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Solved: An unmanned spacecraft is in a circular orbit
Chapter 13, Problem 63P(choose chapter or problem)
Problem 63P
An unmanned spacecraft is in a circular orbit around the moon, observing the lunar surface from an altitude of 50.0 km (see Appendix F). To the dismay of scientists on earth, an electrical fault causes an on-board thruster to fire, decreasing the speed of the spacecraft by 20.0 m/s. If nothing is done to correct its orbit, with what speed (in km/h) will the spacecraft crash into the lunar surface?
Questions & Answers
QUESTION:
Problem 63P
An unmanned spacecraft is in a circular orbit around the moon, observing the lunar surface from an altitude of 50.0 km (see Appendix F). To the dismay of scientists on earth, an electrical fault causes an on-board thruster to fire, decreasing the speed of the spacecraft by 20.0 m/s. If nothing is done to correct its orbit, with what speed (in km/h) will the spacecraft crash into the lunar surface?
ANSWER:
Solution
Step 1 of 5
In the given problem, a unmanned spacecraft of mass m is rotating around moon in a circular orbit at an altitude h=50 km with speed . Due to electrical fault in the midway, the speed decreases by 20 m/s, that is equal to
-20 m/s. We need to calculate the speed of the spacecraft into the lunar surface during the crash.
Given data,
Mass of moon, M=7.35
Radius of moon, r=1.74m
Gravitational constant, G=6.673N.
Height, h=50 km=50
Mass os spacecraft = m
To find,
Orbital speed of spacecraft, =?
Midway speed, -20 m/s
Final speed at the lunar surface,