I got ##F=0.3849 \cdot F_{0}## and the approach from my first post gave me formula of:
$$\dot{R} = \frac {2 \cdot 0.3849 \cdot F_{0} AR^2_{0} v} {GMm} \approx 3.5 \frac m s$$
With canted at an angle sail I have:
The formula for F:
$$F = F_{0} \cdot cos^2(\alpha),$$
tangential component:
$$F_{t} = F_{0} \cdot cos^2(\alpha) \cdot sin(\alpha)$$
Now I find for what ##\alpha## the ##cos^2(\alpha) \cdot sin(\alpha)## is maximum then calculate the rate of potential energy...
There was a hint in the problem:
"Maximize the power transferred to the spacecraft by radiation pressure."
I also assumed that the sail always stays perpendicular to the radius.
Due to radiation pressure, force is exerted on the sail.
I wrongly assumed that total energy at ##R## will be of form ##E_{total} = - \frac {GMm} {2R}##. With solar sail the orbit will no longer be a circle. I will try to solve EOM:
$$m \frac {d^2R} {dt^2} = -F_{G} + F_{S},$$
then get the radial component of velocity, that should be it.
In order to change the radius, additional energy is required, the total energy of mass m on a circular orbit is given by:
$$E_{total} = - \frac {GMm} {2R},$$
The change in energy between orbits ##R## and ##R_{0}## is:
$$\Delta E_{total} = \frac {GMm} {2} \cdot \left( \frac 1 R_{0} - \frac 1 R...
Some time after my PhD I decided to study physics (again) on my own and with my own (maybe bit slow) pace. I do not work in the field, changed to IT but I kept physics as my hobby. The self study really brings me joy, can take it slow, rethink with no rush on terms, exams, etc. Currently, trying...