Question

Power Used by E.T. A modern SETI search using the 300-meter diameter Arecibo radio telescope in Puerto Rico could pick up a 10-million-watt signal from 1000 light-years away (assuming that the broadcasting aliens had a transmitting antenna that was also 300 meters in diameter). Suppose we wish to use Arecibo to search the far side of the Milky Way Galaxy (roughly 80,000 light-years away) under the same assumptions about our setup and the transmitting antenna. What would be the required power of the alien transmitter for us to detect the signal?

Short answer

The aliens would need a 64 billion watt transmitter.

Step-by-step solution

Understanding the Inverse Square Law

The power received by the Arecibo radio telescope is influenced by the distance from the source due to the inverse square law. This law states that the power per unit area ( \( P_r \) ) is inversely proportional to the square of the distance ( \( d \) ) from the source: \( P_r \propto \frac{1}{d^2} \). We need to adjust the power for a distance of 80,000 light-years.

Calculate Required Power Increase Factor

First, we determine the factor by which the power needs to increase due to greater distance. Since the original signal is detected from 1000 light-years away, and we now want to detect from 80,000 light-years away, the increase in distance is \(80,000 / 1,000 = 80\) times. The square of the distance increase factor is \(80^2 = 6400\).

Calculate Transmitter Power Required

Given that the initial signal was 10 million watts at 1,000 light-years, multiply this power by 6400 to find the required power at 80,000 light-years: \( 10,000,000 \text{ watts} \times 6400 = 64,000,000,000 \text{ watts} \).

Conclusion

To detect a signal with the same initial strength at 80,000 light years, the transmitting aliens would need to send out their signal at a power of 64 billion watts.

Key concepts

Arecibo radio telescope

The Arecibo radio telescope was one of the most iconic instruments in the field of radio astronomy and the Search for Extraterrestrial Intelligence (SETI). Located in Puerto Rico, the telescope was a giant with a diameter of 300 meters.
Its size made it incredibly powerful for detecting faint radio signals from outer space. Arecibo was primarily used to study distant galaxies, pulsars, and conduct radar observations of planets. It also played a crucial role in SETI by scanning the skies for signals that might indicate extraterrestrial intelligence.

• Arecibo functioned as both a radio receiver and a transmitter.
• Its large size allowed it to detect extremely weak signals, which is essential when looking for signals from distant star systems.
• The telescope's design was inspired by a natural limestone sinkhole, leveraging its geography for efficient data collection.

The unfortunate collapse of the Arecibo dish in December 2020 marked the end of its historic contributions, but its legacy continues to influence modern radio astronomy projects.

Inverse Square Law

The Inverse Square Law is a fundamental principle of physics that describes how a measurable quantity decreases with distance. When we talk about the power of a signal from a source, like a radio wave or light, the Inverse Square Law tells us how this power diminishes as the signal travels away from its source.
Imagine a light bulb illuminating a room, the intensity of light is much stronger close to the bulb. As you move away, the light gets dimmer because the light spreads out over a larger area. This spreading out reduces the intensity of the light an observer perceives.

• The law is expressed as: the intensity of the signal is inversely proportional to the square of the distance from the source, or symbolically: \( I \ ernal{^}{\propto} \frac{1}{d^2} \).
• For SETI, this implies that signals from further away are exponentially weaker.

This understanding is crucial in determining the required transmission power to detect signals at varying distances in space.

Milky Way Galaxy

The Milky Way Galaxy is our cosmic home, a vast spiral galaxy composed of billions of stars, planets, and various stellar phenomena.
It is estimated to be around 100,000 light-years in diameter, and our solar system is located about 27,000 light-years away from its center. When considering searching for extraterrestrial signals across the galaxy, it's important to appreciate its sheer size and complexity.

• Our galaxy features a flat, spiral disk structure filled with stars, gas, and dust, making radio astronomy a key tool for peering through its layers.
• The galaxy's core, bulging with older stars and likely harboring a supermassive black hole, presents unique challenges and opportunities for signal detection.
• Detecting signals from the far side of the Milky Way requires powerful telescopes and a deep understanding of astrophysical processes that can affect signal travel.

The vast distances within the Milky Way underscore the challenges of SETI and the need for sensitive equipment and powerful transmitters to bridge interstellar gaps.

Radio Telescope Sensitivity

Radio telescope sensitivity is an essential feature that determines how effectively a telescope can detect faint signals from space. It refers to the instrument's ability to pick up weak radio signals emitted by celestial bodies or artificial signals from potential extraterrestrial intelligence.
A radio telescope's sensitivity is impacted by several factors, including its size, design, and the technology incorporated into its receivers.

• The larger its dish, the more sensitive the telescope since it can collect more radio waves from space.
• Advanced receivers and cooling technologies reduce noise, improving the clarity and strength of detected signals.
• Arecibo, with its 300-meter diameter, was exceptionally sensitive, making it ideal for detecting weak signals over vast interstellar distances.

In the quest for discovering extraterrestrial transmissions, sensitivity is pivotal, enabling researchers to glean insights from the tiniest of signals that could indicate another intelligent civilization.