NOTE: Wherever applicable, you may use μ = 398600 km³s-2 and Re = 6378 km. Problem 1 A spacecraft in a prograde Earth orbit passed periapsis exactly 28.5 hours ago with a specific angular momentum of 81574.30 km²s-2. The spacecraft will reach apoapsis in exactly 7.5 hours. a. Compute the eccentricity, e.
Given that:
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Specific angular momentum (h): The angular momentum per unit mass of an object in orbit.
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Eccentricity (e): A measure of the shape of an elliptical orbit, where e = 0 corresponds to a circular orbit and e = 1 corresponds to a parabolic orbit.
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Periapsis: The point in an elliptical orbit that is closest to the central body.
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Apoapsis: The point in an elliptical orbit that is furthest from the central body.
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Time of flight (T): The amount of time an object takes to travel from one point in its orbit to another.
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Semi-major axis (a): The average of the periapsis and apoapsis distances in an elliptical orbit.
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Average velocity (v_avg): The average speed of an object over its entire orbit.
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Average radial distance (r_avg): The average radial distance from the central body of an object in its orbit.
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Gravitational parameter (μ): A measure of the strength of a central body's gravitational pull.
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Radius of Earth (R): The distance from the center of the Earth to its surface.
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