The curvature of the earth error associated with leveling shot of 1000 ft is most nearly?

To determine the curvature of the earth error associated with a leveling shot of 1000 ft, you can use the formula that approximates the curvature drop over a distance due to the Earth's curvature. The formula is based on the geometric relationship that defines the drop due to curvature as:

[ \text{Drop (ft)} = \frac{d^2}{2R} ]

where (d) is the distance in feet, and (R) is the radius of the Earth, approximately 3960 miles (or about 20,902,880 ft).

First, convert the distance into proper units for calculations:

1. Convert 1000 ft into miles (since R is in miles): [ d = \frac{1000 \text{ ft}}{5280 \text{ ft/mile}} \approx 0.1894 \text{ miles} ]

2. Use the formula to calculate the drop: [ \text{Drop} = \frac{(0.1894^2)}{(2 \times 3960)} ]

3. Calculate the drop value: [ \text{Drop} = \frac{0.03583516}{7920