$12.(16$ points$)$ The cruel crew of the Tom Osborne has marooned you on the small, isolated, boring, desolate, completely useless chunk of rock called Awoi. Awoi is a sphere $500$ m in radius and has a mean density of $2\mathrm{.}3$ g cm$3.$ You have managed to acquire a sphere, with an albedo of $0\mathrm{.}6,$ radius of $1\mathrm{.}5$ cm$,$ and a mass of $32\mathrm{.}0$ g$,$ that contains the technical readout of the Osborne$$s unmatched offensive and defensive capabilities, and you hurl it at an initial velocity of $22$ m s$1$ in the general direction of Star Fleet command; you also give the sphere a rotation period of $0\mathrm{.}06$ s$.$ What will be the final velocity of the sphere?

Shortly after sending the sphere on its way, you remember that you have hidden an Osborne blaster in your suit. This laser$-$like device is powered by a radioactive decay process whose half$-$life is $15\mathrm{.}6$ years. By firing the blaster at the sphere $($on stun, of course$),$ you use the radiation pressure in the beam to accelerate the sphere. The power of the beam is proportional to the number of atoms decaying per unit time; when the blaster is first fired $(15$ minutes after throwing the sphere$)$ the power is $6\mathrm{.}51012$ erg s$1.$ The wavelength of the radiation is exactly $6564\mathrm{.}6563$A$.$ The beam of the blaster does not diverge $($i$.$e$.,$ does not spread out with distance$),$ and assume that all reflected photons are sent back in the direction of the blaster.

What is the maximum speed that the sphere acquires? What is the temperature of the sphere after one year? $($Ignore Doppler$/$relativistic effects.$)$