Why standing up lets you see farther.

The formula above, d = √(2Rh + h²), gives the exact straight-line distance to the horizon — not an approximation. Two simplifications worth knowing: real light bends slightly as it passes through the atmosphere, pushing the true horizon about 7% farther than shown here; and this is straight-line distance, not distance along the curved ground, which is a bit shorter still at large heights. The diagram is schematic — a real world's curve is far too gentle to draw at true scale, so the curvature here is exaggerated to make it visible — but the dashed sight line is always a genuine tangent, recalculated every time the slider moves. Jupiter has no solid surface, so its radius and height are both measured from its cloud tops, and the English Channel marker always shows Earth's real 34 km width, even when you're comparing other worlds, just as a familiar yardstick. See Wikipedia: Horizon — Distance to the horizon.