The perihelion of Mercury advances \(2^{\circ}\) 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?

Orbital mechanics, also known as celestial mechanics, is the study of the motions of celestial objects under the influence of gravitational forces. For instance, the orbits of planets around the Sun are dictated by these principles. Mercury's orbit, like those of other planets, follows an elliptical path. One interesting phenomenon related to Mercury's orbit is the perihelion advance. This refers to the gradual shift in the closest point of Mercury's orbit to the Sun.

This shift occurs due to various gravitational influences, primarily from other planets and relativistic effects predicted by Einstein's theory of General Relativity. Understanding Mercury’s perihelion advance helps astronomers test and refine their models of planetary motion. It's a fascinating aspect of orbital mechanics that shows the complexity and precision needed to study celestial movements.

Angular measurement is crucial in astronomy to quantify the positions and movements of celestial objects. An angle can be measured in degrees, arcminutes, and arcseconds. There are 360 degrees in a full circle, 60 arcminutes in a degree, and 60 arcseconds in an arcminute.

In the context of Mercury's perihelion advance, we start with 2 degrees per century. This needs to be converted into smaller units like arcseconds to understand annual changes better. For practical purposes, converting it step-by-step helps:

• 0.02 degrees/year (since 2 degrees/100 years)
• 1.2 arcminutes/year (since 0.02 degrees/year * 60)
• 72 arcseconds/year (since 1.2 arcminutes/year * 60)

These calculations aid in determining the precision required to measure such astronomical phenomena accurately.

Astronomical observation involves using various tools and techniques to measure and study celestial objects and their movements. Precision is key, particularly for phenomena involving small angular changes like Mercury's perihelion advance.

Observatories use high-powered telescopes equipped with precise instruments capable of measuring increments as small as arcseconds. The perihelion advance of Mercury is significant enough (72 arcseconds per year) to be detected and measured using these tools.

Advanced software and imaging technologies further enhance the accuracy of these observations. This allows astronomers to test theories, like Einstein's General Relativity, by observing predicted orbital changes. Consistent advancements in observation techniques continue to refine our understanding of the universe and its mechanics.