Eros comes on stage, finally a useful asteroid
Discovery
On Saturday night, August 13, 1898, Eros was discovered photographically by Gustav Witt, director of the Urania Observatory in Berlin, Germany. Six hundred and seventy five miles to the southwest it was independently photographed on the same date by August H. P. Charlois from Nice, France. 1, 2 August 14th was a Sunday and the next day (15th) was a holiday, so the French planet hunter did not examine his plate until August 16th, thus losing the honor of being the discoverer or at least the codiscoverer. Within months about 20 prediscovery photographs taken at Harvard Observatory were found, covering from October 1893 to June 1896. 3
Some Terms (not rigorous definitions)
Aphelion A planet's farthest point from the sun in its orbit.
AU Astronomical Unit, the mean distance between Earth and the Sun.
Ecliptic The Sun's apparent path through the sky
Ecliptic Plane The plane of the Earth's orbit.
Opposition An object is in opposition (opposite the sun) when its celestial longitude is 180° from the sun's celestial longitude. Celestial longitude is an angle measured along the ecliptic.
Perihelion A planet's closest point to the sun in its orbit.An unusual orbit
As soon as an orbit was calculated it was clear that an unusual object had been found. All the asteroids up to that time orbited between Mars and Jupiter. Eros came inside the orbit of Mars, its mean distance of 1.458 AU was actually less than Mars' mean distance of 1.524 AU and Eros came as far in as 1.133 AU. Remember earth's mean distance is 1 AU, so Eros can get quite close. But when Eros is closest to the sun, at its perihelion, earth is also not far from its perihelion, in late January Earth is about 0.984 AU from the sun. So Eros can get as close to Earth as about 0.15 AU (14 million miles). The orbit of Eros has an eccentricity of 0.223, so it covers quite a range of distance from the sun: 1.783 AU to 1.133 AU (1.458*(1±0.233)). The orbital period of Eros is 1.7609 years. The orbit of Eros crosses the orbit of Mars, but is inclined 10° 49´ to the ecliptic plane, crossing that plane near perihelion. So it passes above or below the orbit of Mars, never coming closer than about 0.24 AU as compared to 0.15 AU for the Earth. 4 Orbits of planets and asteroids may change over long time periods, so the above values may also change but should be quite good for hundreds of years.Close approaches
Earth reaches the point in its orbit closest to Eros' perihelion about January 22 each year. If Eros is then at its perihelion point the distance from Earth will be minimum, about 14 million miles. But if Earth passes Eros (that is, Eros is in opposition) any time during January or February it is nearly as good. Favorable oppositions are somewhat rare and unfortunately a very favorable opposition occured 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 July opposition can be as far as 0.77 AU. Eros was discovered at an unfavorable opposition, which occurred August 14, 1898 at a distance of 0.74 AU, one day after discovery. The next opposition after discovery was on November 11, 1900 at a moderate distance of 0.32 AU, but Eros stayed farther 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. 5 The missed opposition of 1894 was closely repeated on January 13, 1975 at 0.15 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). 6 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:Many light curves have been measured for Eros in the past, one of the latest was made by the NEAR spacecraft itself. This light curve gives an idea of Eros' brightness variations but does not correspond to ground based light curves since Eros was viewed at a larger phase angle (a crescent phase for a more spherical body) than ever possible from earth.
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 pole orientation, but also give a fairly good idea of the overall shape. A 1937 estimate by Watson (not likely the same Watson that left money in his will to compute orbits for his asteroids) found that the brightness variations could be accounted for by assuming Eros had the shape of a cylinder 22 miles long and 7 miles in diameter and rotating about an axis at right angles to the long axis. A 1938 estimate by Roach and Stoddard found an ellipsoid 22 miles long, 10 miles wide, and 5 miles thick, rotating about the shortest axis. The 1945 astronomy book listing these estimates went on to state "The numerical values are rough, and Eros may be much more irregular in shape." 7 The images from the NEAR spacecraft proved that Eros was indeed much more irregular in shape, but also proved the early size estimates to be quite good. NEAR gives a size for Eros of 22 x 8 x 8 miles, in very good agreement with the past estimates. Flyby images and flyby images with the shape model show the irregular shape of Eros as 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 observers reported 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 indicated by the light curve. This is a very interesting claim, could they possibly have detected the elongated shape of Eros by direct observation through that size telescope? A computer simulation of telescopic views of Eros allows that story to be investigated in more detail in Appendix A. There is even a simulated view of what the Hubble Space telescope would see, also a discussion of telescope resolution.
Eros and the solar parallax
Speaking of Eros, Fred Whipple said: It is a real pleasure to find a use for an asteroid because asteroids are generally more of a nuisance than a help in astronomy.
Fred Whipple, Earth, Moon and Planets (Philadelphia: The Blakiston Company, 1941), p. 47.
