Originally Posted by
effortless
So his question is, how far from earth does an astronaut stop seeing more of the earth.
Supposing the astronaut is looking out the cupola of the ISS 400km above the surface of the earth I calculate a distance to the horizon of
just under 2300km.
That means she sees the horizon 2300km from her vantage point.
The distance along the curvature on the ground an ant would have to travel will be slightly different. More different as your altitude above earth increases. Looking down from the moon almost the whole hemisphere will be visible and distance along the line of sight would be dominated by the distance from earth in the first place.
The math is just using the pythagorean theorem:
r=6400km
v=400km
The distance d from the Observer O to a point H on the horizon is given as the square root of
2*r*v+v^2