Why does 10 degrees of latitude have a different distance at the equator than at the poles?
All lines of latitude come together at the poles.
http://www.nationalatlas.gov/articles/mapping/a_latlong.html
I have another question if its alright to ask. why does the distance of 10 degrees of longitude decrease as you go from the equator to the pole? is it the same reason?
Yes, it's the same reason.
http://www.google.com/imgres?imgurl=http://www.k12science.org/curriculum/boilproj/images/Reference%2520Material_world_pol98.jpg&imgrefurl=http://www.k12science.org/curriculum/boilproj/links.html&h=920&w=1576&sz=210&tbnid=57uaV-EGH86CJM:&tbnh=88&tbnw=150&prev=/images%3Fq%3Dmap%2Blongitude&zoom=1&q=map+longitude&hl=en&usg=__jYs2Tl3tt3keitPJkfh4ik8AczM=&sa=X&ei=ls9ZTe2dKIjegQf019ijDQ&ved=0CCwQ9QEwBA
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The distance covered by 10 degrees of latitude varies between the equator and the poles because the Earth is not a perfect sphere but rather an oblate spheroid, meaning it is slightly flattened at the poles and bulges at the equator. This shape is due to the rotation of the Earth, which causes centrifugal force at the equator to push the mass of the planet outward, creating the bulge.
To understand why there is a difference in distance, we can use the concept of circumferential distance and angular distance. Angular distance refers to the number of degrees between two points on a sphere, while circumferential distance is the physical distance along the equator or any other parallel on the Earth's surface.
At the equator, one degree of latitude covers a larger circumferential distance compared to the poles. This is because the equator is located farther from the Earth's axis of rotation, and therefore, its circumference is larger. The Earth's equatorial circumference is about 40,075 kilometers (24,901 miles), which means that 10 degrees of latitude at the equator covers around 1/36th (1/360 degrees) of the equatorial circumference.
On the other hand, at the poles, the distance covered by 10 degrees of latitude is much smaller. Near the poles, the Earth's circumference progressively decreases as we move closer to the axis of rotation. This is because the polar diameter of the Earth is smaller than the equatorial diameter. The polar circumference measures around 40,008 kilometers (24,860 miles), which means that 10 degrees of latitude at the poles covers about 1/36.8th (1/368 degrees) of the polar circumference.
In summary, the distance covered by 10 degrees of latitude is different at the equator and the poles due to the Earth's oblate spheroid shape, with the equator being farther from the Earth's axis of rotation, resulting in a larger circumference compared to the poles.