Dimensions of the earth

[TheBigDog]

OK, I have been thinking about this for a while now, and I have finally decided to do it.

 

I am going to do a project with the kids to calculate the diameter of the earth by experimentation or observation. I know that in ancient times various people found ways to calculate the dimensions of the earth with varying degrees of accuracy. So I plan on trying it out for myself. But I am giving myself some rules...

 

• I cannot use a computer or a calculator :hihi:
  
• I need to take any measurements manually :)
  
• I cannot use information that I cannot observe naturally or through experimentation :)
  
• I am not going to use any clocks unless I build them myself (probably not going to happen) :D
  

I will document the process with pictures and post them here on Hypography so that others can try and duplicate or improve upon my results. If someone else tries this as well I will try to duplicate their experiment as well.

 

Stand by for progress reports. Now to figure out how to do this...

 

Bill

[Tormod]

Can't wait! Excellent initiative.

[Turtle]

Stand by for progress reports. Now to figure out how to do this...

 

Bill

 

I have an experiment in mind for this- after I couldn't get it out o' my head last night.:eek: :cup: :confused: I need to make some drawings & think it through before posting it, plus I don't want to taint your angle BigDog. Great idea!:confused:

[TheBigDog]

The game is afoot! I have my design planted firmly in my head, and the wood in the garage to build my measuring device. I have taken some hints from history as well as from Hypography in designing my experiment. My method will be similar to what the Greeks did in measuring shadow of pillars. But I hope to impove upon the method enough so that I can take the readings much closer together.

 

Inspiration has come from Pyrotex and his method of finding flaws in telescope mirrors, and from Gallileo's use of inclined planes to slow gravity to make it more observable. (How's that for good company Pyro?)

 

Here is how it will work...

 

I will have a level table. I will insure it is level using pendulums that hang from the edge on two planes 90 degrees from each other. This table will be very secure because on it will be my measurement equipment. This device will rely on the table being level for a great deal of its accuracy. It will have a row of boards that will be leaning at an angle that approzimates the sun's angle at it's highest point. Each will be at a slightly different angle. At the top of each board will be dowel that sticks out 1 cm. There will be a line extending straight down each board from each dowel. As the sun moves across the sky I will rotate the device so the shadows of the dowels stay centered on the line of each board. I will mark the shadow lengths until they have reached their shortest point. This will be the highest point in the sky of the sun. Then using the known angle of each board I will use the shadow length to find the angle to the sun. Because I am doing these at a low angle I will get longer shadows and be able to measure smaller distances. Using the readings from the several boards I will can get a range of readings to minimize error. After taking these readings from day one I will pace off to where I will repeat the process on day two. I will then go back to the location from day one and repeat and then back to day two and repeat. By doing it four times on consecutive days I can account for daily variation in angle. After having the four readings I will begin the task of calculating the dimensions of the earth. I will do all of this within easy walking distance from the house.

 

I will not use any clocks and I will either pace the distance between the readings, or use some other method of measuring. Maybe triangulation like a surveyor? Hmmm....

 

Anyway, I will post some pictures as I begin building all of this. Probably be next week as I will be on vacation from work. I will document the whole thing here. If anyone wants to try it themselves, or just use my readings to see what answers you get, you are more than welcome to play along.

 

Here is where the experiment will be taking place...

 

I will be taking the first readings up by the lake. Then the second readings probably in the church parking lot at the south end of the picture. Before I settle on this I will make sure that it fits with my experiment. It I do not have access at the correct distance on the correct heading I will need to move the experiment to more open space.

 

Bill

[Jay-qu]

sounds good! let us know how it goes :shrug: and how close your values are

[ronthepon]

Mind if I make a suggeston, TheBigDog?

 

Create a very convinient unit for yourself.

Take a cylinder for instance and let it's circumference be the unit.

Then use this unit in all your calculations.

 

Because I think that you wish to do this right from the fundementals.

[UncleAl]

Plumb line for true vertical.

Pendulum or clepsydra for measuring time interval.

Compass and straightedge (stretched sting) to construct right angles and make proportionate measures.

Lake for geoid surface.

Calibrated straight pole (Euclid)

Narrow angle of view telescope (grind the lenses if you must - strong concave, weak convex)

Firecracker.

 

Measure apparent height of a calibrated pole set vertically at reference equilibrium height vs. water surface several miles away from the telescope mounted exactly horizontal (plumb line plus right angle) at a known height above the water surface. The lake assures you are on the geoid for the entire path. You now know the drop/run or curvature of the circle (assuming a spherical planet overall) hence its radius if you know the separation of the two points. Euclid tells you how to fit a unique circle to two known points (or a unique sphere to three).

 

Pop the firecracker at night and measure the time delay between flash and bang across the same path. That measures the distance vs. soundspeed. Do the same against a measured path to a distant wall (remember the double path for the echo) to calibrate soundspeed. Wind matters - calm conditions. About 1000 ft/sec.

 

Then, Euclid.