Orbital mechanics of impulsive launch

A method of closing a timing difference between a vehicle launched using an impulsive force and a satellite of rendezvous or a desired vehicle location, comprising applying a series of forces to the vehicle to provide a change in vehicle velocity Δv that is divided into a first Δv increment and a second Δv increment, wherein

• a. a first force of the series provides the first Δv increment and temporarily places the vehicle into a first orbit having a first orbital period that differs from an orbital period of the satellite or the desire vehicle location so as to reduce a time difference between the vehicle and the satellite or the desired vehicle location in an integer number of orbits, and
• b. a second force of the series provides the second Δv increment and is sufficient to establish the vehicle in a circular orbit with the satellite or the desired vehicle location wherein
• c. the vehicle follows a path of an elliptical trajectory having a ballistic apogee and a ballistic perigee;
• d. the first force is applied to the vehicle at the ballistic apogee to establish a second elliptical orbit having a second apogee and a second perigee, the second elliptical orbit being an ascending elliptical orbit, wherein the second perigee has an elevation equal to an elevation of the ballistic apogee, and
• e. the second force is applied when the vehicle is at the second perigee.

A method of closing a timing difference between a vehicle launched using an impulsive force and a satellite of rendezvous or a desired vehicle location, comprising applying a series of forces to the vehicle to provide a change in vehicle velocity Δv that is divided into a first Δv increment and a second Δv increment, wherein

• a. a first force of the series is applied to the vehicle during a launch trajectory which reintersects Earth and which provides the first Δv increment that temporarily places the vehicle into a first orbit having a first orbital period which differs from an orbital period of the satellite or the desired vehicle location so as to reduce a time difference between the vehicle and the satellite or the desired vehicle location in an integer number of orbits, and
• b. a second force of the series provides the second Δv increment and is sufficient to establish the vehicle in a circular orbit with the satellite or the desired vehicle location, and wherein
• c. the launch trajectory is an elliptical trajectory having a ballistic apogee and a ballistic perigee;
• d. the first force is applied to the vehicle at the ballistic apogee to establish a second elliptical orbit having a second apogee and a second perigee, the second elliptical orbit being a descending elliptical orbit, wherein the second apogee has an elevation equal to an elevation of the ballistic apogee, and
• e. the second force is applied when the vehicle is at the second apogee.