is Chicago ever the "front" of the planet?

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is Chicago ever the "front" of the planet?

Postby loki1913 » Thu Feb 18, 2016 7:00 pm UTC

i am writing a fictional book about super heroes, but i want to get my science right. i recognize that the Earth spins on an angle as it revolves around the sun, and the sun (in turn) is traveling through the universe with nine little planets (and assorted moons) like a bunch of hyperactive kids running around a soccer ball.

I would like help with the following questions: is there a specific line around the planet charting the Earth's actual rotation, and if so, does that line have a name that would make images of it easier to find on Google? further, does this line pass anywhere near Chicago? and finally, assuming this line of rotation does pass remotely near Chicago, would someone standing on this line have the full energy of the Earth's 30km/second rotation beneath their feet? what other forces (rotation, time of year/proximity to the moon) would lessen the "impact" of this location? (extra points if someone could tell me the day, year, and time that this place might be the "front" of the planet. also for how long?)

in my book, a particularly clever super villain uses the natural motion of the Earth to smack a super hero. for added hilarity, i intend to include a sidenote that the villain in question actually emailed Randall Munroe for help on this problem, assuming Mr.Munroe gives me permission to acknowledge him in this manner. just so you all know why i'm asking.

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Re: is Chicago ever the "front" of the planet?

Postby gmalivuk » Thu Feb 18, 2016 7:27 pm UTC

loki1913 wrote:i am writing a fictional book about super heroes, but i want to get my science right. i recognize that the Earth spins on an angle as it revolves around the sun, and the sun (in turn) is traveling through the universe with nine little planets (and assorted moons) like a bunch of hyperactive kids running around a soccer ball.

I would like help with the following questions: is there a specific line around the planet charting the Earth's actual rotation, and if so, does that line have a name that would make images of it easier to find on Google? further, does this line pass anywhere near Chicago? and finally, assuming this line of rotation does pass remotely near Chicago, would someone standing on this line have the full energy of the Earth's 30km/second rotation beneath their feet? what other forces (rotation, time of year/proximity to the moon) would lessen the "impact" of this location? (extra points if someone could tell me the day, year, and time that this place might be the "front" of the planet. also for how long?)

in my book, a particularly clever super villain uses the natural motion of the Earth to smack a super hero. for added hilarity, i intend to include a sidenote that the villain in question actually emailed Randall Munroe for help on this problem, assuming Mr.Munroe gives me permission to acknowledge him in this manner. just so you all know why i'm asking.

I don't know of any simple way to calculate the point that is "leading" in Earth's movement around the Sun at a specific time, but it is definitely limited to the same places that can have the Sun directly overhead, which means the tropics.
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Re: is Chicago ever the "front" of the planet?

Postby EdgarJPublius » Thu Feb 18, 2016 9:37 pm UTC

So, I think you can roughly estimate the longitude that is 'leading' the earth around the sun at any given moment by just going 90* West of wherever it is currently noon. I'm not sure if sidereal or solar time would be the best approximation, but I suspect the solar clock ( so Local Mean Time) is what you'd want to use.
That means the best time to do the thing would be at or about exactly 6:00am LMT
If I'm wrong and sidereal time is the better approximation, what you want is Local Apparent Sidereal Time (Last).
These are both used in navigation and astronomy, so people keep track of them.

As gmalivuk said, the plane of Earth's movement around the sun is in line with the sun (this concept is related to, but not really the same as, the ecliptic plane), so the latitude that is in line with the movement around the sun varies over the year. You can probably find exactly what date & time the sun is directly over head any given line of latitude with some work/google but if you want the action to be in/about Chicago it's never gonna happen (unless the axial tilt shifts radically and the Tropic of Cancer ends up in Canada) But you can figure out very easily when the Sun is as far North (and therefor as close to Chicago) as it gets. That's just the Summer Solstice.
However, I'm not sure that longitude actually matters. I think it would only have an effect on the vector angle, not the absolute kinetic energy transferred.

