Concept explainers
(a)
Find the increase in speed required at point A for the satellite to achieve the escape velocity and enter a parabolic orbit.
(a)
Answer to Problem 12.104P
The increase in speed required at point A for the satellite to achieve the escape velocity and enter a parabolic orbit is
Explanation of Solution
Given information:
The altitude of circular orbit of the satellite from the surface of the earth (r) is 19,110 km.
The radius of the earth (R) is 6,370 km.
Calculation:
Find the equation of product (GM) of the constant of gravitation G and the mass M of the earth using the equation:
Substitute
Find the altitude of circular orbit of the satellite
Substitute 6,370 km for R and 19,110 km for r.
Find the velocity of satellite
Substitute
Find the escape velocity of satellite
Substitute
Find the decrease in speed
Substitute
Thus, the increase in speed required at point A for the satellite to achieve the escape velocity and enter a parabolic orbit is
(b)
Find the decrease in speed required at point A for the satellite to enter an elliptic orbit of minimum altitude 6370 km.
(b)
Answer to Problem 12.104P
The decrease in speed required at point A for the satellite to enter an elliptic orbit of minimum altitude 6,370 km is
Explanation of Solution
Calculation:
Find the radius
Find the angular momentum per unit mass h using the equation.
Substitute
Find the velocity at A
Substitute
Find the decrease
Substitute
(c)
Find the eccentricity of the elliptic orbit.
(c)
Answer to Problem 12.104P
The eccentricity of the elliptic orbit is
Explanation of Solution
Calculation:
Write the equation of angle at B.
Apply cosine on both sides.
Find the constant C using the equation:
Substitute
Substitute
Substitute
Find the eccentricity
Substitute
Thus, the eccentricity of the elliptic orbit is
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Chapter 12 Solutions
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