One arc second (1″) is a unit of angular measurement used in astronomy, geodesy, navigation, and other fields. It is defined as 1/3600 of a degree, or approximately the angle subtended by a circle of radius 1 astronomical unit (AU) from an arc of length 1 meter.

History of the Arc Second
The concept of the arc second has been used for centuries to measure angles in the sky, with its origins likely traced back to the ancient Babylonians. In the 16th century, the Dutch astronomer Tycho Brahe used arc seconds to make highly accurate measurements of the positions of stars, which contributed significantly to the development of modern astronomy.
Applications of the Arc Second
Arc seconds are widely used in various fields:
Astronomy:
- Determining the sizes and distances of celestial objects
- Tracking the motions of stars and planets
- Searching for exoplanets
- Calibrating astronomical instruments
Geodesy:
- Measuring the shape of the Earth
- Establishing reference points for surveying and mapping
- Determining the relative positions of continents and oceans
Navigation:
- Determining the latitude and longitude of ships and aircraft
- Guiding ships and aircraft to their destinations
- Calculating the trajectory of projectiles
Equivalents of One Arc Second
- 1 arc second = 1/60 arcminute
- 1 arc second = 1/3600 degree
- 1 arc second = 4.84813681 × 10^-6 radians
Tables
Table 1: Equivalents of One Arc Second
Unit | Value in Arc Seconds |
---|---|
Degree | 3600 |
Arcminute | 60 |
Radian | 4.84813681 × 10^-6 |
Table 2: Arc Second Conversions
From | To | Multiplication Factor |
---|---|---|
Arcsecond | Arcminute | 1/60 |
Arcsecond | Degree | 1/3600 |
Arcsecond | Radian | 4.84813681 × 10^-6 |
Radian | Arcsecond | 206264.806247 |
Radian | Arcminute | 3437.74677078 |
Radian | Degree | 206264.806247 |
Table 3: Sizes of Celestial Objects in Arc Seconds
Object | Angular Diameter |
---|---|
Sun | 1925″ |
Moon | 1800″ |
Earth | 57″ |
Jupiter | 50″ |
Saturn | 20″ |
Table 4: Accuracies of Measurement in Arc Seconds
Application | Accuracy |
---|---|
Astronomy | < 0.1" |
Geodesy | < 1" |
Navigation | < 5" |
Surveying | < 10" |
Strategies for Achieving High Accuracy in Arc Second Measurements
- Use high-quality measuring instruments and techniques
- Calibrate instruments regularly
- Use reference stars or other known objects for calibration
- Take multiple measurements and average them
- Consider atmospheric effects and make corrections as needed
How to Measure One Arc Second
Measuring one arc second requires specialized equipment and techniques. Here is a step-by-step approach:
- Set up a high-precision optical instrument: This could be a telescope, theodolite, or other specialized device.
- Calibrate the instrument: Ensure that the instrument is properly adjusted and aligned.
- Identify a target object: This can be a star, planet, or other celestial object.
- Measure the angle between the target object and a reference point: Use the instrument’s crosshairs or other measuring device to measure the angle accurately.
- Correct for atmospheric effects: Atmospheric refraction can cause errors in the measurement, so apply appropriate corrections.
Frequently Asked Questions
Q: Why is the arc second an important unit of measurement?
A: The arc second provides a precise and standardized way to measure angles in astronomy, geodesy, navigation, and other fields where accurate angle measurements are critical.
Q: How small is one arc second?
A: One arc second is approximately the angle subtended by a circle of radius 1 AU from an arc of length 1 meter. In practical terms, it is the angle at which an object of size 1 meter would appear from a distance of 40,000 kilometers.
Q: Is there a creative new word to describe applications of the arc second?
A: “Nanoradians” is a coined term that refers to precision angular measurements on the nanoscale, utilizing sophisticated technologies such as laser interferometry to achieve sub-arcsecond accuracy.
Q: How can I improve the accuracy of my arc second measurements?
A: Use high-quality instruments, calibrate regularly, consider atmospheric effects, and take multiple measurements and average them.
Q: Is it possible to measure sub-arcsecond angles?
A: Yes, using advanced techniques such as Very Long Baseline Interferometry (VLBI), Adaptive Optics (AO), and laser interferometry, it is possible to measure angles at sub-arcsecond resolution.
Q: What is the largest angle that can be measured in arc seconds?
A: The largest angle that can be expressed in arc seconds is 360,000″, which represents a full circle.
Q: What is an astronomical unit (AU)?
A: An astronomical unit is the average distance between the Earth and the Sun, which is approximately 150 million kilometers.