When I was a Christian I was also a skeptic. Now, I thought I was open-minded enough, but when it actually came to crunching numbers and finding out for myself, I was more than willing to just draw my own conclusions and leave it at that. After all, I had the Bible ~ honestly, what else did I need?
I hope to explore some of the answers I’ve found and some of the answers I’ve had to review, for that matter. First up? How in the world do scientists claim to know that stars are ‘billions of light years away?’. How could they possibly know that? I didn’t think they were wrong, per se, but at the same time, I had no idea how they got those numbers – just seemed a little far-fetched.
My own reluctance to really tracking down the information at the time is in no way meant to reflect on any individual Christian or Theists in general. This is presented as my own ‘mea culpa‘.
But first – as an aside and a little bit of fun:)
With Distance and the angular size of an object in arc seconds we can determine the size of things.. ya know, like other planets and stars. How cool is that??!?
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Small-Angle formula
D = Linear Size of an object
α = angular size of the object, in arcsec
d = distance to the object (kilometers)
But what is “206,265”? – This is the number of arcseconds in a complete circle (360°/2π)
But what is 2π? – This is the ratio of the circumference of a circle to that circle’s radius.
But what is π? π = 3.14 and represents the ratio of a circles circumference to its diameter.
Diameter = a straight line segment that passes through the center of a circle and whose endpoints are on the circle.
So, the Circumference of a circle is derived from:
- 2r or 2 times the radius of a circle equals the diameter of a circle.
- C = πd which means that the circumference of a circle is derived from the diameter times π (3.14).
TEST IT OUT: if you have a circle with a radius of 2 inches, what is the circumference of that circle?
2 = radius. 2r = D x π = C. = 2(2) = 4(D) x π = C =
4 x 3.14 = 12.56(C)
But what does this mean in relation to 2π?
Remember, this is the ratio between the circumference of a circle and the circle’s radius. If our circumference is 12.56 and we know the radius is 2, then the ratio between these two figures, whatever they happen to be, will always be 2π (6.28).
How do we test this? Well what does ratio mean? It means the relationship between two numbers of the same kind. In other words, the relationship between a circle’s circumference and a circle’s diameter will always find expression with 2π.
What exactly is 2π? It is 2 times 3.14 = 6.28
Ok, so what is our circumference (12.56) divided by our radius (2)? It is 6.28.
Let’s try another? Find the Circumference of r if r = 18.
R -> D = 2R, 2(18) = 36 diameter
Circumference = πd, C = π(36) = 113.04
Ok, so what is our circumference (113.04) divided by our radius (18)? It is 6.28.
And what is 2π? = 2(3.14) = 6.28
Now back to the Small-Angle formula:
States that the (D) linear size of an object can be derived by dividing the (α) angular size of an object times the (d) distance of the object by 206,265 (or the total number of arcseconds in a complete circle).
By the way, linear size refers to the actual size of an object in relation to the (α) angular size. As an object moves further away, the larger it must be to fill the same (α) angular size. Hold up your thumb to cover up a car that is driving away from you. At first, the car appears much larger in relation to your thumb (α) angular size – but as the car moves away, it appears to be smaller and smaller until your thumb completely covers it up. If the car was ten times further away it would have to ‘grow’ very large to reach the same linear size it held when it was near enough to be exactly covered up by your thumb. (Hope that helps).
One more note on 206,265 before we take this baby out for a test drive. Since we are using arc seconds in our formula, we must express α (angular size) in arc seconds as well. So let’s have some fun.
IMAGINE.. we can determine the size of anything (Linear size) so long as we have two bits of information: (α) angular size and (d) distance to the object. I find that pretty remarkable. So how big, exactly is Jupiter?
Jupiter December 11, 2006
D = ?
(α) angular size = 31.2 arc seconds
d (distance) = 944,000,000 km
= = 142,791.06km
YAY!
What is the diameter of Mars? Aug 27, 2003
55.76 million km
25.11 arc seconds
This IS fun and very interesting, but I admit, it begs a question.. how do we know the distances? If we don’t have a solid way of determining the distances, then the small-angle formula is useless to determine the size of far away objects?
Hopefully, I’ll be dealing with that soon so stay tuned!
Dropping all Pretense 