How do I find out the diameter of the sun with only a yard stick and knowing distance of Earth and the sun?

Question

The distance of the Earth to the Sun is about 93 million miles, or for lazy people who can't remember how many 0's are in 93 million, 93,000,000.

distance from the Earth to the Sun is 93,000,000 miles...
This is for my honors science class, and my teacher doesn't take an incorrect answer, so I need your help, please ^_^

Answer 1

Sorry, next time use metric ^_^

I'd guess you can't, practically. Depends how exact you want to be. I mean, if you're rounding to the nearest million miles, just answer that the diametre of the sun is zero.

Answer 2

As others have said, use similar triangles and it isn't safe to look at directly at the Sun. Lucky for you the Moon appears the same size in the sky as the Sun does. Sure, the Moon is really smaller than the Sun, but it is also closer, so it SEEMS the same size as the Sun. Actually, that fact is another demonstration of the power of similar triangles. You will need to find an object small enough so that it seems to be the same size as the Sun when viewed from a distance you can measure with a yard stick. Try this. Hold the yard stick up against the sky at arm's length and measure how many inches wide the Moon is. It will definitely be less than one inch. Then measure how long your arm is, or how far from your eye the yardstick is. This gives you a long thin triangle, some fraction of an inch for the base and many inches for the height. A similar triangle with a height of 93 million miles would have a base equal to the diameter of the Sun. So just convert 93 million miles to inches by multiplying by 5280 and 12, and then divide that giant number by the length of the long side of your triangle. That result will be how much bigger the triangle that goes all the way to the Sun is than your little one. Then multiply that number by the size of the small side of your triangle to get the diameter of the Sun in inches. Convert back to miles by dividing by 12 and 5280. Use a calculator if you know what is good for you!

Answer 3

Ok, seriously, It is possible to calculate the diameter of the sun. You need to use the law of similar triangles, which holds that all triangles with their three angles the same will also therefore have the same ratio of their sides. So find a pebble and measure its height and then slide it along the yardstick until its height just covers the sun's disk. Then note the distance at which the sun's apparent height matches the pebble's apparent height on your yardstick. You then have a pair of similar triangles, so the two heights will have the same ratio as the two distances. (the distance from your eye to the pebble versus the 93,000,000 miles known distance to the sun.) Then solve your ratio problem for the unkown, which will give you the actual height (or diameter) of the sun. Since it is only the ratio that you need, the units of the height of the pebble(in inches, say) must be the same as the units of its distance on the yardstick, (also in inches, I would gather) and if you are going to use miles for the distance to the sun then your solar diameter will also come out in miles, even if you used inches with your yardstick. (The units of measure cancel out when you are doing ratios.)

Answer 4

ly on the floor and point the yard stick towards the top of the sun by looking through it as you would pointing a gun. now at the tip of the yard stick, the one facing the sun and not you, measure the perpindicular distance from the tip to the level ground. use triginometry and find the angle x: look below
----- /|
--/----|
/x __|

now do this again pointing the yard stick to the bottom of the sun and measure that angle. since you know the distance from the earth to the sun, and the angle between the top and bottom of the sun, draw out the large diagram (should be 2 triangles) and you can solve for the diameter of the sun using simple triginometry. of coarse ur accuracy might be off by a few percent, but ur using a yard stick :P

Answer 5

Can't use a yard stick. How big do you think the sun appears to us? You can easily cover it with your thumb held outright.

In fact there is a standard for specifying how big things appear, and is taken as 25cm (about 10 inches for you slow to find metric Americans). Which means if you measure the size of any distant object by holding your measure 25 cm from your eye, you have a standard (yardstick). In our case we can use thumb and forefinger as a measurer (do this with the moon, as the sun will blind you, and they actually appear exactly the same size.

You will be suprised at how small the sun and moon really appear, about 2mm or 0.08 inch.

So, if the sun appears about 2mm in size measured from 25 cm, the calculation is simple with metric.

Sun is about 150 million kms away.

Therefore, since linear size drops off proportionally with distance,
the sun is

150 million x 1000 (to get to metres) x 4 (to get to 25cm)

times bigger than 2mm

= 6 * 10^11 times bigger than 2mm

If we now know how many 2mm in a kilometer and divide the result by that, the answer should pop out.

There are 1 million mm in a km, so

1,000,000 divided by 2 = 500,000.

Divide 6x10^11 by 5x10^5

= 1.25 x 10^6

The sun is 1,250,000 kilometers wide, by quick rough calculation.

Answer 6

there is no formula for this
only one person who did something like this was a greek philosopher who calculated the earths circumference by using the shadow of a stick-he did it with 98% accuracy
good luck

Answer 7

Look directly at the sun!

Answer 8

Please whoever is correct on this equation will teach others. And I think I got it wrong.

/_I 36 inches
93 mil miles

tan 30 = opp/adj
tan 30 = (36 inches)/(93000000)
tan 30 = .000000387 (x)
0.5773502 = .000000387 (x)
(x) = .5773502 / .000000387
x = 1,924,500.7 * 12 inches
x = 23,094,008 feet