### Overview

Engineers can carefully track the location and direction of spacecraft near Earth using a technique known as trilateration. In this activity, students will model this process using cups and string to locate the positions of two imaginary spacecraft.

### Management

• Consider keeping groups between three and four students to ensure that every student is actively participating in the problem-solving process. At least one student should document/diagram the original setup to compare against other groups’ setups.
• Using different colors of string can help students keep track of relative distances to their target. If you don’t have multiple colors of string, each piece can be marked with colored tape or markers to help keep students organized.

### Background

If you’ve ever used your phone or the navigation in your car to look up directions, you’re likely familiar with the term GPS, or global positioning system. GPS uses what is called trilateration to determine your location. It works by measuring the time it takes for a signal to travel from your location to several nearby satellites.

One satellite can only identify the distance between you and the satellite, providing a circular range of your location rather than a specific location.

One satellite can only identify the distance between you and the satellite. Image credit: NASA/JPL-Caltech | + Expand image

However, as we add a second satellite, your location can be further narrowed down to one of the two intersecting points.

Adding in a second satllite helps us narrow down the location to one of two intersecting points. Image credit: NASA/JPL-Caltech | + Expand image

With the introduction of a third satellite, it is possible to pinpoint your exact location at the place where all three circles intersect.

A third satellite allows us to pinpoint a single location at the the spot where all three circles intersect. Image credit: NASA/JPL-Caltech | + Expand image

To find your location on the ground, we use two dimensions, but when it comes to tracking objects in space, we need three dimensions. As a result, when using trilateration to track objects such as spacecraft, we use spherical coordinates captured by a combination of satellites and ground-based antennas. In this case, we can locate a spacecraft by identifying where the spheres intersect.

To find the location of an object in space, we use spherical ranges provided by a combination of ground-based antennas and satellites. Image credit: NASA/JPL-Caltech | + Expand image

NASA tracks spacecraft within about 1.2 million miles (2 million kilometers) of Earth using the Near Space Network, or NSN. The NSN is an aggregate of space-based and ground-based antennas all over the world that allow us to track objects close to Earth’s surface.

In the Mission Control center at NASA's Jet Propulsion Laboratory, engineers track spacecraft using the Near Space and Deep Space Networks. | Take a virtual tour of JPL Mission Control | + Expand image

For example, the Near Space Network is a key component of NASA's upcoming Artemis program missions. The Artemis program is a series of missions designed to send astronauts back to the Moon and establish a sustainable presence on the lunar surface. The trajectory of the Space Launch System, or SLS, rockets that will launch the Artemis missions into space will be carefully tracked by the Near Space Network using techniques similar to those described above.

Meanwhile, the Artemis program's Orion spacecraft, which will carry astronauts to and from the Moon, will be tracked using a slightly different technique made possible by NASA's Deep Space Network, or DSN. Rather than trilateration, this network of massive antennas across the globe uses radio waves to track and communicate with more distant spacecraft. The Orion spacecraft will communicate with the DSN via a technology called three-way Doppler, which requires only two ground-based antennas.

Watch this video to find out how NASA uses giant antennas stationed around Earth to navigate faraway spacecraft. | Video Transcript

As future space exploration continues to expand, NASA engineers plan to use combinations of these techniques and technologies including ground-based antennas, small satellites known as CubeSats, and Earth-orbiting satellites to track the growing number of missions exploring the Moon and beyond.

### Procedures

1. Have students consider how we determine the location of two spacecraft in orbit above Earth. How do we know where these spacecraft are at any given time, if they are a safe distance apart, or how fast they are moving?
2. Divide students into groups of three to four with one group at each station. Provide each group with four to six plastic cups and string in two different colors, if possible.
3. Tell students that each cup will represent a listening antenna on Earth, while each piece of string will represent the signal being transmitted from a spacecraft to the antennas below.
4. Instruct student groups to arrange their cups in any position they choose to represent antenna locations on Earth. It may help to secure the cups to the work surface with tape to prevent them from sliding.
5. Image credit: NASA/JPL-Caltech | + Expand image

6. Have one student in each group place one hand above the cups at any height or position they desire. The placement of their hand will represent the location of an imaginary spacecraft.
7. Have another student cut lengths of string that cover the distance from their teammate's hand (spacecraft) to the cups (antennas) below. Students should tape one end of all the strings to each antenna and have the student representing the spacecraft hold the other end of the strings. There should be one piece of string between each antenna and spacecraft, making a "network" of signals.
8. Image credit: NASA/JPL-Caltech | + Expand image

9. Repeat with the other hand for a second spacecraft any height or distance from the first. If possible, have students use different colors of string for each spacecraft.
10. Image credit: NASA/JPL-Caltech | + Expand image

11. Students should document the positions of their spacecraft and network signals by either drawing it out or taking a picture. This will serve as the answer key for other student groups.
12. Each group should then disassemble their network by removing the string from their antennas while keeping the cups in place and leaving the pieces of the string on the table between the antennas. Once students are ready, have groups rotate to another student station.
13. Image credit: NASA/JPL-Caltech | + Expand image

14. Each group should now reattach the strings to the antennas and determine the locations of the spacecraft by matching the lengths of string to a fixed point above the cups below. Have student groups compare against the answer key created in Step 8.

### Discussion

• In this activity, we represent signals from the spacecraft to the antennas as a straight line, but in reality, signals are sent in a cone shape or even in all directions. How would trilateration work if not just the spacecraft but also the antennas were in space? How would this look in three dimensions?
• The string shows the location of the spacecraft but not where it’s going or how quickly it’s moving. To know this, we use the Doppler effect, which will tell us if a spacecraft is moving toward or away from us based on how the frequency of its signal is changing. Recall that the Doppler effect results in frequency increasing as an object moves toward you, which you hear as a higher pitch in the case of sound. Frequency decreases as something moves away from you, which results in a lower pitch.

NASA engineers can use the Doppler effect to gather information about the trajectory of the Orion spacecraft, which will take astronauts to and from the Moon, by sending a signal with a known frequency from Orion to two ground stations on Earth. The small but measurable differences in frequency received at each antenna will allow us to fill in the missing pieces of the puzzle that a third station would offer. We simply determine whether the frequency has become higher or lower at each station and by how much.

What's your prediction for how the signal would change as a spacecraft moves away from one antenna and toward another?

### Assessment

• Students will check their proposed spacecraft locations against the answer keys created by other groups.
• Consider assessing students not just on their final determination of location, but also on how their group managed different roles within the team.

### Extensions

• For an additional challenge, try reducing the number of antennas. Having fewer ‘antennas’ means less data to verify the location of the spacecraft.
• If certain groups need an even greater challenge, try having them place their antennas at different levels as well, such as on the desk and floor.
• Students can also map their x and y coordinates on separate graph paper to create a more precise map of their antenna, and try to capture the z axis for the height of their spacecraft.