If you really want to get the most bang, then the Moon and tides do have a notable impact, but I'm not sure what the optimal arrangement is. Whatever the optimal arrangement is should occur roughly every 27-28 days or so. Unless I'm wrong about the longitude not mattering, in which case the proper alignment is gonna be much less frequent. On the order of once every some number of hundreds of years probably (a wild ass-guess).
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Re: is Chicago ever the "front" of the planet?

Postby gmalivuk » Thu Feb 18, 2016 10:08 pm UTC

EdgarJPublius wrote:But you can figure out very easily when the Sun is as far North (and therefor as close to Chicago) as it gets. That's just the Summer Solstice.
The problem is, this isn't helpful, because at the June solstice the northern half of the axis is tilted toward the Sun, so the "leading" point is right on the equator.

What you actually want is the September equinox, when the northern end of the axis is maximally prograde around the Sun. The nice thing about it being an equinox is that you don't have to worry about time changes or anything, as it should be right at sunrise that a particular meridian crosses through the plane perpendicular to the radius of the orbit.
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Re: is Chicago ever the "front" of the planet?

Postby EdgarJPublius » Thu Feb 18, 2016 10:22 pm UTC

Ah, of course. Took me a few minutes to figure out why I got it wrong.

So yea, 600 LMT on the Autmnal (September) Equinox is when Chicago is at the closest to the 'leading point' of Earth on it's orbit around the sun.

Again though, I'm not sure the longitude matters for absolute energy transfer. SO you should be fine at 600 LMT any time of year.
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Re: is Chicago ever the "front" of the planet?

Postby gmalivuk » Fri Feb 19, 2016 1:59 am UTC

The point of waiting until the equinox is that the angle between Earth's surface and its direction of movement is closest to perpendicular.

The OP is a bit unclear, but if we assume the attack is something like causing the target to suddenly stop relative to the Sun, then the closer the target is to the "front" of the planet, the more of that impact is going to go into directly "smacking" the target, rather than being a glancing blow.

If we consider a point on the Arctic Circle instead of Chicago, then at the spring equinox it'll be at the "top" of Earth and stopping will result in Earth suddenly sliding horizontally at 30km/s, for zero direct impact. Six months later, the target will hit the surface at that same speed, but an angle 47 degrees from horizontal.

(One kink that occurs to me is that Earth's orbit isn't circular, so apart from perihelion and aphelion, which are closer to the solstices than the equinoxes, Earth is never moving *quite* perpendicular to the line toward the Sun.)
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Re: is Chicago ever the "front" of the planet?

Postby thoughtfully » Fri Feb 19, 2016 4:51 am UTC

If you want the cold, hard, data, the US Naval Observatory has a software library for calculating positions of celestial bodies.
http://aa.usno.navy.mil/software/novas/novas_info.php
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Re: is Chicago ever the "front" of the planet?

Postby gmalivuk » Fri Feb 19, 2016 12:53 pm UTC

The problem is that there's no celestial body that sits directly over the "front" of the planet.
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Re: is Chicago ever the "front" of the planet?

Postby thoughtfully » Fri Feb 19, 2016 7:37 pm UTC

The trouble is, space is big. And mostly space. You can draw a line out from the center of the Earth to the point on its surface that intersects with its orbit on the leading side, but that line will pretty much go on forever without hitting anything, except pretty rarely. It does help that the other planets are mostly on a plane, though. You could try to figure out when that line passes near some interesting object.
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Re: is Chicago ever the "front" of the planet?

Postby lorb » Sat Feb 20, 2016 2:06 pm UTC

loki1913 wrote:I would like help with the following questions: is there a specific line around the planet charting the Earth's actual rotation, and if so, does that line have a name that would make images of it easier to find on Google?


I am not aware of a special name for that line but it is accurately described as the intersection of earths surface with its ecliptic plane. Putting "ecliptic plane" into googles image search will give you nice visualizations.
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Re: is Chicago ever the "front" of the planet?

