What Happens When Vantage Points Are Farther Apart?

What would happen if the vantage points were farther apart?

If you were to separate the vantage points by a larger distance, such as ten feet instead of two feet, you would expect to see a smaller angular shift of the object. This is because the angular shift of an object due to parallax is inversely proportional to the distance between the vantage points.

Understanding Parallax and Angular Shift

Parallax is the apparent change in position of an object when viewed from different vantage points. In astronomy, this effect is used to measure the distance to nearby stars.

When you increase the distance between the vantage points, the angular shift of the object will decrease. The angular shift is the apparent change in the position of the object as observed from different vantage points.

Calculating Parallax Angle

The parallax angle between two vantage points and an object can be calculated using the formula:

θ = arctan(d/D)

Where θ is the parallax angle, d is the distance between the two vantage points, and D is the distance to the object.

As mentioned earlier, the parallax angle is inversely proportional to the distance between the vantage points. So, when you increase the separation from two feet to ten feet, the parallax angle decreases by a factor of five.

Effect on Angular Shift

Therefore, if you observed an angular shift of 0.5 degrees with a two-foot separation, you would expect to see an angular shift of only 0.1 degrees with a ten-foot separation between the vantage points. This decrease in angular shift is a result of the decreased parallax angle.