How Does Mass Loss Influence Orbital Expansion?

[accalternata]

Homework Statement

How much do you expect the Earth-Sun system to expand over the 10 Gyr
main-sequence lifetime of the Sun, given that the Sun is losing mass in the form of
light? And how much
given the mass-loss rate of 3×10−14 M⊙ yr−1 associated with the solar wind?

Relevant Equations

See below

I need help with d) and e).
Currently how I've approached it is by using the fact that e=mc^2 and I can correlate this emission of light with loss of mass.

Then I can use the formulas in a) to correlate this with da/dt. I'm struggling to figure out what the rate of energy loss is though.

 

[pbuk]

I'm struggling to figure out what the rate of energy loss is though.

Have you tried the reference given in the question?