Postby gmalivuk » Sat Feb 20, 2016 4:25 pm UTC

And the front point of the planet is 90 degrees west along that circle from the point directly underneath the Sun at a given time.

The somewhat tricky thing is the math necessary to calculate that point, since the circle is not lined up with latitude or longitude.
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Re: is Chicago ever the "front" of the planet?

Postby mfb » Sat Feb 20, 2016 8:14 pm UTC

At the day of an equinox, the point that is "the front" (in heliocentric coordinates) is at a latitude of +- 23.5 degrees. At the summer and winter solstices, it is at the equator. In between, it is in between.
If you are at 23.5° N or S and "at the front", 3 months later you have winter.

Note that this is a very heliocentric view. Consider it from the center of the galaxy, and the point is somewhere else. Consider it from the frame of isotropic cosmic microwave background, and it is at another different point.
loki1913 wrote:would someone standing on this line have the full energy of the Earth's 30km/second rotation beneath their feet?
That does not make sense at all.

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Re: is Chicago ever the "front" of the planet?

Postby Hypnosifl » Thu Feb 25, 2016 4:58 am UTC

By "front" do we mean the point on the Earth's surface that would lie along a line from the center of the Sun to the center of the Earth, so that if you were at that point at that moment the Sun would be at the very top of the apparent "dome" of the sky? If so, only points that lie in the tropics can ever lie along such a line (that's basically the definition of the tropics).

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Re: is Chicago ever the "front" of the planet?

Postby phlip » Thu Feb 25, 2016 5:21 am UTC

gmalivuk wrote:And the front point of the planet is 90 degrees west along that circle from the point directly underneath the Sun at a given time.

An alternative phrasing: from the centre of the Earth, the cross product of the vector towards the sun, and the vector towards the north ecliptic pole (or possibly south? I was always bad at remembering the chirality of the cross product).

That is, simplifying as though the Earth had a circular orbit, the normal of the Earth's path is towards the sun, and the binormal is towards the ecliptic pole, and we want the tangent.

This is not, specifically, easier to calculate, but just an alternative phrasing.

Hypnosifl wrote:By "front" do we mean the point on the Earth's surface that would lie along a line from the center of the Sun to the center of the Earth, so that if you were at that point at that moment the Sun would be at the very top of the apparent "dome" of the sky?

No, we mean "front" as in "in a reference frame where the Sun is stationary, and the Earth orbits around it, what point on the Earth is the extremity in its direction of motion?"

It's still only points in the tropics, but still.

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Re: is Chicago ever the "front" of the planet?

Postby Hypnosifl » Fri Mar 04, 2016 2:36 am UTC

phlip wrote:what point on the Earth is the extremity in its direction of motion?"

Can you elaborate on the phrase "extremity in its direction of motion"? Are you talking about some vector associated with the point taking an extreme value, and if so is it just its magnitude that is taking the extreme value or is there an extreme angle relative to some reference direction, or something else?

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Re: is Chicago ever the "front" of the planet?

Postby gmalivuk » Fri Mar 04, 2016 2:46 am UTC

Well the direction's already set as "its direction of motion", so it's just the magnitude that is extreme.

If the earth is a car that is driving around the sun, what point on Earth is the front of the car?
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Re: is Chicago ever the "front" of the planet?

Postby Hypnosifl » Fri Mar 04, 2016 2:58 am UTC

gmalivuk wrote:Well the direction's already set as "its direction of motion", so it's just the magnitude that is extreme.

Oh, so are you talking about the magnitude of the velocity vector in a Sun-centered coordinate system rather than an Earth-centered one? If so, are you sure this is what the OP was asking about? I don't see how this would be connected to the question of whether Chicago is the "front" of the planet, it seems like it would be a question about whether Chicago is ever the fastest-moving point on the planet.

