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A satellite is initially in a circular orbit around the earth with radius ro. This initial orbit is shown in the upper left drawing. At the position marked by x in the drawing the satellite's rocket motor is fired briefly (assume instantaneously), giving the satellite an impulse in the direction of its motion (i.e. tangentially). This impulse changes the velocity of the satellite to Avg. The impulse is such that the farthest point from the earth that the satellite will reach is 2ro. : Find the initial velocity of the circular orbit. Use m for the satellite (a) mass, M for the earth's mass, G for the gravitational constant, and vo for the velocity. (b) of the satellite? Explain your answer, perhaps by saying what is wrong with all the incorrect drawings. Which of the drawings below correctly shows the subsequent path (c) factor by which the velocity must be increased so that the farthest distance from the earth will be 2rg. Use conservation of energy and angular momentum to find A, the Note: the labels in the figure below do not refer to the parts of the problem. (a) (b) (c) (d) (e)

A satellite is initially in a circular orbit around the earth with radius ro. This initial orbit is shown in the upper left drawing. At the position marked by x in the drawing the satellite's rocket motor is fired briefly (assume instantaneously), giving the satellite an impulse in the direction of its motion (i.e. tangentially). This impulse changes the velocity of the satellite to Avg. The impulse is such that the farthest point from the earth that the satellite will reach is 2ro. : Find the initial velocity of the circular orbit. Use m for the satellite (a) mass, M for the earth's mass, G for the gravitational constant, and vo for the velocity. (b) of the satellite? Explain your answer, perhaps by saying what is wrong with all the incorrect drawings. Which of the drawings below correctly shows the subsequent path (c) factor by which the velocity must be increased so that the farthest distance from the earth will be 2rg. Use conservation of energy and angular momentum to find A, the Note: the labels in the figure below do not refer to the parts of the problem. (a) (b) (c) (d) (e)

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A satellite is initially in a circular orbit around the earth with radius ro. This initial orbit is shown in the upper left drawing. At the position marked by x in the drawing the satellite's rocket motor is fired briefly (assume instantaneously), giving the satellite an impulse in the direction of its motion (i.e. tangentially). This impulse changes the velocity of the satellite to Avg. The impulse is such that the farthest point from the earth that the satellite will reach is 2ro. : Find the initial velocity of the circular orbit. Use m for the satellite (a) mass, M for the earth's mass, G for the gravitational constant, and vo for the velocity. (b) of the satellite? Explain your answer, perhaps by saying what is wrong with all the incorrect drawings. Which of the drawings below correctly shows the subsequent path (c) factor by which the velocity must be increased so that the farthest distance from the earth will be 2rg. Use conservation of energy and angular momentum to find A, the Note: the labels in the figure below do not refer to the parts of the problem. (a) (b) (c) (d) (e)
Transcribed Image Text:A satellite is initially in a circular orbit around the earth with radius ro. This initial orbit is shown in the upper left drawing. At the position marked by x in the drawing the satellite's rocket motor is fired briefly (assume instantaneously), giving the satellite an impulse in the direction of its motion (i.e. tangentially). This impulse changes the velocity of the satellite to Avg. The impulse is such that the farthest point from the earth that the satellite will reach is 2ro. : Find the initial velocity of the circular orbit. Use m for the satellite (a) mass, M for the earth's mass, G for the gravitational constant, and vo for the velocity. (b) of the satellite? Explain your answer, perhaps by saying what is wrong with all the incorrect drawings. Which of the drawings below correctly shows the subsequent path (c) factor by which the velocity must be increased so that the farthest distance from the earth will be 2rg. Use conservation of energy and angular momentum to find A, the Note: the labels in the figure below do not refer to the parts of the problem. (a) (b) (c) (d) (e)
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(a) The equation of motion of the satellite is given as,m v02r0  = GM mr02Therefore    v0  = GMR (b) Since it is said that the velocity of the satellite in the final orbit is  λv0 hence it is constant throughout the orbit therefore, the orbit must be circular, from the figures we see that the option (c) is the correct description of the orbit change because the satellite leaves the first orbit tangentially and reaches the second orbit which is also circular. In the figure (a) there is no description of the orbit transfer. Hence it is not the correct drawing, (b) In the figure (b) the final orbit is circular but it is not concentric, therefore it is not the correct drawing. (c) Figure (c) is the correct option as explained earlier. (d) and (e) are elliptical orbits and the velocity of the satellite will not he constant in the orbit, therefore the options (d) and (e) are not correct drawings.  

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