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Friday, April 26, 2024

If you’re in orbit, is it possible to throw something down to earth?

A STAFF REPORT FROM THE STRAIGHT DOPE SCIENCE ADVISORY BOARD

By  Straight Dope Staff
   
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Dear Straight Dope: There is a very cool thing I want to do before I die. Years ago, David Letterman used to heave vegetables off the roof of a three story building with an effect I can only describe as satisfying. I would love to pop open the bay doors of the shuttle and lob God-knows-what earthward and watch it burn. From what I’ve read, shooting stars are no larger than a grain of sand flaming through the atmosphere, yet look at how bright they are as they incinerate. Imagine how pretty a handful of ball bearings chucked at the globe would look! Or how about a bowling ball? I can’t believe no astronaut has tried this yet. “Well, Houston, looks like the satellite is fixed. Guess we won’t need this wrench anymore, so . . . [heave] Whoa! Look at her BURN!!” This idea has pay-per-view written all over it. How do I get the ball rolling? Dear Straight Dope: I understand that the International Space Station is in orbit around the earth, and thus in a state of constant free fall. If the astronauts took a box of baseballs out side the station on EVA, could they throw them down to earth? If so, how long would they take to get here based on a 93 MPH fast pitch? How many additional rotations around the earth would they make on the trip down? And finally, as I’m standing in my backyard gazing at the night sky would I see the baseballs burn up in the atmosphere or are they too small to cause any “shooting stars”? Tim; Bert

Chronos replies:

Couple things before we get into this. First of all, Tim, take a good, long look at Bert’s letter. Notice anything? That’s right, he actually asks questions. Makes it much easier to answer. Second, at the risk of casting a pall over the discussion, I should say that Tim and Bert submitted their notes, and I wrote my answer, before the Columbia disaster. We’ve waited these past few months to post the article for obvious reasons. The topic is interesting, though, and time marches on. So here we are.

With that out of the way, let’s take a look at orbital dynamics. You can’t actually throw anything (or yourself) out of orbit–all you can do is throw an object, or move yourself, from one orbit to another. If you want to go to a higher orbit, you need to increase your speed in the direction you’re traveling. If you want to go to a lower orbit, you need to decrease your speed. Just trying to thrust straight up or down won’t work too well: Thrusting down, for instance, will lower you temporarily, but now you’re going too fast to stay in that lower orbit, and you’ll end up oscillating back above your original orbit. As science fiction author Larry Niven put it, “East takes you out, out takes you west, west takes you in, and in takes you east.”

To get those baseballs to earth, you want to throw them back from the shuttle. Now they’re traveling slower. The effect of this is to put them into an elliptical orbit, whose apogee–the point furthest from the center of the earth–is at the same height as the shuttle. If the orbit is elliptical enough, then its perigee–the point closest to the earth’s center–will be closer than the surface of the earth, and the ball will collide with the earth after half an orbit or less. But if it doesn’t hit the earth (and if we ignore atmospheric friction for the moment), it’ll stay in that nice comfortable elliptical orbit indefinitely.

Now for the specific problem of astronauts throwing fastballs: The space station is at a height of about 390 km over the surface of the earth, for a total distance of 6,768 km from the center, and it’s traveling at about 7,674 m/s. Our 93 MPH pitch translates to about 42 m/s, so the total speed of the ball is then about 7,632 m/s. Given that energy and angular momentum are conserved, it’s straightforward (if a bit tedious) to calculate that, at perigee, the ball will be 6,623 km from the center of the earth, which is still a comfortable 245 km above the surface.

But this is all figured without the atmosphere. Won’t friction from the topmost layers of the atmosphere cause the ball’s orbit to decay, and eventually bring it down? Yes, but that would happen even without pitching the ball. If left on its own, the space station itself would eventually fall to earth, but they boost the orbit every so often to prevent that. In fact, that’s why Mir was deliberately brought down: The Russians didn’t want to keep boosting it any more, and they knew that eventually it would come down on its own.

Finally, if an object the size of a baseball were to re-enter the atmosphere, it would certainly be visible. Most of the “shooting stars” you see are caused by particles the size of a grain of sand or so, and a baseball is much larger than that.

Chronos

Send questions to Cecil via cecil@straightdope.com.

STAFF REPORTS ARE WRITTEN BY THE STRAIGHT DOPE SCIENCE ADVISORY BOARD, CECIL’S ONLINE AUXILIARY. THOUGH THE SDSAB DOES ITS BEST, THESE COLUMNS ARE EDITED BY ED ZOTTI, NOT CECIL, SO ACCURACYWISE YOU’D BETTER KEEP YOUR FINGERS CROSSED.