What is the distance, in km, from 80 to 90 degrees N along the Prime Meridian?
Here is a high-accuracy site that I use for these problems. The distance is 1116.826 km, at standard sea level. You could also get a good estimate by just using a round Earth approximation. Polar circumference is 40,007.86 km, and 80 to 90 is 10/360 of the whole circumference. 40,007.86 * (10/360) = 1111.329 km. <== approximation, off by 0.49%.
How did Isaac Newton calculate the radius of the earth?
He took data from people who measured the distance between two points, along with astronomical observations to determine the latitudes (that is, how many degrees they had moved along the surface). From there it's a straightforward calculation: [math]\mathrm{arc length = angle \times radius}[/math]. Convert angle to radians, and solve for the radius. In his own words:Our countryman, Mr. Norwood, measuring a distance of 905751 feet ofLondon measure between London and York, in 1635, and observing the difference of latitudes to be 2° 28′, determined the measure of one degree to be 367196 feet of London measure, that is 57300 Paris toises. M. Picart, measuring an arc of one degree, and 22′ 55″ of the meridian betweenAmiens and Malvoisine, found an arc of one degree to be 57060 Paristoises. M. Cassini, the father, measured the distance upon the meridian from the town of Collioure in Roussillon to the Observatory of Paris; and his son added the distance from the Observatory to the Citadel of Dunkirk. The whole distance was 486156½ toises and the difference of the latitudes of Collioure and Dunkirk was 8 degrees, and 31′ 115/6″. Hence an arc of one degree appears to be 57061 Paris toises. And from these measures we conclude that the circumference of the earth is 123249600, and its semi-diameter 19615800 Paris feet, upon the supposition that the earth is of a spherical figure.The Mathematical Principles of Natural PhilosophyHe got largely the same result people had been getting for thousands of years. What Newton really added is that the earth isn't a sphere, and thus doesn't have a single radius. The earth is flattened by its own roation. Newton calculated the flattening, and got it mostly right.
How can we calculate the radius of the earth?
There are many ways to calculate the radius of the earth, but most of them require knowing quite a few universal contstants or some physical law. I believe you are looking for a method which doesn't require knowledge of any such constants.So here is a method for which all you need to know is that a day is 24 hours long.Go to a beach on a non-cloudy day so that the sunset can be observed clearly. Lie down on the ground and wait for the sunset. Stand up, when you can no longer see the sunand start your stopwatch. On standing up you will be able to see a tiny part of the sun. Wait for the instant when the sun is no longer visible and record the time difference between the 2 sunsets. This time difference (t) and that fact that the earth takes 24 hours for 1 rotation is enough to calculate the radius of the earth. See the figure for a better understanding.Now we need to find expression for theta in 2 different ways, one in terms of your height and another in terms of the time difference (t)Cos(theta)=R/(R+h) This is by the definition of cosAlso theta=360*t/(24*60*60) Since it takes 24*60*60 seconds to rotate by 360 degrees we just take the ratio to find angle by which the earth rotates in t seconds(unitary methodFor a person of height 1.7m, t turns out to be around 9.5 seconds.So theta=0.03952 degrees (using the second equation)cos(theta)=0.0006894Using the first equation we get R=7153798m=7153 kmThe actual radius of the earth is 6400 km. So our estimate isn't off by much.
What is best way to calculate the distance between two latitude and longitude?
(F)latitude (i.e. breadth)Lines of latitude are called parallels and in total there are 180 degrees of latitude. The distance between each degree of latitude is about 69 miles (110 kilometers).So 180 x 110=19,800 kmThe five major parallels of latitudes from north to south are called: Arctic Circle, Tropic (i.e. Turning) of Cancer, Equator, Tropic(i.e. Turning) of Capricorn, and the Antarctic Circle.LongitudeLongitude lines run north-south and mark the position east-west of a point. Lines of longitude are known as meridians(middle day as per Sun point of view). These lines run from pole to pole, crossing the equator at right angles. There are 360 degrees of latitude and the latitude line of 0 degrees is known as the Prime Meridian and it divides the world into the Eastern Hemisphere and the Western Hemisphere (-180 degrees degrees of longitude west and 180 degrees of longitude east).The distance between longitudes narrows the further away from the equator. The distance between longitudes at the equator is the same as latitude, roughly 69 miles (110 kilometers) . At 45 degrees north or south, the distance between is about 49 miles (79 kilometers). The distance between longitudes reaches zero at the poles as the lines of meridian converge at that point.Source