ok these questions are sort of linked and i really hope this question belongs in this board since it does deal with astronomy
Question 1 In a scale Universe with the sun the size of a spherical grain of fine sand (diameter= 0.2 millimeters), how big a box (in cubic meters) would you need to hold all the stars in the Milky Way Galaxy. Packing efficiency of sand is a very complex problem, but assume that each grain of sand occupies 0.023 cubic millimeters.
i believe i got this one right and that the 0.2mm isn't used. here is what i got
200 billion grains of sand
Density of a grain of sand = 0.0023 mm3
200 billion x 0.0023mm3 = 460000000mm3
460000000mm3 = 0.46m3 (google.com)
The box would have to be the size of 0.46m3
ok but the next problem is tricky and I think i am really doing it wrong
Question 1b How big, in meters, would the Milky Way galaxy be in this scale universe? If the center of the Milky way was centered on Toronto, approximately where would the edge of the galaxy be? (eg, near Kitchner? Near Jupiter?).
I was told to scale the sun to a grain of sand so i have to use the 0.2mm from Question 1 to help figure this out
i really dont know if I am doing this right here is what i got
Milky Way = 100,000 light years in diameter = 9.4605284 × 1020 m
Sun’s diameter = 1,400,000 km (Taken from 100,000 light years = 946,091,000,000,000,000km
(100,000 x 9.46091E+12)
Sun’s diameter = 1,400,000 km
0.2mm
946,091,000,000,000,000km divided by 1,400,000km x 0.2=135155857142.857142
i really don't know what i did wrong here it seems that what i am doing is correct but this numer seems wrong so i am wondering if any one can help me with this question
soory again if this question does not belong in this board and in another one here
First lose the excessive precision, at least some of your data is only correct to between 2 and 3
significant digits.
Then:
c ~= 3 10^8 m/s
1 yr ~= 60*60*25*365.24 s ~=3.2 10^7 s
1 ly ~= 9.5 10^15 m
L1=10^5 ly ~=9.5 10^20 m
L2=Dia of Sun ~= 1.4 10^9 m
scalled size of Galaxy=L1/L2*0.2 ~= 13.6 10^11 = 1.36 10^12 m
RonL
For future reference, the symbol ^ means 'raised to the power of'. So yes, 10^15 means 10 'raised to the power of' 15.
The way CaptainBlack was writing the numbers is called "Scientific Notation." It's a way of writing very big or very small numbers so that it's easy to see exactly how big or small they are. For example:
312 000 000 000 000 000 000 just looks like a big number, but exactly how big is it? We can write this number in scientific notiation as:
3.12 * 10^20 ... The 10^20 means that we would take the decimal in 3.12 and move it to the right 20 spaces.
Now we can easily see that this number is 20+1 = 21 digits long, and we can start using this number in equations without too much difficulty.
c is the speed of light. CaptainBlack used this to find out how long 1 light year is in meters.
I would go more in detail, but I have to go. Hopefully someone else can finish up this explanation.