5 April 2019
Last time, I talked about Cruithne, and what a weird thing it was. From the Earth, it looks as though it orbits the Earth in a horseshoe shape, going one way around, stopping, then going back the other way. It’s explainable if you look from a different perspective, because the Earth and Cruithne both orbit the Sun in the same period of time. It’s just that it looks like some bizarre orbit from the Earth.
I also said that if you've got access to a large telescope you'd be able to see Cruithne - just. When I said "just", I really mean it. This is a magnitude 17-18 object, so it's incredibly dim. My low-magnification rig has imaged down to magnitude 14, when I got a photo of Uranus' moons Titania and Oberon. This was a 10 second exposure, so I'm thinking it's worth a try.
Those of you with larger-aperture rigs should be able to do this.
Of course, the alternative is to join the Astronomical Society of Victoria and use their equipment. A 44 inch reflector ought to do it!
To find where Cruithne is, I use Stellarium, the free planetarium software. Stellarium will show you where Cruithne will be at any given moment. (You might have to download extra data to get the object.) Stellarium shows you all sorts of information, including distance from Earth, so you can find when Cruithne is close and when it isn't. Obviously it's best for viewing when it's close.
On 10 September 2019, between midnight and sunrise, Cruithne is close to Earth, and will pass in front of the outer fringes of the Great Nebula in Orion! Now, this is four days before September's full moon, but at 5am the moon will be setting in the west. All this action is happening in the north-east, so it should be dark.
The object will move across the field of view passing background stars as it goes. With your mount tracking, take a series of photographs, say, 60s exposures. In the series you should see Cruithne changing position from one frame to the next.
Good luck and make plans now!