Apparent Speed of the Sun

[Kyrisch]

Using a stopwatch, a stick, a ruler, and a shadow cast by my house and the sun, I estimated the apparent speed of the sun.

 

Or so I thought.

 

I ended up with a rough number of 75 mm in 5 minutes. Now, doing the math, we get 900 mm in and hour, and 21,600 in a day. That means the sun's light apparently travels 2,160 cm in a day, or 21.6 meters. This can't be right. Can anyone tell me what I did wrong?

[radman]

err, doesn't the earth move? or have you taken that into account?

[mezarashi]

The "speed of the sun"? As in the apparent speed of the sun across the sky? There isn't much of a meaning to that as far as I can think. It's more like the sun moves 180 degrees across the sky within a certain time frame. From there you can calculate the degrees/minutes/seconds transversed per second assuming uniform rotation of the Earth.

 

As for what you did wrong, if you would elaborate on your experimental setup, because the numbers you have there are just unit conversions from the original 75mm/5min.

[Kyrisch]

err, doesn't the earth move? or have you taken that into account?

 

That's why I said apparent speed of the sun. I am, of course, in essence, calculating how fast the earth turns.

 

As for what you did wrong' date=' if you would elaborate on your experimental setup, because the numbers you have there are just unit conversions from the original 75mm/5min.[/quote']

 

I placed a twig (I know, not very scientific, but it's still effective) on the edge of the shadow cast by my house and started a stop watch. Five minutes later, I measured the distance between the twig and the edge of where the shadow was presently. I arrived at what I said before 75mm/5min. I was going through the conversions because 75mm/5min is not very tangible, but 21.6 meters in a day is more easily grasped. It is obviously wrong, because the sun "moves" across the entire planet in a day. The circumference of the earth is most definitely not 21.6 meters.

[mezarashi]

I placed a twig (I know' date=' not very scientific, but it's still effective) on the edge of the shadow cast by my house and started a stop watch. Five minutes later, I measured the distance between the twig and the edge of where the shadow was presently. I arrived at what I said before 75mm/5min. I was going through the conversions because 75mm/5min is not very tangible, but 21.6 meters in a day is more easily grasped. It is obviously wrong, because the sun "moves" across the entire planet in a day. The circumference of the earth is most definitely not 21.6 meters.[/quote']

 

Unless you know more, you cannot tell how fast the Earth is turning in say meters per second. You can tell however, how fast it is turning in radians (degrees) per second. And by that, you can tell how fast the sun is transversing our hemisphere in radians per second as well.

 

What you need to understand is a bit of geometric analysis. You are measuring the speed of the shadow using your house as a reference. If you draw your house out as a thin tower (which is a good enough estimation), then you see something similar to this diagram ( I found it hard to explain without using one unless someone is familiar with such calculations)

 

The goal is the calculate the angle theta I have indicated there. Once you have that. You can will know the sun has moved x degrees in 5 minutes. There is a total of 180 degrees (approx. since the Earth is curved). You need to use only the sine rule and other basic geometric rules for triangles.

 

Hint: Theta is equal to (Angle a - Angle b)

[Kyrisch]

I already know that the earth moves 15° per hour, common knowledge; I wanted to see if I could figure out an actual linear measurement, which, apparently, I cannot.

[Martin]

Using a stopwatch' date=' a stick, a ruler, and a shadow cast by my house and the sun, I estimated the apparent speed of the sun.

 

Or so I thought.

 

I ended up with a rough number of 75 mm in 5 minutes. Now, doing the math, we get 900 mm in and hour, and 21,600 in a day. That means the sun's light apparently travels 2,160 cm in a day, or 21.6 meters. This can't be right. Can anyone tell me what I did wrong?[/quote']

 

Trig, kyrisch

 

near sunset, shadows on flat ground lengthen very rapidly

 

around noon shadows change length only very slowly

or move very slowly, if you are watching the shadow of a twig move

 

at what time of day did you measure the change-rate of the shadow?

[Kyrisch]

Between noon and three.