if you have the ISS circle a globe, it's orbit is 1/16 of an inch above the surface. ?

Factual Questions
1

I heard Neil DeGrasse Tyson say something like this: “If you take a globe and imagine the ISS orbiting around the globe, it’s height above the globe surface would be 1/16 of an inch.”

He didn’t specify the size of the globe. Now, my addled brain couldn’t get the math to work to see if this is true. My assumptions: the ISS is 230 miles above the surface of the earth. The earth’s radius is 4000 miles (approx.).

So, is this true? How big would the globe have to be to make this true? And what is the math (simplified!) to show this is true?

Thanks,
Jeff

2

.0625/x = 230/4000, x = 1 inch.

3

First, let’s convert units.

If the ISS is 230 miles above the Earth, that’s 230 * 5280 * 12 = 14572800 inches

If the Earth’s radius is 4000 miles, that’s 4000 * 5180 * 12 = 253440000 inches.

Therefore, the conversion factor is 16 * 14572800 or 233164800

253440000 / 233164800 = 1.08, or about an inch and a sixteenth radius of the globe.

That’s a pretty small globe, unless I fudged the numbers somewhere. Sounds like it should be even closer.

4

NM - mathed wrong.

x/.0625 = 4000/230

x = 1.0869 inches.

5

A reasonable globe of 12" diameter, with a 6" radius, would have the ISS about .345" off the surface - somewhere between 5/16" and 3/8".

6

The radius of Earth is 3959 miles, and your run of the mill 12" globe has a radius of 6 inches. The radius of the ISS orbit is 4189 miles, so on that 12" globe it would be ~0.35 inches off the surface.

4189/3959=1.0581

6*1.0581=6.3486

So more like three-eighths of an inch.

(Ninja’d, but I’ll post anyway.)

7

It’s turns out, that’s pretty much what Tyson said:
http://blog.al.com/space-news/2010/12/astrophysicist_neil_degrasse_t.html

8

Using the 3/8" number for the ISS, how far out is geosynchronous orbit?

Sorry, my math is in the shop this week.

9

Geostationary orbit is 22,236 miles above the surface. We were using 4189 for the ISS orbital height, so geostationary would be 5.3 times that, or almost exactly 2 inches!

10

Sweet. Thanks, chrisk!

11

That doesn’t seem right… 22,236 miles divided by about 4000 mile radius would be about 5 and a half times the radius or about 2 and 3/4 feet ?

12

Whoops, sorry! Math only works if you plug in the correct numbers! :smack:

22236 / 230 * (3/8) = 36.25 inches, or a little over three feet away!

13

Ah! Even better! :slight_smile:

14

See here:

The white dot at the upper right corner represents an object at about 600km from the surface of the earth. The ISS is even closer than that at 300-400 km