The perihelion of Mercury advances 2 degrees per century. How many arcseconds does the perihelion advance in a year? (Recall that there are 60 arcseconds in an arcminute and 60 arcminutes in a degree.) Is it possible to measure Mercury's position well enough to measure the advance of perihelion in 1 year?

An arcsecond is a unit of angular measurement equivalent to 1/3600th of a degree. To visualize it, think of a full circle, which is 360 degrees. Divide each degree into 60 equal parts called arcminutes, and then each arcminute into 60 equal smaller parts, which are arcseconds. This very fine measurement is crucial in astronomy for tracking celestial objects with high precision. Understanding arcseconds helps us appreciate how detailed our observations can be.

Converting degrees to arcseconds is fundamental in astronomy. A degree can be broken down into smaller units progressively:
- 1 degree = 60 arcminutes
- 1 arcminute = 60 arcseconds

This leads to the equation:
- 1 degree = 60 x 60 = 3600 arcseconds

Knowing this, you can convert any angle in degrees to arcseconds by multiplying the number of degrees by 3600. For example, if we need to convert 2 degrees, we get:
- 2 degrees x 3600 arcseconds/degree = 7200 arcseconds

This conversion is essential for tasks that require high precision, such as determining the perihelion advance of Mercury.

For determining how much Mercury's perihelion (the closest point in its orbit to the Sun) advances in a year, we start with the perihelion advance per century. Given that it advances 2 degrees per century, we can convert this to arcseconds:
- 2 degrees = 2 x 3600 = 7200 arcseconds per century

Next, we find the annual advancement by dividing this by the number of years in a century (100):
- 7200 arcseconds / 100 years = 72 arcseconds per year

Measuring this advancement is a challenge of precision. Modern astronomical instruments can capture positions with such accuracy, detecting changes as small as a fraction of an arcsecond. Therefore, observing and quantifying Mercury's perihelion shift yearly is both feasible and significant for studying gravitational interactions and General Relativity.