Describe the points on the earth’s surface that are visible to a viewer who is 100 miles
above the North Pole.
Would it be half of the surface area of Earth?
No. Draw a diagram and it will how how far the horizon is at that altitude.
Hint - the radius at the horizon makes a right angle at the surface.
No, it would not be half of the surface area of the Earth. When a viewer is 100 miles above the North Pole, they would be able to see a specific portion of the Earth's surface. To visualize this, imagine a sphere representing the Earth. The viewer's line of sight would extend as far as the horizon, which is the farthest point on the Earth's surface that can be seen.
From the North Pole, the horizon extends in all directions. However, due to the Earth's curvature, the viewer's line of sight would gradually slope downward toward the Earth's surface, forming a cone shape. The base of this cone would be the horizon at ground level, and the apex would be the viewer's position 100 miles above the North Pole.
The angle of this cone depends on factors like the viewer's elevation and the Earth's radius. For instance, if the viewer is at an elevation of 100 miles (or around 560,000 feet) above the Earth's surface, the cone formed would have a half-angle of approximately 76.63 degrees.
Therefore, the points on the Earth's surface that are visible to a viewer 100 miles above the North Pole would be limited to a cone-shaped region, rather than encompassing half of the Earth's surface.
To determine the points on Earth's surface visible to a viewer 100 miles above the North Pole, we need to consider the concept of the observer's line of sight. When someone is above the North Pole, their line of sight extends in all directions, eventually reaching the horizon.
The horizon is the furthest distance an observer can see before the Earth's curvature blocks their line of sight. In this case, since the viewer is 100 miles above the North Pole, their horizon will be 100 miles away from them in every direction.
To visualize this, imagine a circle with a radius of 100 miles centered directly above the North Pole. This represents the observer's field of view. Any point on Earth's surface that falls within this circle is visible to the viewer.
Therefore, the visible points on Earth's surface from an observer who is 100 miles above the North Pole form a circle with a radius of 100 miles. This circle covers a small portion of the Earth's surface, but it is not half of the total surface area. The entire surface area of the Earth cannot be visible simultaneously from any single point above the planet.