A WLBOTT RESEARCH PROPOSAL
[Thanks to UC#1 for his research proposal]
One of the great unsolved mysteries of life is, “How can I watch the missing ‘Dr Who’ episodes?” Extensive research has been done in BBC archival sites, personal collections and homes of known hoarders, but many of the early episodes remain lost to the world. (https://en.wikipedia.org/wiki/Doctor_Who_missing_episodes)
In this preliminary research document, we investigate one possible solution, to travel out into space, far enough that the original TV broadcasts emanating from Earth could be received. The first broadcasts were analog transmissions in 1963, which means those broadcasts are now 61 light-years away, or possibly closer if there were any later re-runs.
This solution presents several technical difficulties which we investigate in more detail below.
To assist us in our research, we invoked the resources of ChatGPT (the original, free version). In the following, “Q” indicates a question posed to ChatGPT and “A” is the subsequent answer.
Problem #1. We currently don’t have the technology to enable us to travel that far in any reasonable amount of time.
Q: Using the best technology that exists in the early 21st century, how long would it take to travel 61 light-years?
A: Traveling 61 light-years with current technology would take an extremely long time. Here are some comparisons using various methods:
Conventional Spacecraft: The fastest spacecraft to date, the Parker Solar Probe (https://en.wikipedia.org/wiki/Parker_Solar_Probe), travels at about 430,000 miles per hour (700,000 km/h). At that speed, it would take over 6,700 years to travel 61 light-years.
Voyager 1 (https://en.wikipedia.org/wiki/Voyager_1): Currently the fastest spacecraft relative to the Sun, Voyager 1 travels at about 38,000 miles per hour (61,000 km/h). It would take roughly 73,000 years to cover the same distance.
Theoretical Propulsion: Concepts like the Alcubierre “warp” drive (https://en.wikipedia.org/wiki/Alcubierre_drive) or other speculative technologies could reduce this time dramatically, but they remain theoretical and are not yet feasible.
In summary, with our best current technology, traveling 61 light-years would take tens of thousands of years.
To further compound the problem, after travelling 6,700 years to arrive at a point 61 light-years from Earth, the original television signals would have moved on another 6,700 light-years. Even the hardiest of Dr. Who fans would probably find this frustrating.
And finally, we cannot assume that the original BBC transmitters were exactly aligned with a single destination point 61 lightyears away. In reality, due to the spin of the Earth, these transmissions will project outward from the Earth in a spiral pattern. (Illustration needed).
Using a simplified calculation, the reception point for each transmission would be moving in an arc, completing a full circle every 24 hours. Thus, the reception point, at a distance of 61 lightyears would be moving at approximately 1.5079×1013 km/h in the same direction as the spin of the Earth and moving away at a rate 1/365 lightyear/day.
The problem can be slightly simplified by the fact that the earlier transmissions were only 25 min in length.
Problem #2. Assuming that a suitable receiver could be positioned approximately 61 light-years away from Earth, the signal from the transmissions of the most powerful TV stations of the time, operating at a power of 100 Kw with a zero-gain vertical omni-directional antenna in the 405-450 Mhz band, would be extremely weak at this distance.
Q: What would be the signal strength from a 100 KW tv transmitter operating on 405 Mhz at a distance of 1 km?
A: To calculate the signal strength from a 100 kW television transmitter at a distance of 1 km at a frequency of 405 MHz, we can use the free space path loss (FSPL) formula:
FSPL (dB)=20log10(d)+20log10(f)+20log10(4π/c)
Where:
-
- d is the distance in meters (1000 m)
- f is the frequency in Hz (405 MHz = 405,000,000 Hz)
- c is the speed of light (approximately 3×1083×108 m/s)
First, let’s calculate the FSPL:
Convert the frequency to Hz: f=405×106 Hz
Calculate 20log10(1000)=20×3=60 dB
Calculate 20log10(405×106)≈20×8.607=172.14 dB
Calculate 20log10 (4π/c)≈−167.56 dB
FSPL≈60+172.14−167.56≈64.58 dB
Now, we convert the transmitter power from kilowatts to decibels:
Power(dBm)=10log10(100,000)=10×5=50 dBm
Finally, we find the signal strength at 1 km:
Received Power (dBm)=Transmitter Power (dBm)−FSPL (dB)=50−64.58≈−14.58 dBm
So, the signal strength from a 100 kW TV transmitter operating at 405 MHz at a distance of 1 km would be approximately -14.58 dBm.
Using the same formula, we calculate the signal strength at a distance of 61 lightyears to be:
-309.8 dBm
A typical modern television receiver will pick up an analog signal down to about -70 dBm. Clearly, this signal would be far too weak to receive without amplification.
Q: Using a parabolic antenna, how large would the antenna have to be to receive a television signal that has been attenuated to -309.8 dBm?
A: To calculate the size of a parabolic antenna needed to receive a weak signal like -309.8 dBm, we can use the following formula that relates antenna size, gain, and received power:
G=4πAλ2
Where:
G is the gain of the antenna (in linear terms, G=10GaindB10G=1010GaindB)
A is the area of the antenna (in square meters)
λ is the wavelength (in meters)
Step 1: Calculate Wavelength
The frequency f is 405 MHz, so we can calculate the wavelength λ using the formula:
λ=c/f
Where c≈3×108 m/sc
λ=3×108/405×106≈0.7407 meters
Step 2: Convert Received Power to Linear Scale
Given the received power is -309.8 dBm, we convert this to milliwatts:
Pr=10−309.8/10≈1.26×10−31 mW
Step 3: Determine Required Gain
The gain needed to receive the signal can be calculated by considering the effective area of the antenna and the received power. We also need to consider the system noise and desired signal-to-noise ratio (SNR). For simplicity, let’s assume we want at least a minimal gain to detect the signal:
To find gain G in terms of power:
G=Pr/Pinput (assuming a specific input power)
For this calculation, we can simplify by estimating that we want a gain that would effectively make the received power detectable.
