Hi again all. Today we are going to try to find Mars. This is going to be the beginning of an interesting exercise and it may be a bit advanced for the average reader but I will try to make it as simple as possible. At the moment we have:
Mercury = 12 units (exactly)
Venus = √505 or 22.47221
and Earth = 31 units (exactly)
What will Mars equal ?
The diagram I have started has some unusual properties which we will discover later but for now let's do another one of those right angled triangle calculations. This time we are going to use the distance from The Sun to Mercury added to the distance from The Sun to Venus. This gives us 12 (Mercury distance) plus √505 or 22.47221 (Venus distance) and we get 34.47220505. This will be our "B" side. Our "A" side will be 19 units so we will have this configuration: Our "B side is in red and our "A" side is in baby blue.
So our long side is remembering our formula of c = √a² + b² or C = √34.47220505² + 19² so doing the math we find that our C side is equal to √1549.33292130186 or 39.361566550403727100264412305514. Forgive the long number here but it is imperative to show the accuracy of my next point. Here is the diagram:
Okay now it is back to NASA for the correct distance to Mars. Checking their website (NASA's) we find that the semi major axis (remember just the average of furthest and closest) of Mars is equal to 227,939,100 km. Now a by product of this diagram is a very interesting relationship. We find that if we take 5/6ths of Mercury's inches or 10 inches we find this:
Mars is 227,939,100 km
Mercury is 57,909,050 km
The ratio ( or the number of times Mercury's distance can be divided into Mars distance) is 3.9361567837842272
And now if we divide 10 (our new distance for Mercury) and divide it into our pink line above of 39.3615665504037271 we get 3.93615665504037271
On checking for the accuracy of this we find this:
3.9361567837842272 / 3.93615665504037271 = 0.999999967 or 33 billionths or a virtual match !
Okay but what can we find still using Mercury as 12 inches. Well really the only thing I could come up with to find a close match was to take the distance from The Sun to Earth or 31 inches and add 51 divided by Pi to it. Why it works I don't know at the moment but we really are just teaching Grade 3 here. So 51 / Pi = 16.2338042 and if we add this to Earth or 31 inches we get 47.2338042 inches. if we divide this by our Mercury base of 12 we get 47.2338042/ 12 or 3.936150349614444. since we already know what it should be from above (The ratio ( or the number of times Mercury's distance can be divided into Mars distance) is 3.9361567837842272) we get a ratio or accuracy rating of:
3.936150349614444 / 3.9361567837842272 = 0.99999837 or 1.7 millionths ! So now we have the four inner planets easily drawn and easily remembered. They are as follows:
Mercury = 12 units or inches
Venus = √505 units or inches
Earth = 31 units or inches
Mars = Earth + 51/Pi or 31 + 16.2338042 or 47.2338042 units or inches
And we arrive at this image:
I hope this has made it easy for you and you should now be able to remember and draw our solar system with no trouble at all.
But this diagram shows us so much more and this we will discuss in our next posting.