Determination of Earths radius with known latitude and sun travel times

[frozenguy]

Homework Statement

You and a friend decide to determine the radius of the Earth. You synchronize watches; then your friend drives 50km due west, at latitude 40°. Each of you determines the time when the Sun lies due south -- on the meridian Your friend observes the Sun to be on her meridian 140 seconds after you observe the Sun on your meridian. What is your determination for the Earth's radius?

Homework Equations

rθ=s
θ=2π(140s/86400s)

The Attempt at a Solution

With those equations I can find the radius of the latitude 40° disc section.

If I can find the height h from the center of the Earth to the center of my latitude 40 disc, I can use Pythagorean theorem to find radius of the Earth R. Is this the correct way to go about this? If so, how do I find the straight line height from center of disc to center of earth?

 

[ehild]

Think, what latitude means? Draw a picture and show the radius of the disc at latitude 40.
ehild

 

[frozenguy]

Think, what latitude means? Draw a picture and show the radius of the disc at latitude 40.
ehild

Hi thank you for responding.
I have done that. What do you want me to see? It is not the radius of the earth. It is just the radius of a flat disk.

 

[gash789]

Firstly find the radius of the Earth of your latitude by considering the quantities you have. Personally I would approach this by using ratio's you know the length of a day, the time between you and your friend and finally the distance. Once you have this radius you need to assume the Earth is spherical and translate the radius to the equator.

 

[frozenguy]

Thanks for responding.
I have the radius of the disc at lat 40.
How do I translate the radius to the equator?

 

[ehild]

I have done that. What do you want me to see? It is not the radius of the earth. It is just the radius of a flat disk.

I do not want anything from you, it is you wanting to see the solution. Make a drawing of the Earth like the one I attach. Show both the radius of Earth (R) and the radius of disk (r).
Do you know the angles of the yellow triangle? How are they related to the latitude?


ehild

 

[frozenguy]

I do not want anything from you, it is you wanting to see the solution. Make a drawing of the Earth like the one I attach. Show both the radius of Earth (R) and the radius of disk (r).
Do you know the angles of the yellow triangle? How are they related to the latitude?


ehild

I apologize... I didn't really mean what do you want in that way. I shouldn't of said it like that.

I had drawn it many times but never like that. I think I need some sleep.
So R=r/cos40. :)

Thank you for your help. And again I didn't mean to sound rude or non appreciative.

 

[ehild]

It is all right. You are welcome.

ehild