Explanation Given information: Consider the two asteroids are asteroid 1 and asteroid 2. The mass of asteroid 1 is 40 kt with speed relative to Sun is 29.9 km/s . The mass of asteroid 2 is 12 kt with speed relative to Sun is 35.5 km/s . Calculation: Determine the total mechanical energy of the asteroid 1 ( E asteroid 1 ) using the relation: E asteroid 1 = − G M S m r + 1 2 m v 2 (1) Here, G is the constant of universal gravitation with the value of 6.67 × 10 − 11 N ⋅ m 2 /kg 2 , M S is the mass of the Sun, m is the mass of 2012 DA 14 asteroid, and v is the speed relative to Sun. Refer “Appendix E” in the textbook for the Astrophysical data of Sun. The mass of the Sun is 1 .99 × 10 30 kg . The radius of the Sun is 1 .5 × 10 11 m . The mass of asteroid 1 is follows: m = 40 kt = 40 kt ( 10 6 kg 1 kt ) = 4 × 10 7 kg Substitute 6.67 × 10 − 11 N ⋅ m 2 /kg 2 for G , 1 .99 × 10 30 kg for M S , 4 × 10 7 kg for m , 1 .5 × 10 11 m for r , and 29.9 km/s for v in Equation (1). E asteroid 1 = [ − ( 6.67 × 10 − 11 N ⋅ m 2 /kg 2 ) ( 1 .99 × 10 30 kg ) ( 4 × 10 7 kg ) 1 .5 × 10 11 m + 1 2 ( 4 × 10 7 kg ) ( 29.9 km/s ) 2 ] E asteroid 1 = − 3.5395 × 10 16 + 1 2 ( 4 × 10 7 kg ) ( 29

Essential University Physics, Volume 1 and Volume 2 - With Access

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ISBN: 9780134645490

Author: Wolfson

Publisher: PEARSON

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Chapter 8, Problem 64P

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The orbit of the two asteroids.

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Chapter 8, Problem 63P

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