Explanation The spacecraft with the mass of 1.00 × 10 4 kg is moving in a circular orbit at an altitude of 500 km above the Earth’s surface. The engine is fired in a direction tangent to the orbit and the engine is at the apogee distance of 2.00 × 10 4 km measured from the Earth’s center. The radius of the Earth is 6.37 × 10 6 m and the mass of Earth is 5.98 × 10 24 kg . Write the equation for energy for elliptical orbits, E = − G M m 2 a (I) Write the equation for the major axis, 2 a = r p + r a (II) Here, a is the semi major axis, G is the gravitational constant [ G = 6.67 × 10 − 11 N ⋅ m 2 / kg 2 ] , M is the mass of ring and m is the mass of the object. Conclusion: The initial distance between the center of the Earth and the spacecraft in a circular orbit is a = ( 6.37 × 10 6 m ) + ( 50 × 10 3 m ) = 6.87 × 10 6 m . Substitute 6.67 × 10 − 11 N ⋅ m 2 / kg 2 for G , 1.00 × 10 4 kg for m , 5.98 × 10 24 kg for M and 6.87 × 10 6 m for a in equation (I) to find the value of U E i = − ( 6.67 × 10 − 11 N ⋅ m 2 / kg 2 ) ( 1

Physics for Scientists and Engineers With Modern Physics

9th Edition

ISBN: 9781133953982

Author: SERWAY, Raymond A./

Publisher: Cengage Learning

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Chapter 13, Problem 64AP

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The energy required from the fuel for the spacecraft to achieve the orbit.

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Chapter 13, Problem 63AP

Chapter 13, Problem 65AP

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