Another Reminder... & Physics

They definitely won't let us rest! These people... always reminding us when the deadlines are, what we have at risk. Today another presentation of what is due, what will be due, and time for us to judge whether we are already falling behind within the second week.
For one thing I know, I am sort of behind since my EE is screwed...

I suppose they might as well do this every week since it IS the last year already, and we definitely don't want to regret our actions. But can't I request that the reality check be a little less harsh? The stats they provided are really good, (which shows the admins, senoir or not, are doing lots of things... that's good!) because they showed us a breakdown of students who entered which university in Singapore, and which countries the other students went to. I am surprised that UK is more popular than America (guess it's because of the SATs)
I tried taking a picture of the slide with the said pie chart, but my phone's flash went too, and several people turned around. Well I was lucky, they were only students.

Physics... well, so before all those statistics came out on screen, it was the typical reminders about work and stuff, and I could not be bothered to listen for the umpteenth time, so I worked on solving a problem that I gave myself (physics problem that is). Here it is:

During the lesson before this lecture session, my teacher was enlightening us on how to calculate the power the Earth recieves from the sun by using the inverse square law, and then considering the earth's expose surface as a circle, to calculate the power recieved. Well, if anyone is picky, this assumption is bad (but as usual, we simplify things for our syllabus sake) The Earth may look like a circle to the sun, but since it is closer to a sphere than a circle, the center is nearer to the sun, hence an increased intensity at the middle.

So to solve it, I first tried to find the surface area of a hemisphere by integration. This allowed me to find the basic unit area that I can use to plug into the intensity formula to find power on each miniscule surface area of the Earth. Through integration, which is rather lucky, because we just learnt one of the techniques that helped me integrate that formula, I managed to arrive at a final formula to calculate the power that the Earth receives from the sun.

Now I remember our teacher was saying, "The Earth's radius is sooo small compared to the orbit radius that it would not matter!"... but WAIT! the orbit radius is based on the center of the earth! Hence EVERY part of the Earth in real situation that is recieving light from the sun is CLOSER than or at least at the orbit! Closer would mean higher intensity and hence higher power received! Hence the formula we are learning is flawed!

Checking with my GDC proved that the power that is calculated using the circle assumption is HALF! the "actual" power received using the new formula! (this is using real values of our Sun's power, Earth's mean radius, and mean orbit radius) Which is really bad as scientifically concerned. It is a whole 100% error! So TAKE THAT all you people!

Which reminds me... in Primary school, I had always faced this irritating problem of the syllabus over simplifying things, and at that time I did not have the ability to get the "real stuff". I'm definitely glad that I can do it now...

21:23 15 Jan 2009
Personal,School,Power from Sun to Earth