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Ask Marilyn!

(May 13, 1997)
Oops! I blew it here. In the following article, I used the wrong number to get the circumference of the Earth at the latitude of Cape Canaveral, which ironically is what I accuse Ms. vos Savant of as well! To be fair and honest, I have included the correct, more detailed math below. Her number is not very far off, but then again neither was mine! ;-) I will quote the original Bad News section, then explain how I was wrong.

(Note added January 19, 1998: I have found an article where I believe Ms. vS is truly incorrect. It is on this page).

What I originally said:

Why do the NASA space shots all leave the Earth in an easterly direction instead of a westerly one?

She answers correctly, stating that when you launch a rocket east, you get an added boost from the rotation of the Earth. She then says that the added velocity is 1370 feet per second.

That number is wrong. At the Equator, the Earth spins at 1000 miles per hour (the Earth is 24,000 miles around, and spins once every 24 hours). This is 1467 feet per second. Now, as you move up in latitude that velocity decreases. Imagine standing at the North Pole; you are not moving at all, but simply spinning in place. The velocity changes with the cosine of your latitude. I looked up the latitude of Cape Canaveral, and it's 28.5 degrees North. The cosine of 28.5 = 0.88, so the rotation of the Earth at that point is 0.88 * 1467 = 1290 feet per second. Now, her number isn't really very far off, but it is incorrect. I wonder where she got it from? I am guessing she misread the latitude of Cape Canaveral off a map. The number she gets corresponds to a latitude of 21 degrees, which is 500 miles farther south.

Like, I said, it's a nit pick, but it gives me a chance to show the math behind the actual number presented!

Incidentally, there is a web site devoted to Ms. Vs's errors. The webmaster appears to really have it out for her! I recommend that site because it does have some interesting explanations to some of the questions.

The correction:
I said that the Earth is 24000 miles around, which is not quite right. The equatorial radius of the Earth is 6378 kilometers, or about 3986 miles. But the Earth is spinning, and this spin tends to flatten it a bit along the equator. The radius measured through the poles of the Earth is a bit less: 6357 kilometers, or about 3973 miles. If you were to slice the Earth in half through the poles, the cross-section would be an ellipse, not a circle. The math is a wee bit hairy, but not too bad, to calculate the circumference of the Earth at Cape Canaveral assuming the Earth is an ellipse with these numbers. The circumference I get is 35191.9 kilometers, or about 115,459,000 feet. The Earth rotates once every 23 hours and 56 minutes, giving a rotational speed at the Cape of 1340 feet per second. I believe this to be the most accurate number available without doing really hairy math! Note that it is closer to her number than mine. I still don't know how she came to her number; it seems logical that she also assumed a circular Earth but put in the wrong latitude. I chose the wrong radius! Given the uncertainty in the numbers going into the equation, I would say that the numbers we both derive are pretty close (though I point out again hers is closer than mine). There's bad astronomy, then there's Bad Astronomy. ;-)

Another minor correction: A loyal Bad reader pointed out to me that the original question asked why we launch rockets East instead of West. The reader then pointed out that you get a boost of 1340 fps over a non-rotating Earth, but twice that over launching West! This is really true. Silly of both Ms. vS and me. I stand corrected.

Special and humble thanks to Herb Weiner, curator of the Marilyn is Wrong web site and Craig Gentry for pointing out my error.

(Another note added November 20, 1998: I should be careful to add that in the entire preceding argument, we are discussing equatorial orbits. For a polar orbit, you don't launch East or West! The rocket needs to go in a northerly or southerly direction. Polar rockets are launched from Vandenberg Air Force Base in California. I have been informed by Bad Reader Lauren Pomerantz (from The California Space and Science Center) that polar rockets are launched towards the South, to avoid populated areas if the rocket should fail.

©2008 Phil Plait. All Rights Reserved.

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