Astronomy 101- Asteroid 87 Sylvia and its two moons Romulus and Remus 87 Sylvia

Question

Astronomy 101- Asteroid 87 Sylvia and its two moons Romulus and Remus 87 Sylvia was the 87th minor planet to be discovered. It was first observed from the Observatory of Madras (India) on May 16, 1866, by the Astronomer Norman R. Pogson. The two moons were discovered in 2001 and 2004 Use Kepler's third law as formulated by Isaac Newton to determine the mass of asteroid 87 Sylvia. The data for the innermost moon Romulus is: S/2001(87) 1 (Romulus) Period = 3.65 days Orbital radius = 1356 km Action item 1. Estimate the mass of Sylvia. Show your units -remember to use seconds and meters in Newton's formulation. We make the assumption that the system mass derived is that of 87 Sylvia since it is 384 km across, while Romulus is only 20 km across. The gravitational constant G = 6.67 x 10-11 Nm-kg-2 all your calculation and remember to watch Msylvia + mRomulus ~ MSylvia = (4 / G) (a3 / P2)

Explanation / Answer

Third law of Kepler, the square of the orbital period of a planet is directly proportional to the cube of semi major axis of its orbit.this capture the relationship between the distance of the planet from the sun and their orbital period.

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