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Cruithne (3753 Cruithne) is in a near Earth orbit. Technically, a horseshoe orbit, because it orbits the sun so close to Earth's orbit that it almost, but never, passes us. When visible, which is rare, it appears to move in a horseshoe pattern.

https://en.wikipedia.org/wiki/3753_Cruithne

Horseshoe orbit of Cruithne from the perspective of Earth.gif Source

It also crosses the orbits of Mars and Venus and even Mercury.

Why, if it is so close and so large (over a mile and a half) haven't we tried to probe this small world?

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    $\begingroup$ This asteroid would be hard target. Why? The key concepts are "delta V", "rocket equation" and "vis viva equation". If we calculate delta V we'll see the mission requires very large velocity change, much larger than for example to fly to Bennu asteroid. Also crossing orbit of Mercury means harsh thermal conditions, so more sofisticated and expensive spacecraft is needed. $\endgroup$ – Heopps Feb 18 at 13:11
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    $\begingroup$ @Heopps that looks sufficient to be posted as an answer $\endgroup$ – Carl Witthoft Feb 18 at 13:15
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    $\begingroup$ @Carl Witthoft - maybe, but currently it's just words without proof ) And the proof (links, formulas) require much more time that I haven't now, unfortuntely. I'm sure somebody can write better answer. $\endgroup$ – Heopps Feb 18 at 13:53
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3753 Cruinthe ranks as target number 16832 in JPL's list of near earth asteroids that might be worth visiting, someday. With 16381 better targets, that "someday" most likely will be a long time from now, if ever.

The problems with getting to Cruinthe are twofold. One issue is that its orbit is rather eccentric (0.51485). Changing an orbit's shape is an expensive operation in terms of delta V. The other issue is that its orbit is quite inclined with respect to the Earth's orbit about the Sun, by about 19.8°. Plane changes are also extremely expensive in terms of delta V. The combination of the two issues would make a Cruinthe rendezvous cost more than twice as much (in terms of delta V) as would a Moon landing or a Mars rendezvous.

It would be cheaper to send a lander to Ceres than it would be to rendezvous with Cruinthe.

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    $\begingroup$ A flyby's not hard, you can reach Cruinthe with about 3.5 km/s...your encounter velocity just ends up being 20+ km/s. Look at ssd.jpl.nasa.gov/?mdesign_server&sstr=3753%20Cruithne, there's a plotting tool that makes it clear why it's such a hard orbit to reach from Earth. $\endgroup$ – Christopher James Huff Feb 18 at 23:08
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    $\begingroup$ @ChristopherJamesHuff - Thanks. I changed flyby to rendezvous. $\endgroup$ – David Hammen Feb 18 at 23:11
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    $\begingroup$ How do JPL rank the list of targets worth visiting? Just delta V, or do other factors play a role? $\endgroup$ – Benjamin Popper Feb 19 at 18:33
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    $\begingroup$ @BenjaminPopper, the JPL list is straight delta-V. $\endgroup$ – Mark Feb 19 at 21:48
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    $\begingroup$ Funny enough, #1 on that list (as of the time of this comment) might be the Apollo 11 lunar lander. $\endgroup$ – Jacob Ford Feb 28 at 17:49

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