It is hard for the human to comprehend how small the planets are in comparison with the sun. If you shrunk the sun from its radius of 6.96E8 m down to the size of a beach ball with a radius of 20 cm, and then shrunk all the planet’s radii by the same factor, our earth would have a radius of 1.8 mm, like a large grain of sand. The largest planet jupiter would have a radius of only 2 cm, the size of marble. This is simply calculated by using a ratio, if you wanted to calculate the rest of the planet’s relative size you could use the relation, r=(0.2m/6.96E8m)R where R is the actual radius of the planet and r is the relative size in our scheme. It puts into perspective why to the early astronomers, and the uninformed observer, the planet’s simply look like stars in the night sky. We see our sun to be an actual circle in the sky, because not only is it very large compared to the planet’s, but also very close compared to the next closest stars. The planet’s appear so small, because they are actually much smaller than the sun. In addition, they are relatively the same distance from earth as the sun, when we consider how much farther it is to any object outside our solar system; the closest visible object is the next closest star, Proxima Centauri, which is 4.2 light years away, 272,000 AU (the distance from earth to sun), or 4E16 m.
Actual stars then are all much farther away from the earth than the planets, and as any person knows, things look smaller as they get farther away. This effect is simply perspective. If one changes their line of sight looking at the object its distance from you can be calculated based of the change in apparent angle of the star. More simply, this change in apparent angle is how fast you perceive the object to move. A perfect example is if you are in a car looking out the side window, you will notice that the houses right next the road move faster than the houses farther away from the road. This is how astronomers first calculated the distance to the stars: They would measure the apparent location of a star and then wait 6 months for the earth to orbit half-way and move 2 AU (2x the distance between the sun and earth) from its initial position, and then measure again, and find out the angular difference. When you take into account this effect of distance, and try to calculate the radius of these far off objects, you realize all the stars on average are about the same size as our sun, or bigger. Thus, the human eye sees stars and planet’s to be about the same size in the night sky, but in reality, only the planets are actually ‘small’ when compared with the sun. Most stars are just so much farther away they appear to be so small.
Another great example of this effect of perspective on the perceived size of an object is the sun and moon. To the average observer of the sky, it is pretty easy to notice that the only actual ‘circular’ objects and not ‘point’ objects, (I’m considering anything that has a angular width of less than a minute of a degree to be a ‘point’) are the sun and the moon. What is even more amazing is that the sun has an angular width of about 31.6′ and the moon has about 29.3′ of width: almost exactly the same! The result of this coincidence is that we are able to have total solar eclipses. If either was smaller or bigger in angular width, our solar eclipses wouldn’t completely cover the sun, or would completely block out the sun. The lunar width depends on the size of the moon and its distance from earth, and the solar width depends on the size of the sun and its distance from earth. In the case of the lunar width, the moon is actually smaller in radius than the earth, about 27% the radius of earth, but its about .0025 AU from the earth, or about 0.25% the distance from the earth to the sun, thus it appears to be large in the sky because it is so much closer. Whereas the sun has a radius about 110 times the size of earth, but is 400 times farther away, thus giving comparably the same angular width by total coincidence. I find this coincidence very puzzling, but beautiful at the same time. Before astronomers could reason the distances to the sun and moon and their sizes, our perspective made us believe the sun and the moon were the same size (not to mention many thought the moon was a perfect sphere!). In reality however, the sun is a massive ball of hot gas/plasma much farther away that humans will never be able to step foot on. Conversely, the moon is a small, cold rock, that is so close to us, it only took humans 300 years after learning the laws of gravity to build a spaceship to travel to it in just 3 days and have a few humans walk around on it.
sources cited
http://en.wikipedia.org/wiki/Solar_eclipse
Bradley W. Carroll and Dale A. Ostlie. An Introduction to Modern Astrophysics. 2nd Edition http://en.wikipedia.org/wiki/Angular_diameter
