We present the ability of small telescopes in solving the orbits of bright asteroids. Where we used observations of a 5-inch apochromatic refractor telescope to solve the orbits of some asteroids. The telescope is located in Al-Khatim Observatory in the desert of Abu Dhabi in United Arab Emirates. The code of the observatory "MPC Code" is M44. In order to test the accuracy of our observations, we used two asteroids with solved orbits published in the Minor Planet Center website based on thousands of observations. These are 1036 Ganymed from Amor group and 99942 Apophis from Aten and PHA groups. The results show a great match between the orbital element sets of both asteroids. The maximum errors were 0.2% and 0.1% for Ganymed and Apophis, respectively. As for the equatorial coordinates generated by both sets, we found that the difference for Apophis is less than one arc minute, and for Ganymed is less than 2 arcseconds. Thus, we conclude that a small telescope with good guiding accuracy can be used to obtain very accurate orbital elements for bright asteroids.