The diameter of the Earth is approximately twelve thousand kilometers, or seven thousand miles, across at the Equator. Scientists can calculate its diameter by drawing a straight line through its center and measuring the ends of the circle’s boundary. Similarly, they can determine its diameter at the poles.
Eratosthenes
Eratosthenes is considered the first person to measure the diameter of the earth, and his measurement was based on the position of the sun and the earth in relation to each other. His method involved measuring the angle of elevation of the Sun at noon in two different cities on the same day. It required two yardsticks, a protractor, a magnetic compass, and a string.
Later, Ptolemy’s circumnavigation changed the value of the earth’s circumference, which was previously accepted. In the second century a.d., Claudius Ptolemy measured the circumference of the Earth using a different method and substituted Eratosthenes’ inaccurate values. Ptolemy’s method covered 50 miles per degree around the equator compared to the 70 miles per degree used by Eratosthenes. His method also involved measuring the motion of shadows over a period of time and calculated a shorter circumference than Eratosthenes.
Eratosthenes’ method was based on observation and basic arithmetic. He observed that at noontime the sun shone directly into the well at Syene. He then used this information to compute the earth’s diameter and circumference. In addition, he used a method based on the angular difference between two vertical directions to determine how many times the earth went around the sun at each location.
Eratosthenes’ diameter of Earth is a measure of the earth’s circumference, and is based on the angle at which the Sun’s rays hit the earth’s surface at noon in Syene and Alexandria. Eratosthenes’ method is no longer used, but his calculations are a good reference for understanding the circumference of the earth.
Eratosthenes’ first measurement
Eratosthenes, the Greek mathematician, invented a method for measuring the diameter of the Earth by observing the distance between Alexandria and Syene, Egypt. He used this distance and the angles he measured to calculate the diameter of the Earth.
Eratosthenes’ measurement was not quite accurate, though it was very close. The equatorial circumference of the Earth is four thousand and seventy-eight kilometers, while its meridional circumference is 40,000 kilometers. The Greek mathematician Hipparchus also measured the distances between the Sun and the Moon. Posidonius, another Greek mathematician, made an attempt to measure the circumference of the Earth using his methods. His method gave him an error of about seventeen percent, which is a decent ballpark figure for the Earth.
Eratosthenes’ first measurement, though, was not as accurate as he may have believed. In fact, his measurements differed from modern measurements by about 15.3%. His calculations of the diameter of the earth are regarded as one of the greatest triumphs in scientific calculation.
Eratosthenes did not set out to prove that the Earth is round; he was simply trying to measure the circumference of the Earth. In the process, he showed incredible intelligence and creativity. Furthermore, his calculations revealed a deep understanding of advanced knowledge.
Sun’s diameter
The diameter of the Sun is equal from the center to the poles. The radius of other celestial bodies varies depending on the speed of their rotation. The Sun takes 25 days to turn on its axis. Compared to this, the diameter of the Earth is comparatively larger. Despite this, the Sun’s diameter is subject to some uncertainty.
A recent NASA spacecraft, Solar Dynamics Observatory, will measure the Sun’s diameter in the future. The spacecraft has three instruments that will aid future examinations of solar size. One of the instruments is the Advanced Technology Solar Telescope, which will measure the sun’s smallest scales. If the measurements are accurate, they can lead to an accurate measurement of the sun’s diameter.
The diameter of the Sun is 864,000 miles (109,560 kilometers). However, it is not quite as big as the planets that orbit it. In fact, the biggest known star to man is VY Canis Majoris, which could be more than two hundred times the diameter of the Sun.
The diameter of the sun can be measured in both angular and linear measurements. For example, the angular size of the Sun is 0.53 degrees, the same angular size as that of the moon. Despite being 400 times bigger and 400 times further away, the Sun is smaller than the moon, which is one of the largest objects in the universe.
Earth’s equatorial diameter
The equatorial diameter of the Earth is 43 kilometres greater than its pole-to-pole diameter. This difference is due to the fact that the radius of the earth is almost exactly twice as large at the equator as it is at the poles. The earth’s radius varies depending on its latitude and rotation.
The earth’s mean radius is approximately 3,959 miles (6,371 kilometers). However, it is bulgier at the equator. Its equatorial diameter is around 7,926 miles (12,756 km) while its meridional diameter is about 7,900 miles (12,718 km). The Earth’s mean diameter, or average diameter, is calculated by adding the polar and equatorial diameters and dividing them by half. Its mean diameter is therefore 12742 km.
In ancient times, the equatorial diameter of the Earth was known. Ancient Greeks had a different definition of the equatorial diameter. Eratosthenes, the chief librarian at the Library of Alexandria, used a method of calculating the equatorial diameter by calculating the distance between two cities on the same meridian. He did this by measuring the shadow angles cast by the sun at noon on the summer solstice.
The Earth’s effective surface gravity varies with latitude, as indicated by the length of a seconds-pendulum. Newton later derived the general variation in latitudinal length. But he was not as concerned with the length ratio between the equatorial diameter and the polar axis.
Equilibrium radius
Equilibrium radius of the earth corresponds to the radius of the earth at its equilibrium state. It is difficult to calculate the exact value of the equilibrium radius due to the complex global network of plate boundaries. Nevertheless, it is known that the rate of increase of density increases with the square of the radius of the earth.
Large bodies in equilibrium have a spherical form, and this is called hydrostatic equilibrium. Even objects with a small diameter are in a state of hydrostatic equilibrium because gravity overcomes the resistance to shear force. A good example of a small object is the asteroid Ceres, which has a radius of 945 kilometers. Another example is the moon Iapetus, which has a diameter of 1470 kilometers and is in hydrostatic equilibrium with Saturn.
The Earth’s rotation rate has slowed down recently, and it may be flattening. It is also possible that the elastic lithosphere has affected the Earth’s rotational shape, reducing the Earth’s ellipticity. However, this effect is small compared to the net non-hydrostatic flattening.
The inverse method has been used to find the density of a planet. Using this method, a planet’s internal density is given by the law of compressibility. The inverse method reveals that there are two cases of the solution – one in which the compressibility is constant while the other one shows a modulus that varies with density.
