This is some exceedingly nerdy shit about the amount of rocket power necessary to move the earth to account for a steadily heating sun.
I'm drunk.
It would blind you instantly, kill you, and probably end all life on the planet, so maybe what it looks like is less important than ya' might think. So earth receives about 1386 watts per square meter under the sun at full brightness. Let's assume, (Although it's a bad assumption) that exactly half the earth gets that at full blast each day. The math of that is: 1,368 * (SurfaceAreaOfEarth/2) = 0.1346796 terawatts Cool. So each day earth receives nearly 1/5th of a terawatt from the sun. In order to be able to see the output of our 68-million-terawatt rocket, we have to assume it's not 100% efficient - If it were, no photons from it would end up striking the object we're trying to move. (AKA "The Earth") Assuming less than 100% efficiency is usually good practice anyway. So let's assume an efficiency of 99.9%. That seems pretty good, right? So 1/10th of 1% of the output of the rocket is going to strike the earth. I wonder how its brightness would compare to that of the noonday sun? Let's assume it strikes half the planet evenly again, just to make out math easier. 68,000,000 / (SurfaceAreaOfEarth/2) = 690,705,942 watts. Per square meter. 500,000 times the brightness of the sun. Ok, so maybe that's not all bad. I mean, sure, it's going to blind us all instantly. But it's not like it's going to cook us alive, right? Right? Well, let's assume, for the sake of ballpark estimation, that is has the same spectral characteristics as sunlight. That means about 50% of its output is going to be in the infrared. Due to my day job, I happen to have the energy required to heat a meter cube of water right here. Assuming the average water temperature was 18C (~64F) a cubic meter of water would boil away in less than a second. You are much warmer than that, and much smaller than that - You wouldn't last nearly as long. Ok, so maybe 99.9% efficiency is too low. Maybe we need to design our rocket a little better. How does 99.999999% efficient sound? That's one photon in each million striking earth! Well, let's do the math: (68000000 / (AreaOfEarth/2)) * 0.00000001 = 6907 watts per square meter. Hey, that's only five time the brightness of the midday sun! We're blind, but not instantly dead! I mean, it's still going to kill us all eventually. It's still dumping enough spare energy to boil about a cubic meter of water every day. I doubt it'd actually boil off much water - Most of the extra heat is going to get spread around the volume of the planet more rapidly than it comes in. But with global climate change, we're worried about a few degrees on average over a century or so... This change would produce far, far worse effects over a far shorter time frame. It's really more of a doomsday device than a way to save the earth. Cheers! EDIT: I completely failed at math here, but corrected myself in the comments. Turns out the rumors of earth's demise were greatly exaggerated!
Yay math! For the record, "giant rocket thruster burning for millions of years" seemed like a pretty stupid solution to a pretty predictable problem. But I dug the geeky nerdy giant number-ness of it. Thus, your answer is awesome. And while I'm right there with ya on the whole "death ray" aspect of it, and am not going to quibble about the orders of magnitude of doom projected, I do think there are some errors on your math. So let's presume that 1368 W/m^2 falls on the earth. That's an "at noon" number for the sun directly overhead. However, when it's noon in New York it's sunset in London and sunrise in Alaska - total energy does not fall on the surface of the earth uniformly, but rather proportionally. Our actual number, then, is not 68e6/(AreaOfEarth/2) but 68e6/piRadiusOfEarth^2) = 1.75e14 W. Whack 12 digits off that and you've got 175 terawatts hitting the earth at any given time. You get .13 terawatts. I get 175 terawatts. Actually, that is* four orders of magnitude. Do me a solid and double-check my math, wouldja? I gotta get back to work.
Oh dear... My brilliant post was actually pretty darn stupid. I had managed to grab a completely erroneous figure for the surface area of the earth - I didn't check my units, and used square miles instead of square meters. You're absolutely right about light falling on the surface of the earth proportionally, and thus you're absolutely right about that being the correct way to math this all out. First off, let's correct my own math, accounting for the new, proper usage of units. Keep in mind that all of this is wrong, due to light falling proportionally. Wattage supplied to the earth by the sun: 1368 * ((5.101 * 10^14) / 2) watts = 348,908.4 terawatts 99.9% efficiency spillover: 68,000,000 / ((5.101 * 10^14)/2) * 0.001 = 266 watts. Time to boil cube of water: N/A 99.999999% spillover: N/A Ok! Now let's do the math while taking into consideration Klein's point about the proportionality of light falling on earth: Wattage supplied to the earth by the sun: 1368 * (3.14159265 * 6378100^2) watts = 174,831.071 terawatts 99.9% efficiency spillover: 68000000 / (3.14159265 * 6378100^2)*0.001 = 532 watts Wow, what a difference! 532 extra watts, while over 1/3rd as bright as the noonday sun, definitely won't blind you instantly, and definitely wouldn't boil you or any water nearby! Your question about what it would look like is entirely valid, and I can't give you an answer better than "bright." It would probably still kill us all, eventually - Assuming it runs day and night, it'd add the equivalent of 1064 extra watts of daylight to every square meter on earth. My knowledge of climate suggests to me that nearly doubling the amount of heat supplied to the earth would be "bad" - Basically defeating the whole purpose of installing the giant light death beam in the first place. Another fun thought experiment would be to imagine what would happen if you pointed this "engine" at another, earth sized planet. 68000000 / (3.14159265 * 6378100^2)*0.999 = 531,547 watts per square meter. Assuming half of it is infrared, that's enough energy to boil everything on the surface of the planet in less than a half hour, even assuming an average starting temperature of 0C/32F. (Again using some mathematics from my game) While I suppose it makes an acceptable engine, it makes a truly terrifying weapon. Anyway, I guess this all just goes to show you - Don't instantly believe the confident guy, particularly when he starts spouting math! Check his claims out and see if they hold water. Cheers!
A couple points:
1) Just want to make perfectly clear you know I'm not Robert Zubrin. because while that would be dope it just ain't so. 2) Your 532W number is presuming 6 nines of efficiency. Reality begs to differ. I think we're still pretty squarely in "holy shit death ray" territory, particularly considering some process or other needs to turn mass into photons and it's going to be terrifying. We're going from (Niagara Falls is 2400 metric tons per second) To ...at which point I don't even care where it's pointed - the engine of doom necessary to drive the conversion scares the shit out of me. I'm almost certain I've seen this movie...Your question about what it would look like is entirely valid, and I can't give you an answer better than "bright."
about 3,780 metric tons per second, equivalent to a modest river 120 meters wide by 30 meters deep, following along at a leisurely 1 meter per second
an exhaust velocity of 60,000 meters per second
Another fun thought experiment would be to imagine what would happen if you pointed this "engine" at another, earth sized planet.
