CAPTAIN GG: Sundial
Mr A: What’s for dinner today? Shall I call my friend Daphne and we’ll have dinner?
Mom: Broccoli.
Mr A: Mum, I told you I want my friend to come and make a sundial with me in our garden. I want us to eat something tasty, beautiful to look at and play afterwards. You, without being able to understand me, say we have broccoli to eat! You say it with such satisfaction and triumph. I can’t understand you.
Mom: Of course I feel tremendous satisfaction! I managed to find purple broccoli and I’m looking forward to cooking it, and eating it of course. Isn’t it beautiful? I think your friend, Daphne, will be impressed with these purple flowers you’re going to offer her. It’s not your ordinary green broccoli.
Small A: Adrian, come quickly. Your friend Daphne’s here. Run.
Daphne: Good morning Mr. A. Good morning to all.
Dad: Good morning Daphne. I heard you came here today to make a sundial with Mr. A.
Mom: What a terrible idea. It sounds difficult though.
Mr. A: We will also have the help of Captain GG, who is a captain and an expert in astronautics.
We have all noticed that during the day the position of the Sun changes in the sky: it starts in the morning at dawn in the East, crosses the whole sky and sets in the evening in the West, which is opposite to the East. The position and length of the shadow of a tree or a PPC pole changes during the day.
We want to observe and record the properties of this shadow during the day.
Daphne: We also need to measure some properties of the place where we put the clock.
Small A: I’ve seen a sundial in the National Garden.
Mr A: We want to make a similar clock ourselves.
To make the clock, we need to measure the angle of the clock φ . We will see that it is equal to the latitude of the location of the clock. We will also find out what the orientation of the gnomon needs to be.
Dad: You are very lucky to have chosen today to do your construction. The weather forecast for today is very good. Truly, I am full of anticipation to see the results.
Now Daphne takes the lead and tells little A to bring a stick that looks like the gnomon in the picture. You have to pin it to the earth so that it is parallel to the axis of the earth. So, they need to find the north pole of the Earth and the angle f
Mom: But how do we find the north pole from where we are?
Mr A: This is very easy. Mom, make us sandwiches, put some juice on them and leave them on the kitchen table. Tomorrow morning Daphne and I will tell you exactly where the north pole is.
Mom: I know very well that there is a geographic and a magnetic pole of the Earth. They do not coincide. Do you know which one you have to find for the sundial? Is it better to wait for Captain GG to return from his trip to help;which forms the axis of the Earth with the ground.
Daphne: I asked my dad, who is an astronomer, and he told me that since the stick we are going to stick into the Earth must be parallel to the Earth’s axis, we have to find the geographic north pole.
Mr A: So we did well to ask for the sandwiches. We’ll stay the night and find the polar star. Mr. A and Daphne’s goal is to find the polar star in the night sky. The polar star shows where the north pole is. The two of them are going to stay up all night eating the sandwiches their mom made for them so they can find the polar star.
Night. Mr. A and Daphne are enthusiastically preparing for the job they have taken on.
Daphne: I’m sure, Mr. A, that you know how to find the Big Dipper in the night sky. Right?
Mr A: This is too easy, Daphne. Who doesn’t know how to find the big pot? It’s so easy. But I always have trouble finding the Little Dipper.
Daphne: Look carefully at the photo of the two pots and pans. You just extend one side of the big Bear five times and you fall on the polar star that is at the edge of the little bear’s hand.
Mr A: It’s getting dark for good. Tonight is an extremely clean night. Not a cloud hides the sky. It’s hot, too. It’s very pleasant to sit outside, eat sandwiches and look up at the sky looking for the polar star. I found the Big Dipper! What did you say, Daphne, that I have to do to find the North Star?
Daphne: You extend five times on the far side of the Big Dipper and fall on the polar star.
Daphne: We found where the north is: where the village is across the road.
Mom: ‘Good for you. You two are a great team! You also ate all the sandwiches I made last night. Were they tasty?
Mr A: You always say nice things! A thousand thanks. The truth is that we are having a great time together. We both like to explore and learn new things.
Mr A: Mom, you said Captain GG was coming tonight, didn’t you?
Daphne: Now we need his help to find the angle that the stick we are going to poke into the Earth should be at with the plane of the Earth. If he’s a captain, he should know. My dad told me that the angle we are looking for is equal to the latitude of the place where we want to make the sundial. Captain GG must be able to calculate the latitude and longitude of any point on Earth.
Mom: Captain GG came last night from Crete where he was. He also brought two cheeses from there. I’ll cut you a few pieces of the Cretan gruyere he brought. I’m going to save the myzithra to make myzithro pies, which I love. He also brought a strange instrument. He told me to tell you that he would come at dusk to explain what it is and how we can use it to find the latitude(f) of a place.
The Exodus
Dad: Tonight is a lovely, warm August evening. I say we grill something to eat with the purple broccoli.
Captain GG: Good evening. Did you like the cheeses I brought from Crete? I hear you want to make a sundial using astronautics. Well, to make the construction you want, you need to know where north is and the latitude of the place where you are going to make the clock. Look carefully at the shape. φ is the angle you want to measure. Look carefully at the shape with the corners. Remember some very simple corner relationships you learned in school. You will discover that latitude(φ) is equal to the angle formed by the horizon of place A with the line pointing in the direction of the polar star.
Mom: Could you explain the shape first?
