The Sciences

At the bottom of Earth's orbit

Bad AstronomyBy Phil PlaitJan 3, 2011 12:10 PM


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[Update: My apologies: due to a cut-and-paste error, I had mistakenly listed the perihelion distance as the average distance of the Earth to the Sun (147 versus 149 million km). To avoid confusion, I simply replaced the error with the correct value. The rest of the post is correct since this wasn't a math error but a typographical one, and I used the right value when doing my calculations below.] Since last July, the Earth has been falling ever closer to the Sun. Every moment since then, our planet has edged closer to the nearest star in the Universe, approaching it at over 1100 kilometers per hour, 27,500 km/day, 800,000 km every month. But don't panic! We do this every year. And that part of it ends today anyway. The Earth's orbit around the Sun is not a perfect circle. It's actually an ellipse, so sometimes we're closer to the Sun, and sometimes farther away. Various factors change the exact date and time every year -- you can get the numbers at the Naval Observatory site -- but aphelion (when we're farthest from the Sun) happens in July, and perihelion (when we're closest) in January. And we're at perihelion now! Today, January 3, 2011, around 19:00 GMT (2:00 p.m. Eastern US time), the Earth reaches perihelion. At that time, we'll be about 147,099,587 kilometers (91,245,873 miles) from the Sun. To give you an idea of how far that is, a jet traveling at a cruising speed of 800 km/hr would take over 20 years to reach the Sun. Of course, since today is when we're closest to the Sun this year, every day for the next six months after we'll be a bit farther away. That reaches its peak when we're at aphelion this year on July 4th, when we'll be 152,096,155 km (94,507,988 miles) from the Sun. Not that you'd notice without a telescope, but that means the Sun is slightly bigger in the sky today than it is in July. The difference is only about 3%, which would take a telescope to notice. Frequent BA Blog astrophotograph contributor Anthony Ayiomamitis took these images of the Sun at perihelion and aphelion in 2005:

This may seem a bit odd if you're not used to the physics of orbital motion, but you can think of the Earth as moving around the Sun with two velocities: one sideways as it sweeps around its orbit, the other (much smaller) toward and away from the Sun over the course of a year. The two add together to give us our elliptical orbit. The sideways (what astronomers call tangential) velocity is about 30 kilometers (18 miles) per second, which is incredibly fast. But then, we do travel an orbit that's nearly a billion kilometers in circumference every year! The velocity toward and away from the Sun (what we call the radial velocity because its direction is along the orbital radius) is much smaller; only about 0.3 km/sec (which translates into the numbers I used in the first paragraph above). That's an average over the course of the year which I estimated very simply by taking the difference between our aphelion and perihelion distances -- almost exactly 5 million km (3 million miles) -- and dividing by the time it takes the Earth to move between them: half a year, or about 182 days. The exact speed changes, because at perihelion, we're closer to the Sun and feel its gravity a bit more strongly, so our speed around the Sun is a bit faster than at aphelion. Together, the tangential and radial velocities add up to gives us our overall orbital velocity, which changes with distance from the Sun. In fact, at perihelion today we'll be moving around the Sun at 30.1 km/sec, and at aphelion in July that will have slowed to about 29.6 km/sec. That's a change of about 1.7%; enough to measure if you have the right equipment, but not anything you'd notice in your daily life. This does bring up another interesting point: when we're closer to the Sun we receive more light -- and therefore energy and heat -- from it than when we're farther away. We can calculate that as well. The amount of energy you receive from an object gets smaller with the square of your distance: double your distance and you only get 1/4 the amount of light from it. Go 10 times farther away and that drops to 1/100 or 1%. At aphelion, we're 1.033 times farther from the Sun, so we get (1.033)^2 or about 1.07 times less light and energy from it. You can flip that around to say that today we are receiving about 7% more sunlight than on aphelion in July! That may seem weird to folks living north of the equator, but seasons are a whole 'nuther issue. Oh, and hey, one more thing. Every now and again I'll hear from a kid or parent who tells me that they had a teacher or friend claim that if the Earth were even a few thousand miles closer or farther from the Sun we'd burn up or freeze. That's clearly silly, since over the course of six months the Earth's distance to the Sun changes by 3 million miles! Not only that, but the Earth is 8000 miles (13,000 km) across and spins once a day. That means at noon you're 8000 miles closer to the Sun than you are at midnight, and I don't general see people bursting into flame and then freezing in a block of ice every 12 hours. So if you ever hear that particular bit of silliness, refer 'em here. So there you go. You may not notice the Sun looking slightly bigger, or being warmer, or moving faster* than usual today, but it is. So if you're having a tough day, remember this: it's all uphill from here. Until July.

^* Relative to the stars it's moving faster, that is, since if you were to measure its speed across the sky as it rises and sets, the Sun would actually appear to be moving more slowly, because as you stand on the Earth its spin moves the Sun left to right relative to you (if you're in the northern hemisphere facing south, or standing on your head in Australia facing north) making a single circuit across the sky once per day, while the Earth's orbital motion moves the Sun right to left relative to the stars making a circuit once per year, with that motion fastest at perihelion, therefore subtracting from or slowing the diurnal (daily motion) of the Sun left to right, so the Sun appears to move in the sky most slowly at perihelion. Got it?

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