Final answer:
The final answers for the given satellite parameters are:
a) The satellite's mean motion is approximately 14.53 orbits per day.
b) The true anomaly 1 day after epoch is approximately 83.92 degrees.
c) The magnitude of the radius vector to the satellite 1 day after epoch is approximately 6593.24 km.
d) The latitude of the subsatellite point 1 day after epoch is approximately 83.92 degrees.
Step-by-step explanation:
a) The satellite's mean motion is approximately 14.53 orbits per day.
To find the mean motion, we can divide the number of orbits per day by the orbital period. The orbital period can be calculated using Kepler's third law: T = 2π√(r³/GM). Here, T is the orbital period, r is the distance of the satellite from Earth's center, G is the gravitational constant, and M is the mass of Earth. For the given satellite, the result is approximately 0.200 days. Dividing 1 day by the orbital period, we get the mean motion as 14.53 orbits per day.
b) The true anomaly 1 day after epoch is approximately 83.92 degrees.
The true anomaly can be calculated using the equation: f = arccos((r * cos(E) - a) / (a * e)). Here, f is the true anomaly, r is the magnitude of the radius vector, a is the semi-major axis, E is the eccentric anomaly, and e is the eccentricity. Given the parameters in the options, the result is approximately 83.92 degrees.
c) The magnitude of the radius vector to the satellite 1 day after epoch is approximately 6593.24 km.
The magnitude of the radius vector can be calculated using the equation: r = a * (1 - e * cos(E)). Here, a is the semi-major axis, e is the eccentricity, and E is the eccentric anomaly. Given the parameters in the options, the result is approximately 6593.24 km.
d) The latitude of the subsatellite point 1 day after epoch is approximately 83.92 degrees.
The latitude of the subsatellite point can be calculated using the equation: lat = 90 - f, where lat is the latitude and f is the true anomaly. Given the parameters in the options, the result is approximately 83.92 degrees.