Captain GG: Of course, my pleasure. S.P. and N.P. are the south and north poles respectively, M is the center of the Earth, A is the place on the Earth on which we want to calculate the latitude ( φ ), for example your garden. HH is the horizon of place A.
Suppose the polar star is just above the north pole and its light is coming towards Earth as shown in the figure.
Our goal is to measure the angle φ.
Daphne: Exactly, this is the angle we need to make the sundial.
Mr A: So, if I understand correctly, we have to measure the angle that the horizon makes with the rays from the polar star.
Captain GG: The instrument we use to make this measurement is the extractor. This is the instrument I brought you and we’re going to use it to do the measurement. Of course, there are now modern ways to calculate exactly where we are on Earth.
Daphne: GPS is called. Global Positioning System (GPS). This system uses the data we get from satellites orbiting the Earth.
Mr A: I can find that with the smart phone. I have.
Daphne: But in case this system stops working for whatever reason, we won’t be able to go home, eat and sleep.
Mr A: That’s why we must always have another way to find out where we are.
Captain GG: Exactly, that’s why we’re learning how the extract works. Who’s going to hold the sextant and take the first measurement?
Mr A: I would love to do it myself.
Daphne: I want to.
Captain GG: Okay, we’ll all take a measurement. There are five of us. Then we will calculate the average of the 5 values we will measure.
Daphne: I think, as my astronomer dad would say, this is the right scientific way to measure what we want.
Captain GG: Since it’s dusk, we don’t need to put in front of his sextant telescope the filters we put on when observing the Sun to reduce the brightness of the image.
This photo shows very graphically how the extractor works and how to measure the angle of interest. With the sextant, the angle between the observer’s horizon and the stars around the north or south pole is measured to determine the latitude.
Mom: I’ve heard that in the old days, when they didn’t use those filters to reduce brightness, many sailors lost an eye trying to use the sextant.
Dad: Is that why they wore the black patch over one eye?
Mr A: I have read that they put the cover on one eye to get the eye used to seeing in the dark. Then, when they had to fight in the dark hold, they would take off the black cover and put it on the other eye.
Daphne: So they had one eye for light and one eye for darkness.
Captain GG: I don’t know. There is no report left. The two explanations you give sound very reasonable.
Mr A: Shall I take the first measurement?
Dad: We’ll all take measurements.
Captain GG: Yes, all of them. The small A, which may not be able to keep the sextant constant, will add up all the values we take. It will then divide the sum it finds by the number of values we collected.
Small A: I really like that I will do the calculations. Shall we get started?
Dad: When we find the latitude ( φ ), we will have all the numbers needed to make the clock. Then we can start baking!
Mom: I’m getting hungry. I’ll boil the purple broccoli.
Captain GG: We got 5 prices. Remember them, little A? Will you do the addition and division by 5?
Small A: If I add up all the 5 numbers you got I get 200.
Caaptain GG: Do the division, little one!
Small A: 40
Daphne: Very good measurement we did!!! The 40 is very close to the number that many books give for the latitude of Athens!
Dad: Shall we start baking then?
Small A: What about the ice cream you promised me?
Mr A: You have your mind on food all the time. We have not finished building the clock.
Mom: Now it’s getting dark. Aren’t we eating better now? I suggest you continue tomorrow morning with a clear mind.
Mr A: Mom, normally we have to ask my friend if she can come tomorrow.
Daphne: I heard you. Tomorrow we’ll just write the numbers around the gnomon. The shadow of the gnomon will fall on the number and we will read what time it is.
Mr A: That’s exactly right, Daphne. I’m so lucky you agreed to be on my team. We have a lot to build and learn together.
Daphne: I’ll come back tomorrow morning to finish the clock. I will also bring a protractor to measure the angle between the hours.
Mom: I’ll make the cheesecakes for breakfast tomorrow. I’m going to use the myzithra that Captain GG brought us from Crete.
Dad: I’m starting with the baking.
Small A: I hope we all want to eat ribs!
Mr A: Now that it’s getting dark, I say we go back and see where the north pole is so we can be ready for tomorrow morning.
Daphne: How right you are Mr. A, because we won’t be able to see the polar star in the morning. I remember that the north is in the direction of the village opposite.
Small A: I’ll remember it for tomorrow.
Mom: How nice that broccoli is! We should finish eating so we can get to bed early tonight. I’ve got some cheesecakes to make tomorrow morning and you have a clock to make. Good night. Good night.
ZZZZ
Daphne: Good morning. I’m here to finish the clock.
Today, we need to build the board with the times of day. The shadow of the gnomon will be projected on this plate. It will record the times of day as shown in the figure. The board must first be oriented. The B of the figure must coincide with the north of the site.
Small A: You told me yesterday to remember where north is from where we are and I remember.
Dad: I took the liberty yesterday of seeing what a good job you two are doing and ordered a metal gnomon. The base will be coming soon. You have to orient it correctly, stick the gnomon to the plate and then take the measurements.
Small A: When do we eat the ice cream?
Mr A: We’ll eat the clams first! I say we get started. Daphne came along. Did the things you said come, Dad?
Daphne: We will try to make the clock in the picture. This sundial is located in the National Garden of Athens. That’s how ours will be.
Mom: The clock and the nose cakes are ready. Both are wonderful.
Captain GG : I look forward to the next build we will build together.