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Re: is Chicago ever the "front" of the planet?

Postby gmalivuk » Fri Mar 04, 2016 12:45 pm UTC

As phlip clearly said, we're talking about the sun's reference frame.

And the OP hasn't clarified, but we are taking "front" to mean what it typically means the rest of the time. If you ask where the front is on a rolling ball, no one says it's the top because that's where the velocity is greatest.

No one is talking about extremity of velocity.
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Re: is Chicago ever the "front" of the planet?

Postby Hypnosifl » Fri Mar 04, 2016 1:00 pm UTC

gmalivuk wrote:As phlip clearly said, we're talking about the sun's reference frame.

And the OP hasn't clarified, but we are taking "front" to mean what it typically means the rest of the time. If you ask where the front is on a rolling ball, no one says it's the top because that's where the velocity is greatest.

No one is talking about extremity of velocity.

OK, your comment Well the direction's already set as "its direction of motion", so it's just the magnitude that is extreme made me think you were talking about the extreme magnitude of a "direction of motion" vector. But I didn't pay enough attention to your subsequent comment about the front of the car--I guess you're saying that if we take a snapshot of Earth at a particular instant, you want to draw a spatial axis extending from the center of the Earth whose direction is parallel to the Earth's instantaneous velocity at that moment (in a Sun-centered coordinate system), and see what two points on the surface this axis intersects, with the point that lies in the direction of motion being the "front" at that moment and the point that lies in the opposite direction being the "back"?

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Re: is Chicago ever the "front" of the planet?

Postby gmalivuk » Fri Mar 04, 2016 1:11 pm UTC

Yes.

I mentioned magnitude because you did. Position is a vector too, after all.
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Re: is Chicago ever the "front" of the planet?

Postby Hypnosifl » Fri Mar 04, 2016 11:35 pm UTC

Looking at the OP again, the lines "finally, assuming this line of rotation does pass remotely near Chicago, would someone standing on this line have the full energy of the Earth's 30km/second rotation beneath their feet?" and "a particularly clever super villain uses the natural motion of the Earth to smack a super hero" almost makes it sound like loki1913 is just asking for which point on Earth would have the largest total velocity, presumably in a Sun-centered reference frame since 30 km/second is the speed the Earth orbits around the Sun (though of course it's possible loki1913 isn't aware of the somewhat counterintuitive notion in physics that there is no such thing as absolute velocity independent of one's choice of reference frame). If that's what's being asked for, I think the answer at any given moment would just be "the point on the equator that's furthest from the Sun (i.e. experiencing the exact midpoint between sunset and sunrise) at that moment", since if you take that point's tangential velocity relative to the Earth's center and project it onto the orbital plane, it will be parallel to the velocity vector of the Earth's center relative to the Sun, and pointing in the same direction.

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Re: is Chicago ever the "front" of the planet?

Postby gmalivuk » Sat Mar 05, 2016 12:49 pm UTC

If you want to "smack" somebody, what good does it do to have the ground racing past at 30km/s?

I've already explained that I understand the idea of smacking something with Earth's orbital speed as the idea that you'd completely stop something and have Earth run into it at full speed. Which has maximum impact if the something is right at the "front" of the planet.
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Re: is Chicago ever the "front" of the planet?

Postby Hypnosifl » Tue Mar 08, 2016 12:05 am UTC

gmalivuk wrote:If you want to "smack" somebody, what good does it do to have the ground racing past at 30km/s?

I've already explained that I understand the idea of smacking something with Earth's orbital speed as the idea that you'd completely stop something and have Earth run into it at full speed. Which has maximum impact if the something is right at the "front" of the planet.

