180: Day 26: How does GPS work?

students creating scale models of GPS satellite orbits

Two summers ago I was able to attend the Einstein Plus workshop at the Perimeter Institute for Theoretical Physics. They provided some great mini-units on ‘Modern Physics’ topics, and I’ve tried to figure out a way to integrate these into my class. This year I realized I could use them as “filler” during our seniors’ Kairos retreats (students are gone for three days, which means I don’t see some of them all week!). I’m pulling out a couple of days worth of work from each unit, and the students who are on the retreat don’t have to make it up (they always have too much to make up anyway). This way, each student will get four mini-units, and miss one.

Today we started Everyday Einstein: GPS & Relativity. Students watch a short video about GPS (8 minutes), then explore uses of GPS, create scale drawings of the GPS satellites above the earth, make some calculations about the time between signal broadcast and its arrival on earth, and finally use an online mapping site to triangulate the position of an object given three cities and distances (would work great for earthquake epicenter location as well). We didn’t get as far as I had hoped, but we can finish the geolocating tomorrow, then start on relativity.

students creating scale models of GPS satellite orbits
Students drawing scale models of the height of GPS satellites vs radius of earth. One group also added the International Space Station, and, with prompting, added the height of the atmosphere.

Solar system model for your classroom ceiling

photo showing the four inner rocky planets.

In my physics classes at Carondelet High School, I had mostly seniors and a few juniors in each class. Seniors graduate two weeks early, so I’m always looking for a project for the juniors to work on during this time (the juniors take their physics final with the seniors). In the spring of 2013, I decide to create a model of the solar system on the ceiling in my classroom (credit). Here’s how we did it:

Planning the model

I have three physics classes, but only one ceiling, so they were going to have to collaborate “across time.” We used a Google document to share ideas and progress from one class to another, and each class had a “recorder” who took notes about our discussion.

How big?

photo of whiteboard with orbits sketched out
Our final whiteboard showing approximate orbits and lab tables.

Before I first presented the plan, I did a quick measurement of my classroom and approximation of the size of the orbits, to make sure it was realistic to fit all the planets in my classroom. I, being up on the current description of planets, left out Pluto, since it no longer is a member of the planet club. This generated a scale where Venus had a fairly small orbit, but it was visible.

When I presented this initial proposal to the students, they said “We can’t leave out Pluto.” This lead to a discussion about what makes an object a “planet,” and why Pluto is not in the club any longer (more info on that here.) After discussing the size of the orbit if Pluto and the Dwarf Planets were to be included, we started looking outside my classroom. There are two science classroom next to my classroom, followed by the library. We got out tape measures, and determined that if we put Pluto and the Dwarf Planets at the far wall in the library (turns out, just above the book mentioned in the footnotes), we could fit the first six planets (Mercury through Saturn) in my room, the seventh (Uranus) in the next classroom, and the eighth (Neptune) in the last classroom.

Orbits vs planet size

With the size of our model determined, we calculated the length of the orbits, then set off to determine the radius of the planets themselves. Upon calculating planet sizes, earth turns out to be about the size of a spec of dust…and that just won’t work. So, we realized we were going to have to use one scale for the orbits, and another for the planet sizes. Setting Jupiter at 2 meters (about as big as we could reasonably get), we calculated the size of the other planets, and the earth and the rocky planets came out to be reasonably visible sizes.

Orbits

Photo showing just pins, no planets yet.
First step in the construction was to place dots at the location of each planet every week/month

Once we had the model-length of our orbits, students cut string to the appropriate length. They then measured the distance the planet would travel in a given period of time–large pins would be placed showing the distance the planets travel in one month. For the rocky planets, however, this distance was long enough that we added smaller pins to represent the distance the planet travels in one week. Students held the strings with one end tacked at “the sun,” and placed pins in appropriate distances apart along the orbits.

Rocky planets models

For the rocky planets, we used foam balls and shaved them to the appropriate sizes. Then students researched the colors of the planets, and painted approximate representations of the surfaces.

Asteroid belt

To demonstrate the location of the asteroid belt, students placed pins in the region of the belt, spelling out “Asteroids” with the pins.

Gas giant models

Since we can’t really fit a two-meter diameter ball in the classroom, we ended up creating only portions of our gas giants, which required calculating the radius of the portion of our 2 meter ball if we only wanted it to hang about 0.30 cm below the ceiling (assuming that the rest of the planet is above the hanging ceiling tiles). We used chicken-wire to create the shape of the planet, then used papier-mâché to create the surface of the planet.

The students had fun visiting the other classrooms to place Uranus and Neptune dots and models in those rooms, with students in those classes asking “What are you doing?” (I, of course, had arranged with permission from those teachers ahead of time.)

