I have a strange problem that you may be able to help me with. I was recently hired by company that manages several communications satellites, and I've gotten stuck with the overnight shift. Earlier this week I was getting some weird interference on the C-band receiver during a pass sometime after midnight. I didn't think too much of it initially, but it reappeared again Friday night, at around the same time. This time I managed to record it:
Time-domain plot
Frequency-domain plot (Spectrogram)
Zooming in on the first few seconds:
Download the signal as audio
Unfortunately it hasn't reappeared since. I want to ask one of my co-workers to scan the source of the signal with the big dish, but I've forgotten which satellite the antenna was pointed at when I recorded the signal! Can you help me figure out where in the sky the signal originated?
Answer
Solution
Right ascension 20 15 17
Declination -27 01 58
Alien Message Translation
Explanation
Page 1 The purpose of this page is to teach us the alien number system. They use a base 3 number system that we call balanced ternary with the '+' symbol defined as +1, the '-' symbol as 0, and the 'x' symbol as -1. In addition they define the '>' symbol as the radix point. In the examples they show us how to represent the numbers 1 through 9.
Page 2 Here they move on to teach us the concepts of addition/subtraction, multiplication/division, and equivalency. In each of the examples the symbols that represent the various operations are defined and can be seen clearly in the above image.
Page 3 Now they demonstrate the properties of the their number system and how it represents decimals. They begin by showing that shift operations in balance ternary are achieved by multiplying by 3 to shift left and dividing by 3 to shift right. They then demonstrate a new symbol 'O' when drawn around any set of digits defines a repeating group identical to bar notation here. They also introduce a 'o' symbol when placed at the end of an equation it means continue the series infinitely.
Page 4 They move on from basic number representation and operations to define the concept of and the symbol representing Pi. They introduce a new symbol '|' that was previously introduced in page two as '>|' to mean equals. Or rather in the previous use it was customary to write equals without a space between other symbols. At the top of the page they appear to be introducing additional equation concepts that utilize perpendicular calculations and back to back operators. I assume that some sort of order of operations and/or the equivalent of parenthesis is implied. Clearly this looks like some sort of series expansion. We see the familiar 1, -1/3, +1/5, -1/7 ... expansion used to calculate Pi.
Page 5 Similarly to the previous page, they derive and define the constant 'e'. They also define the concept and syntax of exponents with two examples.
Page 6 Here they give models representing Carbon, Oxygen, Hydrogen, and Helium atoms followed by a number in alien units. We define this unit as the Alien Mass Unit (AMU). By referencing the various properties of these atoms you can quickly see that they are defining the mass of each atom in terms of the mass of an electron (me).
1 AMU = 9.10938291E-31 kg
Page 7 In this page they show a model of a water molecule with distinguishing characteristics such as the number of protons and the angle between the two hydrogen atoms. The aliens also define an length unit in terms of the bond distance between the oxygen and hydrogen atoms. We define this unit as the Alien Length Unit (ALU). Referencing various materials we can see that the radius of the hydrogen atom is well defined as the Bohr Radius which is roughly 53 pm, and that the O-H bond distance is 95.7854 pm.
1 ALU = 52.9177211 pm
Page 8 Now they show a model of the alien radio transmitter. We translated the antenna diameter, and converted the ALU units to meters and determined that the diameter of the antenna is 2197 m. The number on the lower right of the diagram represents the transmission frequency in alien units and the number in the center of the diagram represents the transmission power also in alien units. We define these units as the Alien Frequency Unit (AFU) and Alien Power Unit (APU) respectively. Since our receive frequency was 4460MHz we can calculate AFU.
1 AFU = 1.170960 Hz
Given that the receive antenna is 10m with a receiver sensitivity of -130dBm we can calculate a reasonable maximum transmission distance. A 10m dish antenna with an efficiency of 0.7 will have a maximum of 50dB gain and the alien dish antenna will have a maximum of 99dB gain at 4460MHz. So the maximum free space propagation can be determined given these quantities and the signal to noise ratio (SNR) of the received signal in addition to the alien transmit power. However the power is currently unknown. But we can determine a reasonable estimate somewhere between 60 and 90dBm. Using these values we can safely estimate a maximum transmission distance of ~200 ly.
Page 9 In this page they depict the aliens planetary system with numbers that represent the distances from the center of their star. The distance units will be determined in later pages.
Page 10 Now they specify the mass and radius of planets 1, 2, 4, and 5 as well as the mass of each moon and distance to the related planet. The mass and radius are in currently unknown alien units which we will define as Alien Planetary Mass Unit (APMU) and Alien Planetary Radius Unit (APRU) respectively. The distance units will be determined in later pages.
Page 11 In this page they continue from page ten with the third planet and its associated moon. The planet and moons are specified in units of APMU, APRU. However when looking at the numbers for the fourth moon of the third planet we see that they have defined an equation. The two equations define the APMU and APRU units.
1 APMU = 1.454E+53 AMU
1 APRU = 4.880E+16 ALU
Again the distance units will be determined in later pages.
Page 12 In this final page of the alien message they show us something unexpected. We see that the aliens have specified a relative distance from their system to another star with additional orbiting planets. Looking at this and the last few pages we conclude that the unit of distance between the moons and the associated planets, as well as, the unit of distance between the planets and the associated stars is in units of APRU. Finally we notice that the aliens use a different unit for specifying the distance between the two stars. As is the case here on Earth we define our unit of distance AU to be the distance between Earth and the Sun. Here we notice that the aliens chose to define their unit to represent the distance between their moon and it's associated planet. We define this unit as the Alien Astronomical Unit (AAU).
1 AAU = 301 APRU
Calculations
star radius (sun)
7.7191e-01, 1.0020e+00
star mass (sun)
7.3138e-01, 1.0027e+00
system distance (au)
1.8251e+06
system 1 planet distance (au)
1.7197e-01, 3.1877e-01, 1.1828e+00, 2.4915e+00, 4.6432e+00
system 1 planet mass (earth)
5.5857e-02, 1.7033e+01, 2.4707e+01, 9.0710e+00, 4.0661e-01
system 1 planet radius (earth)
3.8028e-01, 7.0252e+00, 4.3683e+00, 3.2424e+00, 7.6557e-01
system 1 planet 2 moon distance (au)
2.1058e-03
system 1 planet 3 moon distance (au)
4.4303e-04, 1.1047e-03, 3.1587e-03, 5.1955e-03, 9.6315e-03
system 1 planet 4 moon distance (au)
6.7317e-04, 9.3208e-04
system 1 planet 5 moon distance (au)
3.9700e-04
system 1 planet 2 moon mass (earth)
7.4030e-04
system 1 planet 3 moon mass (earth)
9.3203e-07, 3.1099e-04, 3.8536e-04, 2.2179e-02, 1.8780e-05
system 1 planet 4 moon mass (earth)
3.7184e-05, 1.4874e-04
system 1 planet 5 moon mass (earth)
9.9157e-05
system 2 planet distance (au)
5.2094e+00, 9.5129e+00
system 2 planet mass (earth)
3.1797e+02, 9.5213e+01
Search
Analyzing the above calculations, we recognize that the planets and star in the second system match Jupiter, Saturn, and our Sun exactly. Now searching through the various databases for systems around 28.86 ly away, I found Gliese 785 matches the specifications of the alien system star, planet 2, and planet 3 exactly. Therefore we can conclude that this is the origin of the alien signal transmission. Clearly we are currently unaware of the alien systems other plants and moons. I foresee future space missions.
Here are two of the more helpful online exoplanet databases.
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