• Gem Science: Stev’en Spaaaaaaace

    Leave it to the fandom to think WAY too much about space rocks. We previously did a Gem Science post about how far under the ocean Malachite is and how far into space Steven has been. Well, Zottgrammes is back, with some calculations about space, time travel, and the Diamond authority. If you're into applying real world laws to SU, check after the break!

    Stev’en Spaaaaaaace

    I was thinking about where Pearl wanted to travel in the Space Race episode. Hang on tight everyone, it’s time to take a cartoon about polymorphic space rocks way too seriously! Long, wordy post with some math!

    Space Based Pace

    Pearl said she’d go to the nearest star system. That’s Alpha Centauri! Proxima Centauri is the closest star in that system. It’s about 4.22 light years away. How fast does Steven and Pearl have to travel to reach it in 25 years?
    v = distance_in_miles / time_in_hours
    = (4.22 * light_year_in_miles) / (25 * hours_per_year)
    ~= 24807799074834.82 / 219145.32
    ~= 113,202,505 miles per hour!
    ~= 31,445 miles per second!
    ~= 16% the speed of light!
    That’s honkin’ fast! At that speed, you’d reach the moon in about 7 seconds!

  • Juno is meant to reach Jupiter and is expected to reach 160,000 miles per hour.

  • Voyager has passed Pluto and, by some definitions, exited our solar system! It’s going at ~35,000 mph.

  • Space Probe Plus is set to launch in 2018 and is expected to reach 450,000 mph.

  • So Pearl either created some amazing new propulsion technology (possible, given how gem tech, even 4000 years ago, was advanced enough for space travel), misjudged the time, or lied! I’m gonna go with the former!
    But wow! 16% the speed of light. Some strange stuff starts happening when you travel that fast!

    Traveling Through Time

    It’s well known (though not very intuitive) that time is not separate from space! The dimensions are coupled together in spacetime. Because of this and the constant speed of light, if you move faster relative to some reference frame (Earth, lets say), then time passes more slowly for the mover from the view of the reference frame! Ie. The faster you move, the slower you age! This is called time dilation!
    The explanation is better left to more educated and well-versed people than me. I liked this video in particular.
    1/sqrt(1 - v^2/c^2)
    Eaugh! OK, what does that look like, really? It’s called the Lorentz Factor and it looks like this:

    For human speeds (even jets), v is much, much smaller than c. On that chart, it’d be practically next to the 0 on the x-axis! So the effect is basically negligible! Lets say you were in the world’s fastest jet, the X-15. You’re going at mach 6, or ~4473 mph! What’s the difference in time you experience versus ground control?
    1/sqrt(1 - (4473^2)/(speed_of_light_in_mph^2))
    ~= 1.000000000022253
    Less than a nanosecond, or one trillionths of a second! In general, for time dilation to be a “thing”, you have to be traveling at > 1% the speed of light. Fun fact! GPS actually needs to correct for time dilation!
    But we saw Pearl has to be moving at ~16% the speed of light to reach Proxima Centauri! So what’s the time difference that Pearl and Steven will experience versus Greg Universe?
    1/sqrt(1 - (113202504.51^2)/(speed_of_light_in_mph^2))
    ~= 1.014559223104693
    So for every year Pearl and Steven experience, Greg will experience ~1.0146 years. Meaning, after traveling 50 years in space, Pearl and Steven will return to find Greg, Connie, et al 50.72 years older.

    Ain’t  Got No Time, Just Go for the Bits

    OK! So what if Pearl and Steven were traveling much slower? How far can they go? Lets make a lot of assumptions to keep the math simple.
    Lets assume they’d spend 25 years traveling to her destination and 25 years coming back, they travel in a straight line, and all their destinations are on or observable from that path. One last assumption, which we’ll parameterize: The speed of travel. Lets call it v and place it in units of miles per hour and assume Pearl and Steven instantaneously reach that speed without them or their craft suffering from that kind of instantaneous, massive acceleration.
    OK! We’ve simplified everything to where even I can plug it into an equation and crunch it!
    distance = v * 25 * hours_per_year
    = 219,145 * v 
    Lets plug in different speeds and see how far Pearl and Steven can go!

  • Speed of Voyager: 35,000 mph. Distance: 7.6 billion miles, 82 AUs, 0.0013 light years

  • Speed of Juno: 160,000 mph. Distance: 35 billion miles, 377 AUs, 0.005 light years

  • Speed of Space Probe Plus: 450,000 mph. Distance: 98 billion miles, 1060 AUs, 0.16 light years

  • (AU is “astronomical unit” and is the average distance from the Earth to the Sun.)
    So! Even if they were traveling as fast as future space craft, they’d be nowhere close to Alpha Centauri! They’d be about to enter the Oort Cloud of our solar system! But this does mean they can explore all the planets of our solar system easily!
    Hm! Maybe Homeworld isn’t so far away…! Earth is the only planet in our solar system capable of live as we know it. Gems are something else! They don’t need to eat, don’t need oxygen, can withstand intense temperatures and pressures (and lack thereof). Gems could be classified as extremophiles, ie. organisms that can survive in environments far too extreme for human life! What if … Homeworld is Jupiter? Or Saturn?!
    What if the hexagon vortex on Saturn is really the Diamond Authority HQ?



    Twitter: Emerald