Appendix A: Resolving Eros with a Telescope

Speaking of Eros, a 1945 astronomy text book said ...

The planet's rotation was seen in February, 1937, by van den Bos and Finsen with the 26-inch refractor at Johannesburg. It appear elongated like an unresolved double star of about 0".18 separation. The direction of elongation shifted counter-clockwise, completing a rotation in 5^h 17^m. The earth was then on the north side of the planet's equator, so that the rotation is direct. ¹

This is a surprising claim. Eros was thought to be roughly cylindrical, about 22 miles long by 7 miles in diameter. We now know from the NEAR mission that they weren't too far off, Eros is about 22 × 8 × 8 miles. Is it possible to actually see the shape of such a small asteroid and watch it rotate? We can check out the claim with a bit of work. First note that another reference to this observation, in Sky and Telescope magazine, states that the date was February 1931, not 1937. It further states that the astronomers were experienced double star observers using the 26½-inch refractor of the Union Observatory in South Africa. ²

First, where was Eros in February 1931? That is a bit hard to answer, current orbital elements do not extend well back that far (that's why asteroids were so hard to keep track of). It is possible to obtain historical orbital elements, but to get started, several Sky and Telescope articles give a distance of 0.17 astronomical units. This is 25.4E6 km (see the Solar System Distance Converter). Eros is now known to be 33 km long, at 0.17 AU it would exend an angle of 33/25.4E6 radians which is 0.27 arc seconds. It wasn't stated when in February the Eros observations were made, so this is consistent with the reported 0.18 arc seconds.

We can do better than just verify that it was possible to see Eros rotating. We can actually compute some simulated images through various size telescopes. First though you should read up a bit on what is meant by telescope resolving power, Appendix B.

The simulated images below were computed for an apparent size of Eros of 0.27 arc seconds across. Eros was front lit and viewed from above latitude 60 degrees north. Two raw images are shown: a large version and a small version to scale. Each small view and degraded image is 2 arc seconds on a side for Eros at 0.17 AU. The image degraded by diffraction is shown for four different size telescopes. Eros rotates about its axis by 30° betwen images, starting at longitude 240°

	Longitude 240°	Longitude 270°	Longitude 300°
Large View
Scale View
12 inch scope
26.5 inch scope
60 inch scope
HST

Time lapse view

The 1931 observation was made through a 26.5 inch refracting telescope. The rotation was observed by noting that the orientation changed over several hours, actual movement would have been too slow to see. But the simulated image on the right shows a time-lapse view as an animated GIF. ³ Remember the actual rotation period is 5.27 hours. It appears that such an observation is possible. The actual image would have been much smaller, almost a pinpoint, and jumping around from atmospheric turbulence making it a very hard observation. The observers must have been very skilled.

Back to the Historical account of 433 Eros

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¹ Henry Norris Russell, Raymond Smith Dugan, and John Quincy Stewart, Astronomy (Boston: Ginn and Company, 1945), p. 357.

² Jean Meeus, Eros' Closest Approach to the Earth, Sky and Telescope Magazine, Vol 48, Num 4, (Oct 1974) p. 223.

³ Animated GIF created using GIF Construction Set Classic from Alchemy Mindworks at http://www.mindworkshop.com/alchemy/alchemy.html