Conclusions

  • The model does a great job of showing the vastness of our solar system, as well as the relatively small amount of that space that is occupied by the rocky planets.
  • Because we had to use two scales, there is potential for students not being able to truly understand how small our planets are compared to the distance between them.
  • Since we put all the planets in one line (almost), students may miss the concept that, for example, Mars is sometimes further away from us than Mercury (when it’s on the other side of the sun).
  • This model created a clear visual of the speed of the planets. Students can clearly see that the inner planets are moving faster than the outer planets.

Trying this in your classroom

  • I purposely have left out much of the calculations we did, so if you decide to build this in your classroom, your students won’t just be able to “Google” the answers (plus, your classroom/school dimensions will likely be different from mine).
  • If you want to create a model in your classroom, it will work best if you have ceiling tiles you can push pins into 🙂
  • My advice is to ask for permission from your administration before you undertake this project. Mine was quite excited about the project, and I was sure to invite them up during the process and when it was done.
  • This makes a great demo for Back to School night, explaining to the parents how you use it in your class.
  • I also calculated where the nearest star would be, and it turns out it’s in Sacramento, about 50 miles away from my classroom!

Feel free to add comments below if you have questions or suggestions, or email me directly.

Gallery

Here are some photos of the construction progress, and the rocky planets. Unfortunately, I can’t find any photos of the entire classroom showing the gas giants 🙁 If I find them, I’ll add them.

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Google map

I also created a Google map that shows the solar system in a slightly larger scale in the neighborhood of Carondelet:

Footnotes:

  1. I had seen a similar model before in another school, but am sorry to say I can’t credit the teacher because it’s been too many years and I can’t remember where I saw it.
  2. For further reading on Pluto, I recommend How I Killed Pluto and Why it had it Coming, by Mike Brown. Available in print, or through Audible.

Tentative geology road trip/hikes to Southwest, March 2016

Photo of Mesa Arch

Katie and Ada and I had a great trip through the Southwest earlier this summer, and we’re thinking of doing a similar trip with our SF Bay Area Geology and Natural Sciences Hiking Group. The trip would run nine days, from Saturday, March 26th (early departure) through Sunday, April 3rd (late return), 2016.

Unfortunately, this trip requires a lot of driving (about 2,200 miles), but will include some amazing sites. The three full-day visits (with no real driving) will be Canyonlands and Arches National Parks (near Moab, Utah; one day in each park), and one day at the Grand Canyon.

Along the way, we’ll have short visits to:

  1. Berlin-Ichthysoraus State Park (in Nevada)
  2. Great Basin National Park (Nevada, hopefully a tour of the Grand Palace cave).
  3. A drive through Monument Valley in Navajo Land in Arizona
  4. Petrified dinosaur tracks in Arizona.
  5. Overnight at the CSU Desert Studies Center in Zzyzx, CA.

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Faulting at Devils Slide

Strata at Devils Slide

The opening of the tunnel around Devil’s Slide in San Mateo County allowed for the creation of a mile-long trek to look at some of California’s fascinating geology. In my last geology hike to the trail, I took a photo of the great sedimentary layers at the north end of the trail, then edited the photo to show how well the strata line up on each side of a fault through the sediments. Mouse over the image below to see the image of the current conditions of the strata.

Imagine the strata lined up like this years ago. The red arrow shows the relative motion of the rocks between "then" and now.Hover your mouse over the image to see the current condition of the strata.

After faulting


After pressure and faulting, the strata now looks like this. Slide your mouse back and forth over the image to see the change.

The video below includes a great description of the geology of the area. Click on the “Sedimentary Layers” link to see the main section on the geology.

More resources on the geology of Devil’s Slide:

Hayward’s “D Street” fault creep, curb offset evidence erased

D Street Hayward
D Street Hayward, December 7, 2009

Sadly, improvements in city streets can wipe out geologic evidence. D Street has been a great field trip stop to see earthquake fault creep, and appears in many guidebooks and web sites. But in 1997, Hayward repaved the road, including the sidewalks (they all needed it). When they repaved it, they straightened all the curb lines, thereby erasing the evidence of fault creep. I just visited it in December 2009 (twelve years later), and no evidences of creep has yet presented itself through cracks/offsets in the sidewalk.

But the creep on the Hayward fault in this region is about 0.1 inch per year, so there’s about an inch of stress built up under the sidewalks and curbs. Hopefully (for us geology types), someday soon the sidwalks/curbs will shift, and we’ll be able to return here for tours.

In the photo above, you can see the street runs uninterrupted. The photo is facing east looking across Mission Street.

You can see a photo of the old curb offset on Dr. Sue Hirshfeld’s website here. Her complete tour is here (note: the links on her site have not been updated as of this time, and refer to the old webiste “csuhayward.edu”–if you find any dead links, simply replace the “hayward” portion with “eastbay” and the link will work).