Chapter 3: Gravity and Orbits

3.4
Orbits

Critical Questions:

  • What do the orbits of the planets really look like?
  • What causes the tides?
  • How do artificial satellites orbit the Earth?

Back in Section 2.9, I explained a bit about how orbits work. I said that things in space orbit other things because gravity acts as a centripetal force, resulting in circular motion that goes on forever because there is no friction to slow things down. Now I get to do the fun part: go back and explain why much of what I said then was incorrect.

First of all, no orbits are perfectly circular. Circular orbits require a very specific combination of speeds, forces, and distances, but nature doesn’t like specific requirements, preferring instead the exciting chaos of random numbers. If you take a planet and get it moving near a star, then there are a few possible outcomes depending on speed and distance. The planet may end up with a circular orbit, but that is so unlikely it’s essentially impossible.

The second option is an elliptical orbit. An ellipse is just a circle that has been flattened (a circle is actually just a special kind of ellipse, just like a square is a special kind of rectangle). The ellipse is the shape of all of the orbits we know about, including Earth’s path around the sun and the moon’s path around the Earth. And in an elliptical orbit, the thing that is being orbited doesn’t sit at the exact center of the ellipse, but is located a bit off to one side.

elliptical orbit

This is a highly exaggerated elliptical orbit - Earth's orbit, for example, is almost perfectly circular.

This means that over the course of a year, the distance between our planet and the sun varies by about 5 million kilometers.[1] Now, that may sound like a lot, but the average distance from here to the sun is 150 million kilometers, so if you were eye-balling things from a nearby solar system, you’d probably see our orbit as roughly circular (unlike in the diagram above). This is true of all of the eight planets.[2]

The second thing I lied about was that planets can orbit stars forever without slowing down. In fact, everything that orbits something else loses energy in one way or another, and when an orbiting object slows down enough, it crashes into the thing it’s orbiting. The Earth, for example, loses energy because its atmosphere tends to get pushed around by outside forces like the ‘stellar wind’, a stream of charged particles ejected from the sun.[3] Luckily for us, it would take between a trillion and a quadrillion times the current age of the Universe for the Earth to lose enough of its forwards momentum that it falls into the sun. And it’ll only be a few billion years before the Sun swells up into a ‘red giant’ and consumes our planet anyway, so we don’t have to worry about falling into it first.

Lastly, you can forget about the idea that the thing being orbited remains stationary. Remember, Newton’s Third Law says that all forces, including gravity, are always reciprocal, so both objects are tugging on each other. And besides, there’s nothing holding something in one spot if it’s floating out in space. If you watched the Earth and the moon carefully enough, for example, you’d see the Earth wobbling a little bit in response to the pull of the moon. The sun does the same thing, although its motion is more complicated because of how many planets are pulling it. However, the more massive object moves less than the smaller one, as in the animation below.

Animation of two objects orbiting their center of mass

This is a simplified simulation of two objects in orbit, with relative masses similar to the Earth and Sun.

This reminds me of the tides, which are caused by the moon and the sun. You may know that the tides are caused by gravitational pulls on ocean water, but you probably didn’t know why there are two high tides per day in most of the world. There’s a fairly simple explanation for this phenomenon, and it has to do with the fact that gravity gets weaker at larger distances. If we ignore the sun’s effects (which are weaker than the moon’s), the water on one side of the Earth is closest to the moon, and so it bulges outward as it’s pulled by the moon’s gravity. The moon is also pulling on the solid part of the Earth, causing it to move in little circles as discussed in the previous paragraph. Finally, the water on the other side of the planet also bulges outwards, because the Earth is essentially being pulled away from it. The result is two bulges of ocean water, one on each side of the planet. The bulges correspond to high tide; everywhere else experiences lower tides. When you take the sun into account, you see why the tide gets bigger and smaller throughout the month as the alignment of the moon relative to the sun changes.

Anyway, once we began to understand how all of this orbit stuff worked, we were able to send objects out into space to orbit the Earth. The first such object was the Russian satellite Sputnik, a small metal ball that terrified America because it was launched during the Cold War. Today, there are thousands of artificial satellites orbiting the Earth; these include communications satellites, which broadcast radio, TV, and cell phone signals around the world, as well as research satellites and the ones making up the Global Positioning System (GPS). They move in all kinds of different directions and at a variety of different altitudes. Some have a ‘geosynchronous’ orbit, which means that they orbit the planet at the exact same rate as the Earth’s spin, thus staying directly above the same spot at all times.

One interesting problem with these things is that the vast majority of them are no longer operational, but remain stuck in their orbits due to their forwards momentum. This can cause problems for spacecraft moving through the atmosphere or orbiting the Earth themselves – even small pieces of debris can cause damage if they’re moving fast enough. And every so often, one of these satellites finally loses enough speed that it falls to the Earth. Near the end of 2011, a climate satellite the size of a bus crashed into the Pacific Ocean after 20 years in space. Before it fell, even NASA themselves couldn’t be sure where it would land, giving it only a 1-in-3200 chance of hitting a person. (I’m not making that up.)

Probably the strangest thing to understand about orbits is that an orbiting object is always in freefall: it is constantly ‘falling’ without necessarily getting any closer to the thing it’s circling.

Newton's Cannon - orbit explanation

Newton's explanation of orbits: A cannon firing at different speeds. Shots A and B will fall to Earth, C will enter a circular orbit, D results in an elliptical orbit, and E is fired beyond "escape velocity".

One consequence of this fact is that if you are orbiting the planet in a shuttle or a space station, you feel weightless – even though the ISS (International Space Station), for example, is only at an altitude of about 360 km, or about a three-and-a-half-hour drive down the highway. This is why I always feel a bit nervous whenever I see an astronaut perform a space walk in orbit: the only thing keeping them up there is their forwards speed. A little booster rocket fired in the wrong direction would be disastrous.

Luckily, everyone involved in space travel seems to have a very firm grasp of the mathematics of the situation, and we below don’t have to keep looking up to watch for falling astronauts. Still, it can’t hurt to keep an eye out, just in case.

Big Ideas:

  • Orbits are elliptical rather than perfectly circular.
  • Orbiting objects always lose speed over time, and will eventually fall into the thing they’re orbiting.
  • The gravitational pulls from the sun and the moon cause the tides.
  • Orbiting objects are actually in freefall and thus experience weightlessness.
  1. A lot of people seem to leave high school with the idea that this phenomenon is what causes the seasons, but that is incorrect. During the northern hemisphere’s summer months, the Earth’s ‘upper’ half is tilted towards the sun, meaning it gets more direct sunlight. During winter, the tilt goes the other way, and Australians get to enjoy barbecues and surfing while we’re stuck indoors waiting for the snow plow to come by. It’s the tilt and whether the sun is hitting us straight on or at an angle that results in the temperature differences – the distance to the sun doesn’t change nearly enough to have much effect.
  2. Pluto’s orbit is distinctly un-circular – its solar distance varies from 7.3 to 4.4 million kilometers, meaning that it is sometimes closer to the sun than Neptune. That’s just one more reason why Pluto is not thought to have originated in our solar system like the eight planets did. (That argument has nothing to do with its recent demotion from ‘planet’ to ‘dwarf planet’, however, which had mostly to do with its size.)
  3. It’s also believed (though not yet proven) that a gravitational orbit constantly loses energy in the form of something called gravitational waves.
3.4 Orbits   (from Chapter 3: Gravity and Orbits)


   

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