Friday, October 25, 2013

The House Clock: What Time is it?

In the kitchen of a friend's house is this plate hanging on the wall. On it is a warm, yellow sun shining down on the house and green grass. The plate is located in a place one might find a clock hanging on the wall. Someone inquired about the current time, since they weren't able to read the time from this plate. This generated some discussion as we attempted to answer the the question: According to this plate, what time is it?

The time, according to this plate hanging on the wall, can be decided by the position of the sun. However, we are missing some information. The time depends on the direction we are looking. Since this question is difficult to answer for any perspective, I will only focus on four directions--looking north, south, east, and west.

If we are looking North:
It is approximately 11:00 AM, and we are in the southern hemisphere.

We know the sun rises in the east and sets in the west. So we know it is 11:00 AM because the sun is to our right (east). We know we are in the southern hemisphere because the sun is in front of us. For us to be in the northern hemisphere the sun would have to be behind us and would not have been painted on the plate.

If we are looking South:

It is approximately 1:00 PM, and we are in the northern hemisphere.

Again, the sun rises in the east and sets in the west. If we are looking south, west is to the right which is the direction the sun is moving. (It's a little odd there are no shadows cast by the house. That is one of the few inaccuracy's in the painting. The artist should have painted a stratus cloud cover if they wanted to avoid painting shadows.) We know we are in the northern hemisphere because the sun is in front of us. It is difficult to say our exact latitude because the plate gives us no sense of how far we are from the house. But, if I were to take a guess, I'd say we were north of 50 degrees north due to the low sun angle.

If we are looking East:

We can not determine an approximate time, but we know it is morning in the northern hemisphere.

We cannot tell the time because we cannot determine the solar angle based on the dimensions drawn on the plate. But we do know it is morning daytime hours because the sun is in front of us. If it were afternoon the sun would be behind us. We can also tell that we are in the northern hemisphere because the sun is to our right (the direction of the equator).

If we are looking West:

We can not determine an approximate time, but we know it is after noon and we are in the southern hemisphere.

Again, we cannot tell the exact time, but we know is is afternoon because we can see the sun as the sun begins to set in the west. We also know we are in the southern hemisphere because the sun is to the right (the direction of the equator).

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