Ah, I missed that idea earlier, that makes sense as an interpretation. Though if this was what was intended, it again makes me think loki1913 is probably not understanding the principle of Galilean relativity which holds in Newtonian physics (or the expanded version in Einstein's theory)--if an object is initially at rest relative to the Earth, loki1913 should be aware that it would take just as much energy/force to make it move at 30 km/s relative to the Earth regardless if it was being made to "stop" relative to the Sun or increase its speed relative to the Sun, there's no way to exploit the Earth's motion to increase the impact for a given amount of energy the supervillain spends (unless the supervillain has some special non-Newtonian "stop objects relative to the Sun" power).

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Re: is Chicago ever the "front" of the planet?

Postby Neil_Boekend » Tue Mar 08, 2016 10:57 am UTC

gmalivuk wrote:If you want to "smack" somebody, what good does it do to have the ground racing past at 30km/s?

Nothing. But once you encounter a wall things get messy.
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Re: is Chicago ever the "front" of the planet?

Postby lorb » Tue Mar 08, 2016 4:29 pm UTC

Hypnosifl wrote:
gmalivuk wrote:If you want to "smack" somebody, what good does it do to have the ground racing past at 30km/s?

I've already explained that I understand the idea of smacking something with Earth's orbital speed as the idea that you'd completely stop something and have Earth run into it at full speed. Which has maximum impact if the something is right at the "front" of the planet.

Ah, I missed that idea earlier, that makes sense as an interpretation. Though if this was what was intended, it again makes me think loki1913 is probably not understanding the principle of Galilean relativity which holds in Newtonian physics (or the expanded version in Einstein's theory)--if an object is initially at rest relative to the Earth, loki1913 should be aware that it would take just as much energy/force to make it move at 30 km/s relative to the Earth regardless if it was being made to "stop" relative to the Sun or increase its speed relative to the Sun, there's no way to exploit the Earth's motion to increase the impact for a given amount of energy the supervillain spends (unless the supervillain has some special non-Newtonian "stop objects relative to the Sun" power).


Or the villain/victim are not initially at rest relative to the Earth.
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Re: is Chicago ever the "front" of the planet?

Postby Hypnosifl » Tue Mar 08, 2016 9:17 pm UTC

lorb wrote:Or the villain/victim are not initially at rest relative to the Earth.

True, but in that case Galilean relativity implies all that matters is their velocity relative to the Earth, if you already know that then their velocity relative to the Sun doesn't have any additional relevance, so the villain still wouldn't be in any sense exploiting the Earth's velocity relative to the Sun in order to create a bigger impact.

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Re: is Chicago ever the "front" of the planet?

Postby Soupspoon » Tue Mar 08, 2016 10:25 pm UTC

The whole discussion reminds me of a H.G. Wells short story. (Noting that a cursory glance at the Wiki page suggests that some Bot may have purged an assumed expletive, which actually wasn't... someone ought to sort that out.)

And I don't remember the 2015 film, somehow derived from this tale, with Simon Pegg... Must have snuck under my radar... Although with an apparent 8% rating on Rotten Tomatoes, maybe that's all for the best.


Anyway I'd have thought, if I have it the right way round, that the antisolar point (rather than that which is mutually perpendicular to the solar and polar directions, or however you'd describe it) would have the most 'natural' energy (the back edge of the spinning Earth, currently spinning in the same direction as the orbit) would have the most 'relative' velocity to the Sun. Give or take an adjustment for season, and greatest of all at the moment of Earth's perihelion as well. Assuming that what we're looking at here is something that phases the hero/victim temporarily out of any local influence (physical, gravitational, etc) of his/her original circumstance and relying upon the inertia and 'original kick' from the planet to send them off at a tangent.

If you're at the exact 6AM point (give or take the required seasonal adjustment), Earth's orbit is still sending you tangentially, but its rotation is now giving you a Sun-wise directional component to your velocity. (In such a "force-divorcing" scenario. I think, at least. Off the top of my head.) OTOH, perhaps reinstating localised interactions once more within the sphere of influence of the Sun than the Earth might (on a possibly sun-dipping trajectory) give the person subjected to this fate a slingshot effect if also suitably aligned to the Sun's orbital progress around galactic centre... But I'm not anywhere near working out how 'slingshotty' it could ever get, never mind when's the best time to do this...

