Space and Gravity

Solar flare, with Earth for scale.  Image credit: Karl Battams and NASA SDO.
Solar flare, with Earth for scale. Image credit: Karl Battams and NASA SDO.

Space: An Out-of-Gravity Experience opened last week at the Science Museum of Minnesota. I have seen the exhibit, and it is spectacular.

One of the major points the exhibit makes is about gravity, and whether or not there is gravity at the International Space Station, or on the way to Mars or other planets.

Here on Earth, the influence of gravity is pretty obvious. If you throw a ball, it will fall back to Earth fairly quickly. Were you on the Moon or Mars, you could hop around in your space suit, secure in the knowledge that gravity would pull you back down, and insecure about whether your rocket would take you back to Earth.

I will answer that with two questions, which you could imagine asking a stranger in this order:

  1. Why are astronauts are apparently weightless when here on Earth we’re firmly held?
  2. Why, despite the Sun’s great mass, do we not fall into the Sun?

Why don’t we fall into the Sun?! What an absurd question to think about!

The answer has to do with what it means to be in orbit. Randall Munroe of XKCD explains:*

Space is like this:

Imagine you have a machine which can shoot a baseball horizontally at any speed you choose (under the speed of light, and you probably don’t want it getting near that fast anyway). As with many physics thought experiments, we will ignore air resistance. When you start out at reasonable speeds, similar to that which a baseball pitcher throws, it will hit the ground. As you increase the speed, it goes farther and farther before reaching the ground. Keep this in mind.

The Earth is not flat. Although it can seem that way in some areas, the Earth is indeed roughly spherical. At some speed, the baseball will fall toward the Earth in an arc which parallels the Earth’s surface. That speed is the orbital speed (about 8 km/s).** Above about 11 km/s, the baseball would leave the Earth, never to return unless affected by another body. Orbiting the Sun, Earth is moving around 30 km/s along its orbit.

When astronauts experience weightlessness, it is because the spaceship they are in is falling to Earth at the same rate as they are. Think of it like a roller-coaster starting it’s drop, but that just keeps going down and down and down.

Here’s another question for you: which body exerts more gravitational pull on you, the Earth, or the much-more-massive Sun?

To find out, let’s do some (easy!) math. We know from Wikipedia that the attractive force due to gravity is G*m1*m2*d-2, where G is the gravitational constant, m is the mass of the two objects in question (e.g. you and the Earth), and d is the distance between their centers. Approximate a human mass as 60 kg, use your favorite search engine to find the mass of the Earth and the Sun in kg, the radial distance of the Earth in meters, and the orbital distance of the Earth from the Sun in meters, and plug away.

The result? Earth pulls on you more than the Sun, by a factor of ~1600. This makes sense. If the Sun pulled you more strongly than the Earth, you would move toward the Sun, fall in, and die.

Between the Sun and the Earth, there is a point where the gravitational influences and centrifugal force all cancel each other out. This point is the Lagrangian point L1, and is a gravitational sweet spot much like an orbital speed is just right.

Now that things are just right, I should probably wrap things up. Any further addition will send me diving down the rabbit-hole again!

* Incidentally, xkcd and particularly the xkcd what-if comics are among my favorite things to read. I almost think an Ig-Nobel Prize might be deserved for cartoons which make us laugh, then think.

** The orbital speed is somewhat dependent on orbital distance; things further out have a slightly lower orbital speed.

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