Catching a Whisper from Space

Students will model the mathematics used to communicate with spacecraft. They will use sound waves as an analog for light waves and parabolic transmitters and receivers to represent antennas on spacecraft and on Earth.

• For parabolic dish ear antennas, make copies of the antenna pattern on cardstock and collect recycled 1- to 3-liter soda bottles (one per student).
• Locate an open area at least 120 meters in length, such as a football or soccer field.
• Standard football field yard-line markings may be used for measurement in lieu of measuring tape or a trundle wheel.
• Download a metronome app for your mobile device and program it to beep once every second.
• Although any mobile device will work for this activity, smaller devices such as mobile phones may be easier to hold in place on the shaft of the umbrella.
• Note that the best amplification will occur when the speaker of the mobile device is at the focal point of the umbrella.

NASA has been sending robotic spacecraft into the solar system for more than five decades. These mechanical explorers have ventured out to study Mercury, Venus, Mars, Jupiter, Saturn, Uranus, Neptune and beyond. These amazing robots have also been our eyes and ears on their journeys to far-off planets and even to the edge of the solar system, sending wondrous images and fascinating information back to Earth.

But none of these missions of discovery would have been possible without NASA’s Deep Space Network, or DSN — a worldwide system of sensitive antennas that communicates with interplanetary spacecraft. Signals to and from the spacecraft travel millions, even billions, of kilometers, yet spacecraft communications technology transmits signals at very low power, usually at about the same wattage as a refrigerator light bulb (20 watts). As the signal travels to Earth, it weakens. Signals arriving at DSN antennas on Earth can be as weak as a billionth of a billionth of a watt — that is 20 billion times less than the power required for a digital wristwatch.

How is it possible to hear the tiny whisper of a signal from a spacecraft so far away?

The Deep Space Network is made up of complexes of antennas at three locations around the globe: Goldstone, California (in the Mojave Desert); near Canberra, Australia; and near Madrid, Spain. This arrangement allows for any one station to have a line of sight to a spacecraft as Earth rotates. When a spacecraft “sets” below the horizon as viewed from one antenna station (like the sun does at the end of each day) another antenna station can track the spacecraft as it rises above the horizon at that location. This repeats as Earth rotates and the spacecraft moves out of view of the second station and into view of the third, and then once again to the first station.

To hear the low-power spacecraft signal, receiving antennas on Earth must be very large, with extremely sensitive receivers. The signal from the spacecraft travels in a straight line, and it can be focused by a curved reflector dish (parabolic antenna). For this reason, it’s crucial to have large antenna dishes with precisely shaped surfaces. The Deep Space Network’s parabolic dishes, which range from 26 to 70 meters in diameter, are focusing mechanisms that concentrate power when receiving data and also when transmitting commands. The antennas must point very accurately toward the spacecraft, because an antenna can “see” only a tiny portion of the sky (as though it's looking at the sky through a soda straw).

To hear the spacecraft’s faint signal, the antennas are equipped with amplifiers, but there are two problems. First, the signal becomes degraded by background radio noise (static) emitted naturally by nearly all objects in the universe, including the Sun and Earth. The background noise gets amplified along with the signal. Second, the powerful electronic equipment amplifying the signal adds noise of its own. The Deep Space Network uses highly sophisticated technology, including cooling the amplifiers to a few degrees above absolute zero, and special coding techniques so the receiving system can distinguish the signal from the unwanted noise.

New space missions bring new challenges. NASA’s Deep Space Network is continually improved and enhanced to provide communications, navigation and tracking for distant spacecraft — our robotic explorers of the cosmos. Use DSN Now to see which spacecraft we are communicating with at this very moment.

