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Welcome to our Physics lesson on Planetary Motion around the Sun, this is the fifth lesson of our suite of physics lessons covering the topic of Sun and Planetary Motion, you can find links to the other lessons within this tutorial and access additional physics learning resources below this lesson.
As discussed in other topics, our Solar System is a set of celestial bodies interacting with each other by means of gravitational forces. The Sun is the main contributor to the stability of this structure as it alone has a mass that is much greater than that of all the other celestial bodies of the solar system combined together. Therefore, when studying planetary motion at introductory level (as in this case), we neglect any gravitational interaction between celestial bodies with each other and focus only on their interaction with the Sun, as the results do not vary too much from the true ones.
Because of gravitational force (that acts as centripetal force as discussed in Section 8), planets perform a circular motion around the Sun (they also rotate around themselves and we cover this phenomenon later in this tutorial). When applying the general gravitation law, we obtain important results on a planets trajectory, movement speed in their respective orbits and period of rotation around the Sun. These results are summarized in the three Kepler's Law discussed in tutorial 8.2 (Gravitational Potential Energy. Kepler Laws):
In popular terminology, we call a planetary period a"year" . As the distance from the Sun to the planet increases, you can easily see that the planetary period increases too.
The angle of the Earths' revolution around the Sun depends on the frame of reference. If stars are taken as reference frame, the corresponding period of revolution is known as sidereal (stellar) period, while when the Sun is taken as a reference frame, then corresponding period is known as tropical (solar) period. These periods (that determine the length of the corresponding years) are not the same; they have small deflections due to the effect of the Moon on the Earths' revolution around the Sun. Thus, the duration of one sidereal year is 365.2568 days and that of a tropical year is 365.2422 years. Such differences has led to the use of two different solar-based calendars: Julian and Gregorian ones, we will discuss this in more detail in the upcoming tutorials.
An ancient site is 5300 years old when calculated using the sidereal period (year). How old is this site when using the tropical period (year)?
The age of the ancient site in days is:
where Ns is the site age expressed in number of sidereal years. Substituting the known values, we obtain
This number must be divided by the duration of a tropical year in order to give the site's age in tropical years (Nt). We have
where Tt = 365.2422 days is the tropical year period. Thus, after substitutions we obtain for the site's age in tropical years:
Hence, there is a small deflection when the duration of a year is measured by taking into account the two aforementioned periods of the Earth revolution around the Sun.
You have reached the end of Physics lesson 22.2.5 Planetary Motion around the Sun. There are 10 lessons in this physics tutorial covering Sun and Planetary Motion, you can access all the lessons from this tutorial below.
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