# Circumference of the earth via latitute mesurement

Suppose I know city A is located at latitude 21 degrees exactly and city y is located at latitude 24 degrees exactly. I know the distance between the two cities is 400 kilometers.
I want to find the circumference of the earth approximately

How do I do this?

My feeling is that we
subtract the two latitudes to find 24-21 = 3 degrees

so 3 degrees corresponds to roughly 400 kilometers (1)

so 180 degrees of latitude corresponds roughly to X kilometers (2)

and I find that x = 24000 kilometers

is line (1) and (2) correct or should the second line read

360 degrees of latitude corresponds roughly to X kilometers??

thanks

Integral
Staff Emeritus
Gold Member
That works fine as long as the cities have the same longitude.

You should use 360deg not 180.

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Hi. thank you for that. yes the cities are at the same longitude.
my problem is when i do this calculation with different, more realistic, numbers for latitude and distance than the ones i posted originally.

i.e the more realistic numbers are 37.977 degrees of latitude
41.856 degrees of latitude and 430 km is the distance betwee these two cities.

i get an answer that is exactly a factor of two off from the true circumference of the earth?

when it should be 40000 km.
so that is why i was thinking it should be 360 and not 180 degrees

so why am i off?

thanks

Integral
Staff Emeritus
Gold Member

I get 40,000km

oh wait sorry i didnt see your previous post where you said to use 360. thats exactly my question
why 360?
arent there 180 degrees of latitude?
i understand if i use 360 i get the answer.
but there are 360 of longitude not latitude and we only know the latitudes of the cities?

Last edited:
Integral
Staff Emeritus