Step 4: Calculate Antenna Area
The effective area A of the antenna can be related to gain G by:
A=Gλ2/4π
For typical parabolic antennas, a reasonable gain for a very large antenna might be around 30 dBi (which corresponds to a gain of 103≈1000).
Step 5: Calculate Area for Gain
Now we can calculate the antenna area:
A=1000×(0.7407)2/4π≈43.7 m2
Step 6: Calculate Diameter
The area A of a circular antenna is given by:
A=π(D/2)2 ≈7.46 meters
To summarize the signal strength analysis, a person listening to a 1963 TV transmission from the most powerful TV transmitter in the UK at that time, at a distance of 61 light-years from Earth would need a dish antenna in the order of 7.5m diameter or more. And of course, it would need to be pointed precisely to where the Earth was 61 years ago along an expanding arc moving at 1.5079×1013 km/h.
Problem #3: Multiple signals.
Q: How many individual television transmitters did the BBC operate in England in 1963?
A: In 1963, the BBC operated around 30 individual television transmitters in England. These transmitters provided coverage for BBC One and, to a lesser extent, the early broadcasts of BBC Two, which began in 1964. The transmitters were part of the BBC’s efforts to provide nationwide television coverage, including both urban and rural areas.
This presents an interesting situation. Each BBC transmitter would normally operate on a different frequency from each of its neighbors so as to avoid interference. Frequencies would be re-used by stations further away. If all 30 BBC transmitters were broadcasting Dr. Who simultaneously, then by monitoring each transmitter frequency we could improve the overall signal-to-noise ratio.
On the other hand, there were many more TV stations in the world and many of them operating on the same frequencies as the BBC transmitters. This means that the signal we would be receiving at our monitoring station 61 light-years away would be a jumble of overlapping programs.
Theoretically, we could analyse the voice patterns of the actors from the non-missing episodes and, using AI, search for those patterns in the jumble of data. Given a sufficiently large sample to train with, we could identify and extract the missing episodes. We might also assume that the opening video is the same; this would provide a larger sample for the AI pattern matcher.
Problem #4: Cost
Q: Using current technology, what would it cost to send a large satellite to a point 61 light-years away?
A: Estimating the cost to send a large satellite to a point 61 light-years away using current technology involves several assumptions and hypothetical scenarios. Here’s a breakdown of the factors involved:
1. Current Space Launch Costs
The cost to launch a satellite into low Earth orbit (LEO) using current rockets varies but can range from $2,500 to $10,000 per kilogram. For larger satellites, like those used for scientific missions, the weight could be several tons (e.g., 1,000 kg or more).
2. Distance and Travel Time
Current spacecraft, like Voyager 1, travel at about 17 kilometers per second (approximately 38,000 miles per hour) and would take over 73,000 years to reach 61 light-years.
3. Cost Estimation
To estimate the cost, we can make some rough calculations:
Let’s assume we want to send a satellite weighing 1,000 kg.
Launching cost to LEO: 1,000 kg×$5,000 per kg=$5,000,000
4. Deep Space Missions
The cost of deep space missions (including design, development, and operations) can significantly increase this. For example, missions like the Mars rovers or interplanetary probes can run from hundreds of millions to several billion dollars.
5. Total Cost Estimate
Considering launch, development, and the vast time and resources needed to maintain a mission over tens of thousands of years, you could conservatively estimate the total cost to send a satellite to 61 light-years away might be in the range of hundreds of millions to potentially billions of dollars.
However, it’s crucial to note that with current technology, a mission of this nature is purely theoretical and not feasible. The actual costs would be astronomically higher due to the required advancements in propulsion, life support, and technology to sustain operations over such immense distances and timescales.
To further exacerbate the cost analysis, the satellite would probably weigh considerably more than 1000 kg as it would have to include a parabolic receiving antenna at least 7.5m in diameter.
A POSSIBLE OPTION
None of the above addresses the question of how to return the captured television signals to Earth.
Certain large formations in the universe can “bend” light, giving us a “lensing” effect. It stands to reason the there are some formations that could also reflect light (and therefore, television signals from 1963). Given sufficient numbers of these formations, we could expect that some small portion of the television signals has been reflected back to Earth (where it is now) and by properly aiming our antennae, we should be able to receive these signals. If the reflector is positioned at exactly 30.5 light-years from Earth, we would be able to listen to those shows from 1963.
Q: Are there objects in the universe at a distance of 31-32 lightyears from Earth that would reflect radio waves in the 405 Mhz range?
A: Yes, there are objects in that distance range that could reflect radio waves in the 405 MHz range. Specifically, certain celestial objects like planets, moons, or asteroids can reflect radio waves, depending on their size, composition, and surface characteristics.
However, at 31-32 light-years away, you’re looking primarily at stars or other potential exoplanets. For example, some stars in that range might not reflect radio waves effectively, but they could emit their own radio frequencies.
SUMMARY
This topic requires considerable further investigation, not only to find appropriate reflectors in the universe, but also to identify the actors from the missing episodes and find useable samples of their voices and images so as to allow AI to decode the multiple signals.
Since this project would never receive funding from NASA or any large government agency, or for that matter, any agency of any type, and given that the interested parties are not likely to be multi-billionaires, the task of raising the billions of dollars would have to be crowd-sourced.
The likely outcome of this project will be a severely attenuated, “Who Cares?”
References
Ship Prototypes
Proof of Intellectual Property Theft
Unexpected Cultural Appropriation
The aliens are into 60’s sitcom cosplay.