• Discuss the inverse-square law and how it might apply to the data collected. The inverse-square law applies to both electromagnetic waves and sound waves. Antennas (radio telescopes) on Earth and spacecraft emit electromagnetic waves; a beeping mobile device emits sound waves. The beeping device in the procedure described here is similar to the emitting antenna or spacecraft; the person listening is the receiver, similar to the receiving spacecraft or antenna. When the distance between the beeping device and the listener increases, the volume of the sound decreases by the square of the increased distance. If the volume of the sound at distance r is I, the volume at distance 2r is I/4r², the volume at distance 3r is I/9r², and so on. Diagram courtesy of HyperPhysics ©C.R. Nave,2002, Georgia State University. Used with permission.HyperPhysics is at http://www.phy-astr.gsu.edu.
• Introduce students to the logarithmic scale of decibels. The volume, or intensity, of sound waves can be measured in watts per square meter. The inverse square law can be used easily with these units. However, the preferred units for volume intensity are decibels (abbreviated dB). Decibels do not easily follow the inverse square law because they are logarithmic — every increase by 10 decibels is an increase in sound of 10 times. This means that 10 decibels are 10 times greater than 0 decibels, 20 decibels are 10 times greater than 10 decibels, 30 decibels are 10 times greater than 20 decibels, and so on. Diagram courtesy of HyperPhysics ©C.R. Nave,2002, Georgia State University. Used with permission.HyperPhysics is at http://www.phy-astr.gsu.edu.

Here are the equations to switch between watts per square meter and decibels:

• I := Intensity (of sound) in watts per square meter
• I(dB) := volume intensity in decibels
• log := logarithm base 10
• I₀ := the threshold of hearing, 10^-12 watts per square meter
• I(dB) = 10*log(I/I₀)
• I = I₀*10^(I(dB)/10)

Here are the equations to switch between watts per square meter and decibels:

• I := Intensity (of sound) in watts per square meter
• I(dB) := volume intensity in decibels
• log := logarithm base 10
• I₀ := the threshold of hearing, 10^-12 watts per square meter
• I(dB) = 10*log(I/I₀)
• I = I₀*10^(I(dB)/10)

Observe student ability to follow instructions for recording data and creating ear antennas.

Examine student scatter plots. Data should roughly follow a quadratic model.

• Does the size of the antenna/umbrella make a difference?
• Have students work in groups of four using two additional sizes of umbrellas, a beeping mobile device, and student-made antennas. Students take turns being the Sender (phone/umbrella holder), Listener, Measurer, and Recorder.
• The Sender holds the phone at a fixed height and position as the Listener steps away from the beeping signal until they cannot hear it while using their ear antenna.
• The Measurer measures the diameter of the antennas they are using and the distance between the two students (Sender and Listener).
• The Recorder writes down the measurements in the data tables.
• Repeat the experiment using umbrellas of two different sizes. Try sending the signal from both the umbrella antenna (the Deep Space Network) and the student-made antenna (the spacecraft antenna).
• The students record and compare differences they observe related to the size of the antennas, then analyze their data to see if there is a correlation between the antenna’s diameter and the distance between the Sender (phone/umbrella holder) and the Listener.
• Discuss the results and conclusions of each groups’ experiment.
• Have students determine the equation that defines the umbrella's parabolic shape. Hint: measure the focal distance from the umbrella's apex to the mobile device's speaker when greatest amplification is achieved.
• Have students calculate the percentage of the Voyager spacecraft’s signal that is received by Earth with this problem involving the mathematical constant pi.

• Have students work in groups of four using two additional sizes of umbrellas, a beeping mobile device, and student-made antennas. Students take turns being the Sender (phone/umbrella holder), Listener, Measurer, and Recorder.
• The Sender holds the phone at a fixed height and position as the Listener steps away from the beeping signal until they cannot hear it while using their ear antenna.
• The Measurer measures the diameter of the antennas they are using and the distance between the two students (Sender and Listener).
• The Recorder writes down the measurements in the data tables.
• Repeat the experiment using umbrellas of two different sizes. Try sending the signal from both the umbrella antenna (the Deep Space Network) and the student-made antenna (the spacecraft antenna).
• The students record and compare differences they observe related to the size of the antennas, then analyze their data to see if there is a correlation between the antenna’s diameter and the distance between the Sender (phone/umbrella holder) and the Listener.
• Discuss the results and conclusions of each groups’ experiment.

• The Sender holds the phone at a fixed height and position as the Listener steps away from the beeping signal until they cannot hear it while using their ear antenna.
• The Measurer measures the diameter of the antennas they are using and the distance between the two students (Sender and Listener).
• The Recorder writes down the measurements in the data tables.