by StarstruckKid » Fri Aug 13, 2010 6:44 pm
When first I came to Asterisk
An answer there to find
The postings I discovered there
Overwhelmed my mind
The learned and quotidian quotes
Like arrows pierced my breast
I beat a hasty exit
But could not let it rest...
(apologies to Joan Baez)
As I'm more engineer than scientist, that's my approach here. There's an advantage to that; engineers deal a lot in approximations, and sometimes that's all you need. For instance, common electronics components have a tolerance of +/- 10%, thus a '1000 ohm' resistor may have an actual value between 900 and 1100 ohms - so what's the point of a more precise calculation? Carefully chosen approximations can make calculations significantly easier to do (and thus less prone to error) and the inaccuracies can offset one another, giving a more accurate result than you might think. Here we go:
Assumptions:
1) The moon's orbital distance from the earth is about 235,000 miles.
2) The shadow of the moon moves across the face of the Earth at approximately the same speed as the moon moves in its orbit, since the Earth-Moon distance is swamped in the Earth-Sun distance.
Duration of the eclispe for a stationary observer: 6 min 39 sec.
Duration of the eclispe on the ship: 6 min 42 sec.
First, convert the times to seconds:
6 min 39 sec ==> 399 seconds
6 min 42 sec ==> 402 seconds
Next, calculate the moon's orbital velocity:
Length of orbit is 235,000 x 2 x pi (3.14) ==> 1,475,800 miles
Miles per day is 1,475,800 / 28 ==> 52,707
Miles per hour is 52,707 / 24 ==> 2,196
Miles per second is 2,196 / 3,600 ==> 0.61 miles per second
Next, how far did the moon (and its shadow) move in those extra 3 seconds?
0.61 miles/second x 3 seconds ==> 1.83 miles
So the ship moved 1.83 miles in 402 seconds.
1.83 / 402 ==> .00455 miles per second
.00455 x 3600 seconds per hour ==> 16.4 miles per hour
A completely reasonable answer for a modern cruise ship.
Also consider that, lacking an external reference such as a GPS, currents and winds would likely introduce some uncertainty in the actual speed of the ship. So if my answer is at all correct, the error introduced by my approximations might well be within the range of uncertainty of the ship's measured velocity.
I'd enjoy seeing the number a more precise - and learned - calculation would produce. And as an exercise, try rounding things significantly, like 3 for pi, 30 for the number of days in a lunar month, 25 hours in a day, try to do it in your head, see how close your result is.
Michael
[i]When first I came to Asterisk
An answer there to find
The postings I discovered there
Overwhelmed my mind
The learned and quotidian quotes
Like arrows pierced my breast
I beat a hasty exit
But could not let it rest...[/i]
(apologies to Joan Baez)
As I'm more engineer than scientist, that's my approach here. There's an advantage to that; engineers deal a lot in approximations, and sometimes that's all you need. For instance, common electronics components have a tolerance of +/- 10%, thus a '1000 ohm' resistor may have an actual value between 900 and 1100 ohms - so what's the point of a more precise calculation? Carefully chosen approximations can make calculations significantly easier to do (and thus less prone to error) and the inaccuracies can offset one another, giving a more accurate result than you might think. Here we go:
Assumptions:
1) The moon's orbital distance from the earth is about 235,000 miles.
2) The shadow of the moon moves across the face of the Earth at approximately the same speed as the moon moves in its orbit, since the Earth-Moon distance is swamped in the Earth-Sun distance.
Duration of the eclispe for a stationary observer: 6 min 39 sec.
Duration of the eclispe on the ship: 6 min 42 sec.
First, convert the times to seconds:
6 min 39 sec ==> 399 seconds
6 min 42 sec ==> 402 seconds
Next, calculate the moon's orbital velocity:
Length of orbit is 235,000 x 2 x pi (3.14) ==> 1,475,800 miles
Miles per day is 1,475,800 / 28 ==> 52,707
Miles per hour is 52,707 / 24 ==> 2,196
Miles per second is 2,196 / 3,600 ==> 0.61 miles per second
Next, how far did the moon (and its shadow) move in those extra 3 seconds?
0.61 miles/second x 3 seconds ==> 1.83 miles
So the ship moved 1.83 miles in 402 seconds.
1.83 / 402 ==> .00455 miles per second
.00455 x 3600 seconds per hour ==> 16.4 miles per hour
A completely reasonable answer for a modern cruise ship.
Also consider that, lacking an external reference such as a GPS, currents and winds would likely introduce some uncertainty in the actual speed of the ship. So if my answer is at all correct, the error introduced by my approximations might well be within the range of uncertainty of the ship's measured velocity.
I'd enjoy seeing the number a more precise - and learned - calculation would produce. And as an exercise, try rounding things significantly, like 3 for pi, 30 for the number of days in a lunar month, 25 hours in a day, try to do it in your head, see how close your result is.
Michael