Astrophysics/Energy received by starship shields from a blue giant
Hi! In SciFi tv series Stargate SG-1 a Goa'Uld Ha'Tak vessel goes hiding into the corona of a blue giant star for 10 hours and uses its shields to block the radiation coming from the star. The shields have a diameter of around one kilometer. So could you give me an estimate on how much energy would a medium sized blue giant emit into a spherical shield of 1 kilometer in diameter when it is in its corona per second an the total of 10 hours? I know this might be a little bit hard to estimate but any estimations I'll welcome.
I'll come up with an order-of-magnitude estimate, but I'll describe my process, so you can refine it, if you'd like. Or even find an error I might have made!
A "typical" blue giant has a total luminosity of about 10^4 that of the sun, and a radius of about 8 times the sun's. Lum(sun) = 4 x 10^26 watts, so Lum(blue giant) = 4 x 10^30 watts.
r(sun) = 7 x 10^5 km, so r(blue giant) = 5.6 x 10^6 km.
Your spherical shield is 1 km in diameter, so it's surface area as seen by the star (and receiving the star's radiation) is 0.8 km^2.
Now, the hard part. You said the vessel went into the blue giant's corona. Well, many blue giants don't have a corona! That said, blue giants are a heterogeneous lot, and some might have a corona, so we'll assume this one does. And we'll assume it extends well beyond a million kilometers from the "surface". So we'll assume the vessel approached the star to within a million kilometers.
The area of a sphere at the vessel's location (the entire sphere (Dyson Sphere) would capture the star's total radiation) = 4 x pi x (6.6 x 10^6 km)^2 = 5.5 x 10^14 km^2
The fraction of total radiation received by the shield is (0.8 km^2) / (5.5 x 10^14 km^2) = 1.5 x 10^-15.
The total power received by the sphere is then (1.5 x 10^-15) x (4 x 10-^30 watts) = 6 x 10^15 watts
To find energy:
Total energy received in 10 hours = (6 x 10^15 J/s) x (10 hr) x (60 m/hr) x (60 s/m) = 2 x 10^20 J
This is approximately half of the entire annual global energy consumption.
Please check my work. Hope that helps.
Prof. James Gort