next one won’t be for a long time (maybe over a century?) On the other hand with Pluto near the sun, there would have been a bunch in the last few decades, I am guessing about two a year. I will try to calculate the last one and the next one using the tool suggested.
I will shortly publish an article that gives the (rather frivolous) background for this and leaves the door open for analyses of other objects in the solar system. The distance is sqrt(2) * 2^46 * 2 inches. Click on the solution box for problem 5 in https://www.theproblemist.org/beginner.pl?type=b_fy.
Specify that the white queen must start on the surface of some object, and end on square c2 on the surface of the Earth. We don't worry that intermediate positions will be in empty space. Then I don't think the moon is viable. Nor are Sol, Uranus or Neptune. The following table shows the positive results. Note that Mercury, Venus & Mars appear multiple times.
Number of Chess Moves | Planet* | Frequency |
---|---|---|
81 | Venus | 2 x Earth Year |
83 | Mercury, Venus, Mars | 2 x Earth Year |
85 | Mercury, Venus, Mars | 2 x Earth Year |
87 | Mars | 2 x Earth Year |
89 | Jupiter | 2 x Earth Year |
91 | Saturn | 2 x Earth Year |
95 | Pluto | 2 x Earth Year but only when Pluto is near perihelion |
One might ask about other more distant objects within & outside the solar system. The difficulty is getting a direct hit with the required distance, which is easiest if the object have a highly elliptic orbit.
*or dwarf planet