A spacecraft of mass m moves around the Earth (which we consider stationary) at elliptical orbit with eccentricity e=0.5 and major semi-axis a. At the moment t=0 the boat passes the pericenter of its orbit with speed uo. a) How much should we increase the measure of the boat's speed in relation to uo so that its trajectory becomes parabolic? b) On the parabolic trajectory, at what distance, in relation to the initial one, will where the boat is when its speed again becomes equal to uo? c) What will be the angular momentum of the boat with respect to the Earth in the above distance?

A spacecraft of mass m moves around the Earth (which we consider stationary) at elliptical orbit with eccentricity e=0.5 and major semi-axis a. At the moment t=0 the boat passes the pericenter of its orbit with speed uo. a) How much should we increase the measure of the boat's speed in relation to uo so that its trajectory becomes parabolic? b) On the parabolic trajectory, at what distance, in relation to the initial one, will where the boat is when its speed again becomes equal to uo? c) What will be the angular momentum of the boat with respect to the Earth in the above distance?

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

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Section: Chapter Questions

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Conservation of Energy

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Question

8
A spacecraft of mass m moves around the Earth (which we consider stationary) at elliptical orbit
with eccentricity e=0.5 and major semi-axis a. At the moment t=0 the boat passes the pericenter
of its orbit with speed uo.
a) How much should we increase the measure of the boat's speed in relation to uo so that its
trajectory becomes parabolic?
b) On the parabolic trajectory, at what distance, in relation to the initial one, will where the boat is
when its speed again becomes equal to uo?
c) What will be the angular momentum of the boat with respect to the Earth in the above distance?

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Step 3: c) Find the angular momentum of the boat with respect to the Earth:

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