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Re: is Chicago ever the "front" of the planet?

Postby gmalivuk » Tue Mar 08, 2016 10:47 pm UTC

Yes, there are other ways to interpret what the OP wants.
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Re: is Chicago ever the "front" of the planet?

Postby drachefly » Wed Mar 09, 2016 4:18 pm UTC

This question reminds me most of when Soul used a portal to the far side of the Earth to get a stream of projectiles moving at a relative velocity of the Earth's rotational speed times the sum of the axial radii of the Equator and Tokyo (i.e. took a column of material from the Equator on the far side of the planet and transposed it to Tokyo leaving it with the same momentum)

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Re: is Chicago ever the "front" of the planet?

Postby Sableagle » Sun Apr 03, 2016 11:46 am UTC

I was a little thrown off by "the Earth's rotation" in the OP, at first.

The super-villain is trying to make the super-hero suddenly be falling at 30kms-1 straight down, using a steampunk-styled raygun with a core of solid A Wizard Did It, and wants the maximum velocity relative to the Earth's surface at the point of impact and maximum angle of impact, correct?

I have to wonder about the supposed super-durability of a super-hero who can super-survive suddenly stopping relative to the solar system at any superposition on the ... wait, no. At any point on the Earth's surface. Even if you get the maths wrong and accidentally slap him into the ground at "only" 20kms-1 and at a 45° angle you're still getting a vertical component of 14.14kms-1, up there at Philae speeds. For a 90kg hero, that's 9GJ of impact energy on a smooth surface. The splat would go in a different pattern, but it'd still work on anything except a golem made out of the same stuff as Captain America's shield. 2.15 tonnes of TNT? Don't be near it when it pops.

Chicago's at 41.8339°N according to Google Maps, so on the September Equinox, at 6am local solar time, it's at the front (ignoring the solar system's orbit around the galaxy) plus ( 41.8339° - 23.4372° ), giving an impact angle of 71.6033°, kinetic energy perpendicular to sea level of 427MJ/kg and kinetic energy north along the surface of 142MJ/kg. If he happens to hit W Jackson Blvd just east of S Wacker Dr, that could be very upsetting for people who love the skyline as it is. Here, with swearing, is the sudden release of energy roughly equivalent to 200kg at 30kms-1.

As Neil pointed out, there are non-horizontal surfaces on the Earth. As Soupspoon pointed out, the point on the Equator furthest from the Sun when the Earth is at its highest orbital speed, closest to the Sun, on Jan 4, is the part that's going fastest. Somewhere on Volcan Cayambe there's got to be a big east-facing cliff that'd do well as the impact surface. As a bonus, if you hit that thing hard enough in just the right spot on just the right midnight, even with a squishy flesh bullet, you've got some small chance of having your squishy flesh bullet's remains entombed in a lava flow.

If you just send him to the opposite side of the Earth, he'll be doing 693ms-1 west along the surface, nothing like 30km-1 but still fast enough to make a nasty mess, and he'll be a long way from the nearest hospital.
Oh, Willie McBride, it was all done in vain.

DanD
Posts: 300
Joined: Tue Oct 05, 2010 12:42 am UTC

Re: is Chicago ever the "front" of the planet?

Postby DanD » Fri Apr 15, 2016 3:22 pm UTC

Assuming the intent is to suddenly stop someone relative to the sun, then it's also the wrong way to get the most impact.

Have it happen with the target standing east (I think, maybe west) of a cliff at midnight directly opposite the sun. Then you add orbital and rotational velocity. (I know rotational isn't much, but it's something). Ideally you do it at perihelion (which defines your location) to maximize orbital velocity).

Given that perihelion occurs relatively close to the (northern) winter equinox, I think this works to put the ideal point as close to Chicago as it gets, but that's still down in Mexico somewhere.


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