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A spaceship is in a circular orbit of radius r 0 about a
Chapter 13, Problem 58P(choose chapter or problem)
Problem 58P
A spaceship is in a circular orbit of radius r 0 about a planet of mass M. A brief but intense firing of its engine in the forward direction decreases the spaceship’s speed by 50%. This causes the spaceship to move into an elliptical orbit.
a. What is the spaceship’s new speed, just after the rocket burn is complete, in terms of M, G, and r 0 ?
b. In terms of r 0, what are the spaceship’s maximum and minimum distances from the planet in its new orbit?
Questions & Answers
QUESTION:
Problem 58P
A spaceship is in a circular orbit of radius r 0 about a planet of mass M. A brief but intense firing of its engine in the forward direction decreases the spaceship’s speed by 50%. This causes the spaceship to move into an elliptical orbit.
a. What is the spaceship’s new speed, just after the rocket burn is complete, in terms of M, G, and r 0 ?
b. In terms of r 0, what are the spaceship’s maximum and minimum distances from the planet in its new orbit?
ANSWER:
Step 1 of 3
Here we have to find the new speed of the spaceship, when the engine shuts down.
Before, the orbit of the spaceship was circular with a radius of .
Later on, after firing the rocket in the opposite direction of motion, the orbit became elliptical with a semi-major axis of length .
While in the circular orbit, the gravitational equation and the centripetal force equation were related by,
--------------(1)
Later, the speed became half of the previous speed.
So,
So, the new velocity will be .