## 26 March 2007

### PIZZAQ: my neighbor measures the time it takes for his radar to reach la Lune and return to his backyard

clicking makes it prettier
but not more helpful

4 slices with pepperoni, wild mushrooms and shallots:

My amateur radio neighbor aims his radar dish at the Moon. His radar signal bounces off the Moon, and his parabolic dish receives the echo 2.6367241033 seconds later.

At that moment, how far is my neighbor's backyard from the surface of the Moon? Please give your Answer in kilometers.

#### 6 Comments:

Jim Olson said...

Ok. So, radar signals travel at the speed of light, approximately 186,000 miles/second, or approximately 300,000 kilometers/second.

300,000 km/sec x 2.6367241033 sec = 791017.23099000007 km.

Of course, in the time it took to calculate this equasion, the moon would have moved approximately 50 meters closer or further away, depending on where it was on its orbit.

Tuesday, 27 March, 2007
Bob Merkin said...

300,000 km/sec is an easy-to-remember rule of thumb, but the actual value -- actually a definition -- of the

speed of light in a vacuum =
299,792.458 km/sec

which is the value I used, so you should, too, if you want our answers to agreee close enough for Pizza.

Never mind that the Moon moves thisaway and the Earth travels thataway while the radar signal travels to and from the Moon.

The only instant that matters is the "bounce moment," when the radar signal hits the Moon and its echo starts back to Earth again. We're measuring the distance at that moment.

But your Earth-Moon distance is way out of the ballpark, so you did something else wrong. Try again.

1. Draw a picture, which will help you get the geometry and the logic of the problem clear. (But it's not a trick question in any way).

2. Check and double-check your arithmetic.

I'll try to stalk my neighbor and ask him for some actual time values he gets, and some other nifty hands-on nuts-and-bolts gossip about bouncing radar signals from the backyard to the moon.

Wednesday, 28 March, 2007
Bob Merkin said...

oh, you can also Google "Earth-Moon distance" and that will give you values in km for

perigee (Moon and Earth closest)

apogee (Moon and Earth farthest)

so the distance you want has to be somewhere in between. If you compute something greater than apogee or less than perigee, you've made some sort of mistake.

Wednesday, 28 March, 2007
Jim Olson said...

Oops. I calculated the round trip.

299,792.458 km/sec x 2.6367241033 = 790469.99999675 / 2 = 395234.99999807 km.

Better?

Wednesday, 28 March, 2007
Bob Merkin said...

395235 km ... close enough for Pizza!!! Excellent!

How's your telescope holding up? Seen anything cool?

Thursday, 29 March, 2007
Jim Olson said...

Sadly, I sold it when I moved to Boston. There was no place to put it and I wasn't going to be able to see anything with all the light pollution here anyway. A very nice teenage boy bought it and was thrilled to have it.

Thursday, 29 March, 2007

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