A sense of scale: Beyond the Earth’s paper-thin atmosphere

FIGURE 1. If the Earth was an apple, the apple’s skin might be a good scaled approximation of the thickness of the Earth’s atmosphere. [Image source: Wikipedia Commons]

In yesterday’s blog entry, we tried to come to grips with the actual thickness of the Earth’s atmosphere. To do so, we drew the first four layers of the atmosphere to scale on a single piece of A3-sized paper oriented in the portrait direction. In this model, it was determined that, if the first four layers of the Earth’s atmosphere could indeed fit within a span of 42 cm, then the size of the Earth in this model would need a radius of 53.5 meters. To help put these dimensions into further perspective, imagine a normal-sized apple: the ‘flesh’ of the apple is the Earth, while the apple’s thin skin approximates the thickness of the Earth’s atmosphere!

We then asked four questions of our Earth/Atmosphere model. Each of these questions, and their answers, are presented below.

Click anywhere on the image to enlarge it.

If our model Earth here on the TASIS campus has a radius of 53.5 m, how many kilometers (km) would we have to travel from campus in order to arrive on the surface of the Moon?

  • Answer: 3.23 km from the TASIS campus, which would actually put us into Lago di Lugano if we were to walk 3.23 km from TASIS in a southeastern direction towards Campione d’Italia. [In terms of actual distance, the real Moon is somewhere around 384,400 km away from the real Earth.]

Click anywhere on the image to enlarge it.

If our model Earth here on the TASIS campus has a radius of 53.5 m, how many kilometers (km) would we have to travel from campus in order to arrive on the surface of the Mars?

  • Answer: 458.64 km from the TASIS campus, which would actually put us into central Italy if we were to walk458.64 km from TASIS in a southeastern direction towards Roma/Rome, Italy. [In terms of actual distance, the real Mars is somewhere around 54,600,000 km away from the real Earth.]

Click anywhere on the image to enlarge it.

If our model Earth here on the TASIS campus has a radius of 53.5 m, how many kilometers (km) would we have to travel from campus in order to arrive on the surface of the Sun?

  • Answer: 1’256.64 km from the TASIS campus, which would actually put us into Lago di Lugano if we were to walk1’256.64 km from TASIS in a southeastern direction towards Athens, Greece. [In terms of actual distance, the real Sun is somewhere around 149,600,000 km away from the real Earth.]

If our model Earth here on the TASIS campus has a radius of 53.5 m, how many kilometers (km) would we have to travel from campus in order to arrive on the surface of Alpha Centauri–the nearest star which is not our Sun?

  • Answer: 336,000,000 km from the TASIS campus, which would actually put us…well, that’s a bit more difficult to say. Since the Earth is about 40,000 km in circumference at its thickest point, the equator, one would need to make about 8’400 complete laps around the Earth’s equator in order to travel 336,000,000 km!!! So, we can’t really put a ‘dot’ on the Earth to represent the distance needed by the conditions or our model. [In terms of actual distance, the real Alpha Centauri is somewhere around 40 trillion km (40,000,000,000,000) away from the real Earth.]
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Posted in Middle School Science, Space Science | Tagged , , , , , , | 1 Comment

A sense of scale: The Earth’s atmosphere on a piece of paper

FIGURE 1. First four layers of the Earth’s atmosphere draw onto a single piece of A3-sized paper.

Large/long distances are difficult to experience, let alone imagine. This past week in our middle school science class we tried to develop a sense of scale as it relates to the thickness of the Earth’s atmosphere, a topic that we have been recently studying.

Starting with an A3-sized piece of paper oriented in the portrait format (w: 29.5 cm, h: 42 cm), my students were asked to represent the first four layers of the atmosphere to scale on the paper. On this paper, the scale was 42 cm = 500 km. To put this differently,  every 1 cm = 11.9 km or, in the reverse, every 1 km = 0.084 cm. An example of such a scale map can be seen at right in Figure 1. In Figure 1, a size D Duracell (battery) cell is included to help those unfamiliar with A3-sized European paper to better imagine the actual size of it.

One reality that rather quickly stands out in this representation of the Earth’s atmosphere is just how ‘thin’ the first layer of the atmosphere (the troposphere) actually is when compared to the other layers. This scale map also shows that the next thickest layer is the mesophere, which is followed by the stratosphere, and then the thermosphere. The fifth and outermost layer of the atmosphere, the exosphere, is not represented on this map. But about the size of the Earth? If this scale were actually true, that is, if the thickness of the first four layers of the Earth’s atmosphere were in fact equal to the height of an A3-sized piece of paper, then how large would the radius of the Earth need to be in order to, as we often say in English, be true to scale?

FIGURE 2. Our 4-layer atmosphere is visible on the edge of the nearest outdoor basketball court (A3 paper), but these two courts are still not enough to constitute a properly scaled radius of our Earth.

Is the width of an outdoor basketball court (approx. 13 m) enough?
No, it’s not enough.

How about the the width of two outdoor basketball courts (approx. 26 m)? Would that be enough?
Not yet.

Figure 2 shows our piece of A3 paper laying on the near edge of two rectangular basketball courts on the TASIS campus, just outside of our science building. The combined width of these courts–from the bottom to the top of the image–is approximately 26 meters, but in order to be true to scale, the radius of our model Earth would require us to have two additional outdoor basketball courts stacked beyond the existing courts. Only with FOUR courts could we have an Earth with the radius it needs to be true to our A3-sized paper scale. A four-court Earth would have a radius of approximately 53.5 meters–but remember, the radius is half of the diameter, so in actuality we would need EIGHT basketball courts if we wanted to estimate the ‘true’ size of the (entire) Earth in this scale model!

An Earth the with diameter of EIGHT basketball court-widths, which has a four-layered atmosphere that is the size of an A3-sized piece of paper. Now that is a useful sense of scale…

In tomorrow’s blog, we will expand our A3-sized paper model in an attempt to answer the following questions:

  • If our model Earth here on the TASIS campus has a radius of 53.5 m, how many kilometers (km) would we have to travel from campus in order to arrive on the surface of the Moon?
  • If our model Earth here on the TASIS campus has a radius of 53.5 m, how many kilometers (km) would we have to travel from campus in order to arrive on the surface of the Mars?
  • If our model Earth here on the TASIS campus has a radius of 53.5 m, how many kilometers (km) would we have to travel from campus in order to arrive on the surface of the Sun?
  • If our model Earth here on the TASIS campus has a radius of 53.5 m, how many kilometers (km) would we have to travel from campus in order to arrive on the surface of Alpha Centauri (the nearest star which is not our Sun)?
Posted in Earth Science, Grade 7, Middle School Science, Space Science | Tagged , , , , , , | 1 Comment

Well, it’s about time!!!

What time do you get up in the morning? What time do you go to school? How much time does it take you to eat your lunch? What is your bedtime? What time is it now? We ask questions about time every day. Or rather, to put it differently, we live questions about time every day.

Growing up in the 1970s, 80s, and 90s in the United States, my friends and I mostly used battery powered wrist watches to ‘tell’ time. Nowadays, my middle school students mostly use battery powered smart phones and, most recently, various brands of smart watches. But if you really want accuracy and precision in your time keeping, you will follow an atomic clock.

What is an atomic clock? How can atoms keep time? Watch the creative 2 minute video below and see if it is able to answer some of these questions (and others)…

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