Asteroid Ida was photographed by the Galileo spacecraft in 1993,and the photograph revealed that the asteroid has a small moon,which has been named Dactyl.From the dimensions of Ida and its general features,one can estimate the mass of Ida to be 4.5 × 10¹⁶ kg,and the distance between Dactyl and Ida is approximately 90 km.Assuming a circular orbit,what would be the orbital speed of Dactyl? (G = 6.67 × 10^-11 N ∙ m²/kg²) A)5.8 m/s B)11 m/s C)2.3 m/s D)2.9 m/s E)30 m/s

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Quizplus · Accepted Answer

The orbital speed $v$ of Dactyl can be found using the formula for gravitational force and centripetal force: $v = \sqrt{\frac{GM}{r}}$, where $G = 6.67 \times 10^{-11} \, \text{N} \cdot \text{m}^2/\text{kg}^2$, $M = 4.5 \times 10^{16} \, \text{kg}$ is the mass of Ida, and $r = 90 \, \text{km} = 90,000 \, \text{m}$ is the distance between Dactyl and Ida. Plugging in the values, we get $v = \sqrt{\frac{6.67 \times 10^{-11} \times 4.5 \times 10^{16}}{90,000}} \approx 5.8 \, \text{m/s}$.

Asteroid Ida Was Photographed by the Galileo Spacecraft in 1993,and