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Close approaches
Earth reaches the point in its orbit closest to Eros' perihelion aboutJanuary 22 each year. If Eros is then at its perihelion pointthe distance from Earth will be minimum, about 14 million miles.But if Earth passes Eros (that is, Eros is in opposition) any time duringJanuary or February it is nearly as good. Favorable oppositions aresomewhat rare and unfortunately a very favorable oppositionoccured on January 9, 1894, at 0.15 AU, a few years before Eros was discovered.Unfavorable opositions occur in June, July, or August. A late Julyopposition can be as far as 0.77 AU. Eros was discovered at anunfavorable opposition, which occurred August 14, 1898 at a distance of0.74 AU, one day after discovery. The next opposition after discovery wason November 11, 1900 at a moderate distance of 0.32 AU, but Eros stayedfarther away until the favorable opposition of February 27, 1931 at 0.17 AU.The next favorable opposition was December 4, 1937 at 0.22 AU. Good oppositions occur in pairs, 7 years apart, at intervals of 37 or 44 years.The missed opposition of 1894 was closely repeated on January 13, 1975 at0.15 AU, the closest one observed so far.

Brightness and brightness variations
Eros at its brightest (a perihelion opposition) is about magnitude 7.2, visible to the unaided eye under dark skies to those with good eyesight, and brighter than any other asteroid except perhaps the first 4 or 5 discovered. The orbit of Eros is so eccentric that at the most unfavorable opposition, 0.77 AU, the magnitude of Eros would only be 10.8, and it would take good sized binoculars or a small telescope to see it. At its most unfavorable of all, at aphelion on the far side of the sun, just the opposite of opposition, it would be magnitude 13.5 at its brightest and 15 at its faintest. It would take a pretty big telescope (a mirror or lens larger than 12 inches) just to see it under very dark skies, but it would be close to the sun so never out of twilight.

The brightness of Eros varies with a period of about 5.3 hours. The amount of variation is not constant but ranges from almost nothing to about 1.5 magnitudes, depending where Eros and Earth are in their orbits. The brightness changes were early recognized as due to its rotation once every 5 hours 16 minutes, its elongated shape, and highly inclined equator (that is, its pole is tipped over quite far). When Eros' pole faces toward the earth the light variations are at a minimum since the cross-sectional area doesn't change. When the earth is in the plane of Eros' equator the light variations are at a maximum. This variation in the amplitude of the light curve was used in the past to determine which way the rotation pole of Eros is pointing. Later NEAR could watch the actual rotation as it flew by and after allowing for the motion of the spacecraft could determine the pole direction. The table below gives the increasingly accurate values.

Rotation pole estimates:

Date	Right Ascension	Declination
Pre-1975	0h	+31°
1975 data	0h 40m	+16°
1998 NEAR	0h 45m ± 16m	+20.5° ± 4°
1999 NEAR	1h 02m ± 15m	+16.4° ± 1.8°
2000 NEAR	0h 45m 29s ± 12s	+17.219° ± 0.05°

Early size and shape estimates
The light variations not only give information on the rotation poleorientation, but also give a fairly good idea of the overall shape.A 1937 estimate by Watson (not likely the same Watson that left moneyin his will to compute orbits for his asteroids) found that the brightnessvariations could be accounted for by assuming Eros had the shape of a cylinder22 miles long and 7 miles in diameter and rotating about an axis at rightangles to the long axis. A 1938 estimate by Roach and Stoddard found anellipsoid 22 miles long, 10 miles wide, and 5 miles thick, rotating aboutthe shortest axis. The 1945 astronomy book listing these estimates went onto state "The numerical values are rough, and Eros may be much more irregularin shape."The images from the NEAR spacecraft proved that Eros was indeed much moreirregular in shape, but also proved the early size estimates to be quitegood. NEAR gives a size for Eros of 22 x 8 x 8 miles, in very goodagreement with the past estimates.Flyby imagesandflyby images with the shape model show the irregular shape of Erosas imaged by NEAR.

The Eros close approach of 1930/1931 had a minimum distance of 0.174 AU which occured about Jan 30, 1931. Sometime during February two observersreported that, using a 26.5 inch telescope, they could detect an elongated image for Eros and see it rotate with the expected time period as indicatedby the light curve. This is a very interesting claim, could they possiblyhave detected the elongated shape of Eros by direct observation throughthat size telescope? A computer simulation of telescopic views of Erosallows that story to be investigated in more detail inAppendix A. There is even a simulated view of what the HubbleSpace telescope would see, also a discussion of telescope resolution.