To get an idea of how much of space would be visible from Earth if it were the size of a peppercorn, we can make some calculations based on the typical field of view of a human eye and the known observable universe.
The average field of view of a human eye is roughly 120 degrees horizontally and 90 degrees vertically. Let's assume we can see in all directions equally.
The observable universe is estimated to have a diameter of about 93 billion light-years, which is approximately 8.8 × 10^26 meters.
If we consider Earth as a peppercorn, which has an average diameter of around 5 millimeters (5 × 10^-3 meters), we can set up a proportion to calculate the corresponding diameter of the observable universe at this scale:
(8.8 × 10^26 meters) / (5 × 10^-3 meters) = x / 1
Simplifying the proportion, we find:
x ≈ (8.8 × 10^26 meters) × (1 / 5 × 10^-3 meters) ≈ 1.76 × 10^30 meters
So, at the peppercorn scale, the diameter of the observable universe would be approximately 1.76 × 10^30 meters.
To determine how much of this miniature universe would be visible from Earth, we need to calculate the solid angle corresponding to the human eye's field of view.
The solid angle is a measure of the extent of a cone's surface in three-dimensional space, and it is typically measured in steradians (sr). The full sphere, in which we assume the peppercorn-sized Earth is located at the center, has a solid angle of 4π steradians.
To find the fraction of the full sphere covered by the human eye's field of view, we divide the solid angle of the field of view by the solid angle of the full sphere:
Fraction visible = (120°/360°) × (90°/180°) = (1/3) × (1/2) = 1/6
Thus, if Earth were the size of a peppercorn, approximately 1/6 of the miniature observable universe would be visible from Earth, assuming the human eye's field of view remains the same at this scale.
It's important to note that this is a simplified calculation and doesn't take into account various factors such as the expansion of the universe or the limitations of human vision. Additionally, the actual shape and distribution of the universe are still topics of scientific research and exploration.