US Survey Feet (ft-us) to parsecs (pc) conversion

What is the us survey foot?

What is US Survey Feet?

US Survey Feet is a unit of length used in the United States for land surveying. It is slightly different from the international foot. Understanding its origin and applications is crucial for accurate land measurements and legal descriptions.

Origin and Definition

The US Survey Foot (ftUS) is defined based on the Mendenhall Order of 1893, which related customary units to the metric system using the meter. At that time, it was defined as:

1 US Survey Foot = $\frac{3937}{1200}$ meters

This value equates to approximately 0.3048006096 meters. This differs slightly from the international foot which is exactly 0.3048 meters. The difference, while seemingly small (2 parts per million), can accumulate significantly over large distances, impacting land boundaries and area calculations.

The Issue & Readjustment

The difference between the international foot and the US survey foot caused discrepancies, especially in states that relied heavily on the Public Land Survey System (PLSS). Over time, states have addressed this issue in various ways:

• Many states have officially adopted the international foot for all new surveys.
• Some states continue to use the US Survey Foot. It's crucial to know which definition is in use for any particular survey or land description.
• Conversion factors are often provided in legal documents to clarify which foot is being used.

For more information about each state's definitions of feet, please read NOAA's definition of US Survey foot.

Usage and Real-World Examples

While its use is declining, the US Survey Foot is still relevant in some contexts, especially when dealing with older surveys and legal descriptions. Understanding its magnitude helps grasp spatial relationships:

• Property Boundaries: In states where it is still used, a land description stating a lot is 100 US Survey Feet wide means it is approximately 30.48006096 meters wide.
• Land Area Calculations: Area calculations, like acres, derived from measurements in US Survey Feet will differ slightly from those derived from international feet.
• Geographic Information Systems (GIS): GIS databases may contain data referenced to US Survey Feet, requiring proper transformation when integrating with data using the international foot.

Interesting Facts

• The slight difference between the two definitions of a foot has caused legal disputes related to property boundaries.
• The National Geodetic Survey (NGS) provides tools and resources for converting between the US Survey Foot and the international foot.

What is the parsec?

The parsec (pc) is a unit of length used in astronomy to measure large distances to objects beyond the Solar System, such as stars and galaxies.

Definition

One parsec is the distance at which one astronomical unit subtends an angle of one arcsecond.

$$1\ \text{pc} = 3.08568 \times 10¹⁶\ \text{m}$$

By the 2015 IAU exact definition, 1 pc = 648000/π au = 30,856,775,814,913,673 m. This equals about 3.2616 light-years or 206,265 astronomical units.

Origin and History

The term "parsec"—a contraction of "parallax of one arcsecond"—was coined by British astronomer Herbert Hall Turner in 1913. It arises naturally from the method of stellar parallax: a star one parsec away shifts by one arcsecond against the background as Earth moves from one side of its orbit to the other. The unit gave astronomers a convenient measure tied directly to their primary distance-measuring technique.

Law and Notable Facts

The parsec is accepted for use with the SI in astronomy. Multiples are common: the kiloparsec (kpc, thousands of parsecs) for galactic scales and the megaparsec (Mpc, millions) for intergalactic distances. No star lies within one parsec of the Sun; Proxima Centauri, the nearest, is about 1.30 pc away.

Real-World Examples and Conversions

• Proxima Centauri lies about 1.30 pc (4.24 light-years) from Earth.
• The Milky Way's disk spans roughly 30,000 pc (30 kpc) across.
• The Andromeda Galaxy is about 0.78 Mpc away.
• 1 pc ≈ 3.2616 light-years ≈ 206,265 au ≈ 30.857 trillion km.