The sun then falls below the horizon, and it is nighttime for our little person:

Transcription

1 Venus Update! Problem 6 on Homework 1 in Physics 2A last September asked you to find the distance from Earth to Venus at that time. I gave you the angle between the sun and Venus at that time; you drew some right triangles, and found the answer with a bit of trigonometry. I mentioned in class at the time that Venus was on the western side of the sun. This meant that it was only visible in the early morning hours, just before the sun rose. To see why this is, consider this series of pictures: The dashed line represents the horizon for the little person (it could be you!) on Earth. When the sun is above the horizon, Venus is not visible because the sunlight is too bright. As the Earth rotates, Venus and the sun (and everything else in the sky) move toward the western horizon. When Venus is on the western side of the sun (as it was last September), it falls below the horizon when the sun is still above the horizon:

2 The sun then falls below the horizon, and it is nighttime for our little person: The Earth continues to rotate while it is nighttime for our little person:

3 and hours later, Venus appears above the eastern horizon just before the sun does. So when Venus is on the western side of the sun, as it was in September, we can see it in the early morning hours just before sunrise. Note that as Earth continues to rotate in this picture, the sun would soon rise above the eastern horizon also. I also mentioned in lecture that we would have to wait about six months to see Venus in the evening instead. And that was about... six months ago! What has happened in the past six months? Earth has completed about half an orbit around the sun. But Venus has completed about threequarters of an orbit, because Venus takes only eight months to complete a full orbit. The net effect is that if you can imagine Venus and Earth running laps around the sun (because that s essentially what they do...), Venus has gained a quarter lap. Both planets orbit counterclockwise in this picture (as do all the planets in our solar system; nearly all the planets, as well as the sun, also rotate counterclockwise... just like the Earth in this picture. This is not a coincidence, but a result of how the solar system was formed from a single rotating cloud of gas and dust.) Which means that now, six months later, Venus is a quarter of an orbit further along, relative to Earth. (Note: I do realize that September to April is actually seven months. So Venus has gained a little more than a quarter orbit. But the principle is still the same. And the proof of what I m getting at is right there in the sky... right now.) Which means as of right now, Venus is on the eastern side of the sun:

4 So today, as the Earth rotates, the sun will fall below the western horizon while Venus is still above the horizon:

5 Take a look, you can t miss it. Venus is the brightest object in the sky (other than the sun or moon) and it s hanging out over the western horizon just after sunset. It looks like a very bright star, but compare its brightness to that of actual stars and you will see it is much brighter. In fact, Venus is about 100 times brighter than a typical star. The other visible planets... Mercury, Mars, Jupiter and Saturn... are also usually much brighter than typical stars (although the brightness of any planet varies quite a bit; it depends on its distance from us and the angle between the planet and the sun.) And they always travel across our southern sky, along roughly the same path the sun takes through the day. You can currently see Jupiter on this path as it rises in the east in the early evening... i.e. Venus on the western horizon, Jupiter on the eastern horizon. Jupiter also will look like a bright star, although not nearly as bright as Venus. Saturn and Mars are currently visible in the early morning hours, close to each other and above the eastern horizon (i.e. they come up a couple hours before the sun does.) And Mercury? It also rises before the sun, and is technically visible over the eastern horizon just before sunrise. But its size and proximity to the sun, and the typical obstructions of our view of the horizon, make it difficult to see.