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A logic Puzzle about space, inspired by nondescript’s Herndon Liar series.
One of the youthful dreams many wish is to be an astronaut. The few that make it to space recognize how special it is, and often talk about their achievements to anyone who will listen. Unfortunately, astronauts also have a tendency to stretch the truth when it comes to describing their own achievements. (They tend to be much more truthful when talking about other people.)
Your challenge is to figure out the described orbits to solve this puzzle. During a recent lecture, each of three astronauts described characteristics of the missions undertaken by the trio on each of their two previous trips to space. The shape (or roundness) of an orbit is determined by a value known as eccentricity (e.g. e=0 is a perfect circle, and e near 1 is a very long ellipse). The decimal value of the cache minute location is determined by the eccentricity of each orbit, with North being determined by the first trip; West is determined by their second. The cache is located at N39 01.XXX W077 31.YYY.
Since this puzzle is meant to focus on logic, not necessarily rocket science, here are some valuable definitions for you:
e: Eccentricity, defines the shape of the circle
Perigee radius (rp): the radius of closest approach of the orbit measured from the center of the object being orbited
Apogee radius (ra): the radius of furthest approach of the orbit measured from the center of the object being orbited
Perigee altitude: Smallest distance from the Earth’s surface to the orbiting object
Apogee altitude: Greatest distance from the Earth’s surface to the orbiting object
Radius of Earth = 6378km (for purposes of this puzzle)
So although the focus of this puzzle is on logic, there is math involved. To keep it simple, the variables listed above are interrelated by the following equations:
E=(ra-rp)/(ra+rp)
ra=rp*(1+e)/(1-e)
rp=ra*(1-e)/(1+e)
Other ground rules and assumptions before starting the puzzle:
- No distances in the solutions are over 400,000km from the center of the Earth
- No altitudes below the defined limit of space of 160km (100miles)
- All math will result in exact numbers; if you require rounding, you have done something wrong. (Note – for eccentricity, ‘exact’ is defined as 3 decimal places necessary to develop a lat/long solution)
- Ignore any effects from sun, moon, comets, asteroids, Earth’s atmospheric drag, other cachers, etc. Keep it simple and use the equations provided.
- Due to their public speaking roles, all astronauts tend to speak in the third person about themselves. This is true for this puzzle as well.
- As mentioned, astronauts tend to be sketchier with the truth when talking about themselves (even in the third person). For the purpose of this puzzle, if the speaker is talking about other astronauts, it’s truthful and accurate. If talking about themselves, it’s a lie.
- Several statements refer to specific digits in eccentricity, radius, or altitude. For purposes of clarity and simplicity, treat eccentricity as a simple 3 digit number (e.g. ‘.057’ would be ‘057’ not ‘57’)
- Although I said that this was not meant to be a math problem in the classic sense, use of excel or some other spreadsheet will come in handy when trying to sort out the different clues.
The following statements were heard during the third lecture:
1) Mary’s second perigee radius (rp) was less than Tom’s first rp
2) The first and second digits of Dick’s first eccentricity equal Mary’s first and second digits from her second eccentricity
3) Tom went farthest from Earth; it was his first trip.
4) Dick’s eccentricity values are separated by .136
5) Mary’s first perigee radius is four consecutive numbers
6) Dick’s second perigee radius is a multiple of 273
7) Two of Tom’s eccentricity digits are used multiple times
8) Both of Mary’s perigee radii are greater than 10,000km
9) Tom’s highest altitude was greater than 4,000km
10) One of Dick’s radius values is all 1s and 0s
11) Both Dick’s and Mary’s Delta-e are multiples of 5
12) Tom’s third and fourth digits in his first perigee radius is 5 higher than the first two digits
13) Mary’s apogee radii add to 41,000km
Final notes: This is my first logic puzzle, and although I’ve run it multiple times through to confirm the logic, there may be undetected errors. Feel free to contact me if you have issues.
Here are the other two puzzles.
GC4RPCE Astronaut Tales #1
GC4RPCK Astronaut Tales #2
Also, if you like this (or want to practice), try the Herndon Liar, Liar, Liar series at
Herndon Liar, Liar, Liar #1
Herndon Liar, Liar, Liar #2
Herndon Liar, Liar, Liar #3
Good luck. First to find will recover a fun travel bug and/or take the cool coin.
Additional Hints
(Decrypt)
- Znel fnlf vg’f ivfvoyr jura fgnaqvat arneol
- Gbz fnlf vtaber gur gerrf