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Answer :
Final answer:
The minimum and maximum orbital speeds of a satellite can be calculated using Kepler's laws and Newton's law of gravitation. The minimum speed takes place at the point of the orbit farthest from Earth (apogee), while the maximum speed takes place at the point closest to Earth (perigee). Given variables in the problem (mean orbital altitude and eccentricity) are used to calculate these speeds.
Explanation:
To calculate the minimum or maximum orbital speeds of an object in space, we can use Kepler's laws of planetary motion and Newton's universal law of gravitation. Considering the satellite's specified mean orbital altitude and reported eccentricity, we can find the perigee (closest point to Earth) and apogee (farthest point from Earth) of the satellite's elliptical orbit.
Minimum orbital speed will occur at the apogee (due to conservation of angular momentum) and can be calculated using the formula v_min = sqrt(G*M_E / (r + apogee)), where G is the gravitational constant, M_E is Earth's mass, and r is Earth's radius. Some constant values include G = 6.67 x 10^-11 m^3 kg^-1 s^-2, M_E = 5.97 x 10^24 kg, r = 6.371 x 10^6 m. Please note that apogee = mean orbital altitude * (1 + eccentricity).
Maximum orbital speed will occur at the perigee and can be calculated using the formula v_max = sqrt(G*M_E / (r + perigee)), where perigee = mean orbital altitude * (1 - eccentricity).
Please note that other variables such as the satellite's mass, inclination, and the right ascension of the ascending node do not affect these calculations.
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