You are watching: What is the angular diameter of the sun?

Have you ever before wondered how big a "chunk" the the skies the sun takes up in relationship to the totality thing? together in, if friend think the the skies as a huge half-sphere spanning everything over and approximately you native every allude on the horizon to the zenith directly overhead, what portion of that does the all-important sun consume?

The answer might surprise you, and also the route to acquiring to the is instructive in the locations of both geometry and astronomy.

The planet orbits the sunlight at an mean distance of around 93 million miles, or mi (150 million kilometers, or km; 1.5 × 1011 m). That diameter, or the distance throughout its widest point, is around 870,000 mi (1,400,000 kilometres or 1.4 × 109 m), do it virtually 100 time as broad as Earth. The sun"s irradiate takes about eight minutes to reach Earth, which method that if it all of sudden disappeared, you"d have sufficient time to listen to one or 2 songs prior to you realized something was amiss.

Is this details alone sufficient for you to figure out how large the sunlight "looks"? because that this, you rotate to a quantity in trigonometry called angular diameter.

**Angular diameter** is, in fact, one angle, no a diameter. It is the angle that an item "takes up" as watched by one observer in ~ a stated distance. This have the right to be measured in *degrees* (°) or *radians* (rad). One circle takes increase 360° and also 2π rad, for this reason 1 rad = 360/2π = 57.3°.

If you were encountering north and also standing in front of a massive half-dome the reached precisely to the zenith above you and also to the clues on the horizon to the east and west, the dome would have an angular diameter that 90° (π/2 rad). This method it bring away up half of your obtainable field the view. If you turn your head every the means to the east or of the west, naught changes, however if you rotate around and face south, you obtain to check out the whole remaining 90° of sky if you rotate your head come the east and then come the west indigenous this south-facing stance.

It is necessary to bear in mind that angular diameter is not an natural property of one object. The sunlight would have actually a better angular diameter top top Mercury, the nearest earth to the sun, 보다 it walk on Earth, and also on distant Saturn it would certainly be far smaller.

where arctan method "inverse tangent" and also is frequently represented through tan-1 on calculators. The tangent the an angle in a ideal triangle is the next opposite the angle separated by the adjacent side, with the hypotenuse ignored; for this reason arctan is the angle who tangent has the value specified in parentheses, in this situation D/2r.

\beginaligned α &= 2 \arctan \bigg( \frac1.4 × 109 \text m2×1.5 × 10^11\text m\bigg) \\ &= 2 \arctan (0.0047) \\ &= 2 × 0.270° \\ &= 0.54° \endaligned

If you"ve noticed the the moon and also the sun appear to be about the exact same size (a decision made challenging by the fact that you can"t, or shouldn"t, look straight at the sunlight with the naked eye), you space correct. The moon"s diameter is around 400 times smaller than the sun"s, yet it is also around 400 time closer to earth than the sun is.

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The distance throughout your pinkie finger held at arm"s length is a stormy approximation that a level in the sky. using this formula from Mercury, the closest world to the sun at 36 million miles, provides a an outcome of about 1.4 degrees -- practically three times as large as the sun shows up on Earth.

Kevin Beck hold a bachelor's degree in physics v minors in math and chemistry native the college of Vermont. Formerly with ScienceBlogs.com and the editor of "Run Strong," he has written because that Runner's World, Men's Fitness, Competitor, and also a variety of various other publications. More about Kevin and links to his skilled work have the right to be uncovered at www.kemibe.com.