A list of notable asteroids are below:
Ceres was the first asteroid to be discovered and it is also the largest. It has not been visited by spacecraft but it has been observed by the Hubble Space Telescope. Ceres is approximately 590 miles (950 kilometers) across and was first discovered in 1801.
Vesta was the fourth asteroid to be discovered and has a diameter of 525 kilometers (326 miles) and is smaller than the state of Arizona. It rotates about its axis in 5.34 hours.
NASA/ JHU APL photo
Asteroid 433 Eros
433 Eros is the second largest known Near Earth Asteroid. It has a diameter of 16.84 km and it was discovered on August 13th, 1898 by Schreiben von Herrn G. Witt.
Its companion object Menoetius was discovered on September 22nd, 2001 by William J. Merline, Laird M. Close, N. Siegler, D. Potter, C. R. Chapman, C. Dumas, F. Menard, and D. C. Slater using the Gemini North adaptive optics telescope at Mauna Kea, Hawaii.. It's nearly as large as 617 Patroclus almost 70 miles (112 kilometers) in size.
Patroclus and Menoetius circle each other every 4.3 days at a distance of 680 kilometers. 
The largest of the near earth objects 1036 Ganymede has an estimated diameter of about 25 miles(41 kilometers).
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