We finally come to the reason why Eros was so useful to astronomers. As we have seen in the section on solar parallax, the pinpoint images of asteroids were an advantage when measuring the tiny parallax shifts in position, even though the known asteroids were farther away than Mars. Clearly, Eros, with its unusual orbit is very useful for this technique. Careful observations of Eros when used with Newton's laws of gravitation, gives a very precise orbit for Eros. But in astronomical units, not miles or kilometers. Fred Whipple has a very nice discussion of orbital precision:"By measuring the positions of the planets or asteroids and by applying Newton's law, astronomers can calculate planetary orbits about the Sun and predict future positions with high accuracy. The relative distances can be calculated with a precision equal to that of the most precise distances measured on the Earth, to about one part in a million. The surprising difficulty lies in the fact that these accurate distances are all in terms of the astronomical unit, the mean distance from the Earth to the Sun, not in terms of feet or miles. For purposes of prediction this uncertainty makes almost no difference, but no scientist relishes the use of a measuring rod with an unknown length." 8Right after Eros was discovered in 1898 astronmers recognized its usefulness in measuring the solar parallax. A 1928 book states the following: "In 1900 it came within about 47,000,000 kilometers (29 million miles) and the favorable opportunity was utilized to organize an international campaign for the determination of the distance between the earth and sun, with the result that we now know this value more exactly than ever before." 9Eros would come even closer in 1931, 26 million km (16.2 million miles), but even before that "From the strong perturbations of Eros caused by the earth, Noteboom in 1921 derived the mass of the earth, which provided a parallax of 8.799 arc seconds." 10 Note, this is a different method of finding the solar parallax, the dynamical Eros method.
"For the even more auspicious opposition of Eros in 1930-31 a great campaign of meridian and micrometer observation and photographic plates was started, in which nearly forty northern and southern observatories took part with their best equipment. The reduction took 10 years, and in 1942, during the war, Spencer Jones, then at Greenwich, published the results. It was 8.790"±0.001". Considering the extent of the collaboration, the large amount of observational data, the perfection of the methods used, the watchful elimination of sources of error, the careful discussion, we may say that another determination of the same or higher quality is not to be expected in the near future." 11 The measurements from this opposition were pushed to enough precision that the size of Eros was suspected of being a limiting factor, as tiny as it is it is still not a star-like pin point of light and that can cause some error in its position estimate.
It's not stated what is meant by "near future" but that was from a 1961 book and in 1958 radar observations of the solar system started. Radar has given the best estimates of the solar parallax ever, but independent checks on such important quantities are always desired and Eros was still an important part of the picture in a study by Jay H. Lieske of Yale University Observatory. He used 8,639 Eros observations, from prediscovery photographs of 1893 to observations from 1966. Dr. Lieske compared the observations of Eros to an ephemeris he computed taking into account perturbations from all nine principal planets. He found the mass of the earth-moon system relative to the sun was 1/328,915 with an uncertainty of ±4 in the denominator. Using this dynamical Eros method a solar parallax of 8.79402"±0.00012" was derived. The corresponding length of the astronomical unit is 149,600,400±800 km (92,957,200±500 miles). A bit of inspection shows this to be a rather incredible amount of precision. Remember that the solar parallax is the angle that the earth's radius would subtend at one astronomical unit. An error of 0.00012" corresponds to an error in earth's radius of 87 meters or 285 feet. That's less than the average height of the Coast Redwood trees in California (they average 300-350 feet (91-107 meters) in height.). Looking at it another way, if the earth's diameter is represented by a six foot tall man, then the error would be 1/8 the width of a human hair (assuming a 0.1 mm hair width). The Eros solar parallax compares very well with the value adopted by the International Astronomical Union in 1964 of 149,600,000 km. It also compares well with the present value of the radar astronomical unit which is 149,598,000 km ± 200 km, corresponding to a solar parallax of 8.79414 ± 0.00004. 12 Note the error here corresponds to less than 100 feet at the sun's distance.
In January 1975 Eros made its closest approach to Earth since its discovery. Among the many observations made of it at that time were ones made by radar. So Eros has provided three ways to find the solar parallax: trigonometric (the angular shift against the background stars as seen from different positions on earth), dynamical (using it to find the earth-moon mass and from that the solar parallax), and direct radar distance measurement.
With the solar parallax known quite well and radar being the technique of choice for its measurement, after the flyby of 1975 Eros somewhat faded from interest. That is, until the NEAR mission came along. Eros' historical importance was not a factor in its choice as the target, it was a fairly easy asteroid to reach and had enough gravity to hold a spacecraft in orbit.
Back: The Quest for the Solar Parallax Table of Contents Main Eros page
References
1 Edward A. Fath, The Elements of Astronomy (New York: McGraw-Hill, 1928), p. 169.2 The NEAR Earth Asteroid Rendezvous A Giude to the Mission, the Spacecraft, and the People. (NEAR Press Kit) (Johns Hopkins University Applied Physics Laboratory, 1998), p. 10.
3 Jean Meeus, "Eros' Closest Approach to the Earth", Sky and Telescope vol. 48, no. 4 (Oct 1974): p. 221.
4 Ibid., p. 221.
5 Henry Norris Russell, Raymond Smith Dugan, and John Quincy Stewart, Astronomy (Boston: Ginn and Company, 1945), p. 356.
6 Ibid., p. 356.
7 Ibid., p. 356, 357.
8 Fred Whipple, Earth, Moon and Planets (Philadelphia: The Blakiston Company, 1941), p. 45.
9 Edward A. Fath, The Elements of Astronomy (New York: McGraw-Hill, 1928), p. 169.
10 A. Pannekoek, A History of Astronomy (New York: Interscience Publishers, 1961), p. 347.
11 Ibid., p. 347.
12 "Solar Parallax" Britannica Online.
http://www.eb.com:180/bol/topic?eu=59856&sctn=3#s_top
[Accessed 27 May 1999]
