### Overview

The "Pi in the Sky" math challenge gives students a chance to take part in recent discoveries and upcoming celestial events, all while using math and pi just like NASA scientists and engineers. In this problem from the eighth set, students use the mathematical constant pi to compare the signal strength between traditional radio wave communication and the Deep Space Optical Communication system.

### Background

This artist's concept shows what Deep Space Station-23, a new antenna dish capable of supporting both radio wave and laser communications, will look like when completed at the Deep Space Network's Goldstone, California, complex. Image credit: NASA/JPL-Caltech | + Expand image

NASA uses radio signals to communicate with spacecraft across the solar system and in interstellar space. As more and more data flows between Earth and these distant spacecraft, NASA needs new technologies to improve how quickly data can be received. One such technology in development is Deep Space Optical Communications, which will use near-infrared light instead of radio waves to transmit data. Near-infrared light, with its higher frequency than radio waves, allows for more data to be transmitted per second. In Signal Solution, students can compare the efficiency of optical communication with radio communication, using pi to crunch the numbers.

### Procedures

As more and more data are collected and transmitted through space, NASA needs new technologies to communicate faster and more efficiently with its spacecraft. One such technology is called Deep Space Optical Communications, or DSOC, which uses near-infrared light instead of radio waves to transmit a signal. This allows us to use a higher frequency (shorter wavelength), so more data can be transmitted per second.

The twin Voyager spacecraft launched in 1977 use a 12.5 Watt transmitter paired with a parabolic reflector that creates a circular radio signal with a diameter roughly 0.5 degrees wide. A DSOC system would use a 4 Watt transmitter on a flight laser transceiver, producing a light signal with a diameter of 0.0009 degrees.

If Voyager and a DSOC-equipped spacecraft were both placed 124 AU from Earth (1 AU = 150,000,000 km) what fraction of each original wattage would be received by a 70m antenna back on Earth?

By what factor is DSOC more effective?

### Assessment

Image credit: NASA/JPL-Caltech | + Expand image

### Extensions

#### Pi Day Resources

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