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I'll keep it nice and simple. On a world that does not rotate is it possible to have a mountain that is high enough that when you sit at the top, you can see the divide between daylight and night that spans the planet? If so, how high would it have to be and could a human survive at the top without a spacesuit?

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    $\begingroup$ If it is at the divide it does not even need be a mountain, so the question is rather: Where do you want your mountain to be? Also: by not rotate, do you mean a) tidally locked to its sun? b) rotating at speed so that it does not seem to rotate when looked at from above (e.g. one day = one year) $\endgroup$ – dot_Sp0T Oct 3 '16 at 5:27
  • $\begingroup$ I want the mountain to be at the divide so you can stand on top and look left and see light, then look right and see the dark side of the planet. Yes, tidally locked to the sun, so there is eternal day on one side and eternal night on the other. $\endgroup$ – Ledav Oct 3 '16 at 5:33
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    $\begingroup$ What you're asking is really unclear. If you want to see the divide that spans the entire planet... Well, you can't, 'cause half of it is on the other side. To even see half of it (assuming a perfectly spherical planet), from simple geometry your mountain would have to be infinitely tall. And rotation is irrelevant. $\endgroup$ – jamesqf Oct 3 '16 at 5:34
  • $\begingroup$ I interpreted it to mean you can see some point on tbe terminator that are on opposite logitudes. That’s possible if not at the equator. I agree opposite sides is ambiguous so the question is badly worded; but I thought it obvious that anipodes could not be what was meant because that’s impossible. I found an interpretation that is meaningful. (Maybe I gave him too much credit?) $\endgroup$ – JDługosz Oct 3 '16 at 5:39
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How big is the planet?

Picture the solar latitude, by which I mean the latitude based on the current sun’s angle, not the planet’s pole. The circle of that latitude line is the size we care about. The elevation needs to be high enough to see antipodes of that circle. (Note: This is the meaning of opposite that allows the problem to have an answer. If you meant viewing the antipodes of the planet as a whole, you would actually see the entire terminator if you located the mountain at the equator so you would not speak of two points; and it cannot be done.)

Clearly it gets smaller with decreasing distance to the solar pole. In fact, if you’re at the (solar) pole, you will see half light and half dark on the ground at your feet. So, zero, for some choice of parameters that you did not specify.

More generally, determine the distance to the horizon for a mountain of some given height and planet size. Locate it far enough toward either pole so the opposite sides of the terminator are within this distance.

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Well, not very high at all*, in fact, I can do it from my own house.

enter image description here

*As the time of day does not matter, technically twilight and dawn both allow for what you want, in fact,above shows a perfect depiction of late night meeting early day.

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