Convex optimization is becoming increasingly popular as a prominent candidate for onboard guidance, because
of the availability of high computational capacity onboard computers. To demonstrate the application of the convex
optimization, low-thrust orbit transfer problem is solved using convex optimization. The equations of motion of the
orbit transfer are a coupled non-linear, but convex optimization requires constraints to be linear. So, the problem
is expressed in Second Order Cone Programming. In this process the equations of motion are linearized and
control constraints are convexified. Mission time is taken as the objective function. Three type of discretization are
studied-trapezoidal discretization, pseudospectral and multi-segment pseudospectral discretization. The problem
is solved sequentially to obtain global minimum. The results of three discretization schemes are compared. The
work is extended to adoptive multi-segment pseudospectral discretization to capture shape changes in control. The
scheme has to be implemented to aerodynamic controls. Combined guidance and control problem has to be solved
using the above schemes.