Asteroid satellite. While on its way to Jupiter in 1993, the Galileo spacecraft made...

Asteroid satellite. While on its way to Jupiter in 1993, the Galileo spacecraft made a flyby of asteroid Ida. Images captured of Ida (Fig. P5.66) showed that the asteroid has a tiny moon of its own, since given the name Dactyl. Measurements found Ida to be about 56 × 24 × 21 km (35 × 15 × 13 mi) in size, and Dactyl’s orbital period and radius are approximately 27 h and 95 km, respectively. From these data, determine Ida’s approximate mass and density. Hint: When calculating Ida’s centripetal acceleration and the force of gravity on Ida, it is safe to assume both Ida and Dactyl are spherical.