Question

At time t0 (relative to perigee passage), the position r and velocity v of a satellite in the geocentric equatorial frame are

r=−5,000I −8,000J −2,100 K km,
v=−4 I +3.5 J −3 K km/s.
Find r and v at time t0 + 50 min.

Answer 1

The question is about determining the position and velocity of a satellite at a specific time after its initial starting point and requires knowledge of classical and celestial mechanics. Additionally, a separate part of the problem involves finding a satellite's speed at perigee using the conservation of energy and given parameters for its orbit.

Step-by-step explanation:

The student's question deals with orbital mechanics, specifically finding the position and velocity of a satellite after a certain period from a provided initial condition. To determine the satellite's new position and velocity, one must use the principles of classical mechanics and celestial mechanics to project the motion of the satellite in orbit around Earth based on the initial conditions given. The solution to this problem involves solving the two-body problem or using numerical methods to update the satellite's position and velocity considering the gravitational influence of Earth.

To find the speed of a satellite at perigee when given its speed at apogee, one would use the conservation of energy for an elliptical orbit. The specific mechanical energy (sum of kinetic and potential energy) must be the same at any two points along the orbit. One can calculate the speed at either perigee or apogee using this conservation law and the provided data.