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# The Sun Help

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By — McGraw-Hill Professional
Updated on Sep 16, 2011

## Introduction to the Sun

The Sun has been worshipped, despised, and feared by humans throughout history. Ideas about the Sun are as strange nowadays as they have ever been, but there are some statements about our parent star that we can make with confidence.

### Size And Distance

The Sun is the largest nuclear reactor from which humanity has ever derived energy, and until we venture into other parts of the galaxy, this will remain the case. The Sun has a radius of about 695,000 kilometers (432,000 miles), more than 100 times the radius of Earth. If Earth were placed at the center of the Sun (assuming the planet would not vaporize), the orbit of the Moon would fit inside the Sun with room to spare (Fig. 4-7).

Figure 4-7. Earth-moon system would easily fit inside the Sun.

The commonly accepted mean distance from Earth to the Sun is 150,000,000 kilometers (93,000,000 miles) in round numbers. But the day-to-day distance varies up to a couple of million kilometers either way. Earth’s orbit around the Sun, like the Moon’s orbit around Earth, is not a perfect circle but is an ellipse with the Sun at one focus. Earth’s closest approach to the Sun is called perihelion , and it occurs during the month of January. Earth is farthest away from the Sun— aphelion —in July. Surprisingly enough, for those of us in the northern hemisphere, the Sun is closest in the dead of the winter. It is not Earth-Sun distance that primarily affects our seasons but the tilt of Earth on its axis.

## Measuring The Sun’s Distance And Size

Centuries ago, people did not know how large the Sun was, nor how far away it was. Estimates ranged from a few thousand miles (kilometers hadn’t been invented yet) to a few million miles. The distance to the Sun could not be measured by parallax relative to the background of stars because the Sun’s brilliance obliterated the stars near it. The distance to the Moon had been measured by parallax, as well as the distances to Mars and Venus at various times, but the Sun defied attempts to measure its distance until someone thought of finding it by logical deduction. What follows is an example showing the sort of thought process that was used, and can still be used, to infer the distance to the Sun. Let’s update the measurement techniques from those of our forebears and suppose that we have access to a powerful radar telescope, with which we can measure interplanetary distances by bouncing radio beams off distant planets and measuring the time it takes for the signals to come back to us.

Given a central body having a known, constant mass, such as the Sun, all its satellites obey certain physical laws with respect to their orbits. One of these principles, called Kepler’s third law , states that the square of the orbital period of any satellite is proportional to the cube of its average distance from the central mass. This is true no matter what the mass of the orbiting object; a small meteoroid obeys the rule just as does Earth, Venus, Mars, and Jupiter. We know the length of Earth’s year and the length of Venus’s year; from this we can calculate the ratio (but not the actual values) of the two planets’ mean orbital radii. Knowing this ratio is not enough, all by itself, to solve the riddle of Earth’s mean distance from the Sun, but it solves half the problem.

The next step involves measuring the distance to Venus. If we could do this when Venus is exactly in line with the Sun, then we could figure out our own distance by simple mathematics. Unfortunately, the Sun produces powerful radio waves, and our radar telescope won’t work when Venus is at inferior conjunction (between us and the Sun) because the Sun’s radio noise drowns out the echoes. However, when Venus is at its maximum elongation (its angular separation from the Sun is greatest either eastward or westward), the radar works because the Sun is out of the way. At maximum elongation, note (Fig. 4-8) that Venus, Earth, and the Sun lie at the vertices of a right triangle, with the right angle at the vertex defined by Venus. One of the oldest laws of geometry, credited to a Greek named Pythagoras , states that the square of the length of the longest side of a right triangle is equal to the sum of the squares of the other two sides. In Fig. 4-8 this means that a 2 + b 2 = x 2 , where x is the elusive thing we seek, the average distance of Earth from the Sun.

Figure 4-8. If we know the radius of Venus’ solar orbit and we can measure the distance to Venus at its maximum elongation, then we can calculate our own distance from the Sun.

Now that we know the value of a in the equation (by direct measurement) and also the ratio of b to x (by Kepler’s third law), we can calculate the values of both b and x because we have a set of two equations in two variables. Let’s not drag ourselves through a detailed mathematical derivation here. If you’ve had high school algebra, you can do the derivation for yourself. It should suffice to say that this scheme can give us a fairly good idea of Earth’s mean distance from the Sun if the measurement is repeated at several maximum elongations and the results averaged. However, even this will only give us an approximation because the orbits of Earth and Venus are not perfect circles. In recent decades, astronomers have made increasingly accurate measurements of the distance from Earth to the Sun using a variety of techniques.

Once the distance from Earth to the Sun was known, the Sun’s actual radius was determined by measuring the angular radius of its disk and employing surveyors’ triangulation in reverse (Fig. 4-9).

Figure 4-9. The Sun’s actual radius can be determined by reverse triangulation, on the basis of its apparent radius and its known distance from Earth.

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