Problem 7 Page 40

To give you an example (and introduce you to the back of the book) of the small angle formula I am going to do problem 7 from your book.

Now I notice that the size of the prominence is 5 minutes of arc. The book on page 40 says to use the small angle formula I need this angle in seconds. Well every minute has 60 Seconds, so 5 minutes would be 5 times 60 (5*60) seconds or 300 seconds.

Here and over at vista I am going to write the small angle formula as AD/206,265"=LD/D

with AD being angular diameter, etc.

I know what AD is; 300s
I go to the back of the book (the back of the book is our FRIEND, you can get all sorts of things from the Appendices). I find on page 617 Properties of the Planets. Under earth I find the distance to the sun (semimajor axis, we can't make this easy can we). It is 149.6E6. E6 means ten to the 6th, just like on your calculator. This is the Distance (D).

Let's put the numbers we know in the formula:

300/206,265=LD/149.5E6 Now we solve for LD---> LD=300*149.5E6/206,265 .

ON my computers calculator here is the bottom order: 300*149.5 Exp (One button)6/206265 =

I get (with rounding): LD= 217,000 km. This is my answer. By the way usually I would hit the F-E button on my calculator and get LD=2.17e+5 km. For most of our numbers this is a better way to report. By the way e+5 is hundred-thousands, e+6 is millions, e+9 is billions, e+3 is thousands, etc

By the way, let's say I need to put a negative exponent in say 9.11e-31 (the mass of an electron), here are the key strokes:

9.11 Exp 31 +/- (which is the button under the 2 button).

You are going to be doing just this thing with just this formula for most of your problems this semester. If you need just come in to see me.

David