# Orbital period

Hi,

in today’s short post I will write about orbital period of planets, more accurately synodic and sidereal period.

In the post about year and how difficult it is to determine how long it is, I mentioned that there are some ways you can measure the time it takes for planet to orbit star.

Sidereal period is the time it takes for Earth or other object, orbit once with respect to distant stars.

Now distant stars are great because they tend to be on the same spot most of the time. For example on the Voyager plague there is a map to show the position of distant pulsars, why? Because such things are stable, easy to see and far away. For year we use stars in Milky Way which is still fine, most move by fractions of arcseconds every year which is something you can not notice with eye and has some effects in thousands of years.

Sidereal period of Earth around the Sun is 365.25636 days. (I wonder if you could talk about something like sidereal period of Sun around the center of Galaxy, probably yes)

Synodic period is about two bodies orbiting Sun for example. It is the time that it takes for the two objects to get to same position. So if Mars and Earth are right behind each other (which is called opposition), synodic period is the time it takes for it to happen again. Now of course both planets orbit and the faster one (the one closer to Sun) always has to make at least one revolution. When that happens it just needs to catch up with the slower planet. With this simple thought you can come up with equation that lets you calculate the synodic period:

1/S=1/P-1/p

(lower case p is the sidereal period of the object with longer period)

Thats about it for know, enjoy your winter holiday while/if you still have it!

Dragallur

# How long is a year actually?

Hi,
today I will write about a year. The thing is that as in many other subjects when you look down into the simplest things you might find that they are not as simple as they seem. So how long is year? 365 days? 366 days?

You very well know that every 4 years we have 1 extra day in February. You might also know that this is because year is not 365 days long exactly but roughly 365.25 .. its important to say roughly because it is not perfectly true and it matters how you define one year.

First lets see how we define one day. One would say that it is the time that it takes for Earth to rotate once. Problem is that we need to define some object to compare it to, some ground, some reference point. It might be the Sun, but Sun is too close and since we go around it, this would change the length of the day.

Sidereal day is the day that is defined as a rotation of Earth around its axis compared to very distant stars that are relatively stable. 23.9344699 hours… that is pretty close to 24 that we use, but it is not what we use.

The thing is that we decided to use what is called solar day, which is in fact compared to Sun. As Earth rotates around its axis, it also rotates around Sun, which makes the solar day different length.

This is how the effect looks like. You need to turn Earth n.2 by little bit more since it moved around the Sun too.

Problem is that the length of solar day changes since our orbit is sligthly elliptical and when we are closer to Sun we are faster which means that the solar day is shorter and there is more time needed for the same spot to face Sun again. This effect adds up to almost 365.25 solar days in a year. If it was so simple we could just add one leap day every 4 years to make up this 0.25 difference but it is actually 0.242181 which makes difference over time.

Julian calender ran with 0.25 for a long time but after about 1500 years it was already 10 days behind of the real date and Christians wanted to predict Easter exactly so they changed on Gregorian calendar. This calendar is the same, except that if the year is divisible by 100 it wont be a leap year, though if it is also divisible by 400 it will be a leap year. This almost fixes the problem, though every 3216 years one day is still off from the real time. Yup. Check out this video to see how we can improve this slight mistake: