Space Science Project 2 Goal: Explore the relation between Sun and the Solar System Barycentre (SSB).

According to Kepler's laws, the Earth revolves in an elliptical orbit with the Sun at one of its focii. However, applying Newton's mechanics related to centre of mass, it is seen that the centre of mass of the total solar system does not necessarily coincide with the centre of the Sun. Even though the Sun accounts for nearly 90% of the total mass of the solar system, the mass of the other bodies such as planets, moons, comets, and asteroids are enough to offset the centre of mass of the solar system. This centre of mass is known as the Solar System Barycentre (SSB).

In this project, we shall see how far away from the Sun the SSB is. We shall analyse whether the distance is significant. We shall also plot the 3D movement of the Sun around the SSB over a certain time period selected randomly. The current program is the second version of the previous program. Here, we shall redo the visualization in 3d coordinates. We will be using the NASA toolkit SPICE in Python3 using the wrapper library spiceypy.

First, we compute the position vectors of the SSB wrt the Sun at a randomly chosen time. Let's choose the time as my birthday (24 April 1988, 9AM). We use the spkgps function in spiceypy for this purpose. The calculated value is more than 600,000 km. In other words, the SSB is more than 6 lakh km away from the centre of the Sun on 24th April 1988 at 9AM.

That might seem to be a huge distance. But when it comes to astronomical distances, context is necessary to make it intuitive. So let's compare the value with the Sun's dimensions. The radius of the Sun is considered to be approximately 696,000 km. Thus, on the selected day, although the SSB was not at the centre of the Sun, it was not situated outside the Sun either. Thus, when considered at the scale of the solar system, the difference in positions of Sun and SSB is that significant.

The figure below shows the SSB with respect to centre of Sun on the selected day. For an intuitive visualization, we have scaled the distances to the radius of the Sun.

Let's look at it in 3d as well.

So we calculated position of SSB on one particular moment in time and the difference from position of Sun's centre was noticed. What about other days? Since the position of planets around the Sun keeps changing, the mass distribution of the solar system also varies. This results in shifts in SSB. Let's have a look at how much does the SSB shift over a time period of, say, 30 years. Again using spkgps and matplotlib, we plot the daily position of SSB wrt centre of Sun after scaling the distances to radius of Sun.

Here is a 3D rendering of the same figure.

Isn't it dramatic! The changes in position of SSB is amazing, especially considering the fact that it is effect of the mass of the planets and bodies other than the Sun. It is observed that the SSB stays outside the Sun about 53% of the time n these 30 years. This means that in 30 years since my birth, half the time the centre of the solar system was not the Sun! That's a total of more than 15 years (almost half my lifetime).

In fact, the closest the SSB came to the centre of the Sun was almost exactly two years after the initial time (just one day short). It was only about 44,000 km away. The SSB has moving in a sort of spiral trajectory on or near the Sun. 9 years since the initial time, it was the farthest away (more than 1 lakh km) in 30 years.

The importance of this observation is revealed when we consider the fact that everything in the solar system revolves around the overall centre of mass. This is an extension of the two-body problem where two bodies affected by each other's gravity revolve around the common centre of mass. Our project has shown that the SSB is not necessarily the centre of the Sun and may even be situated outside the Sun. Thus, technically the earth revolves around not the Sun but the SSB. This also means that even the Sun revolves around the SSB. Half the time, when SSB is inside the Sun, the Sun was sort of wobbling while spinning. The other half of the time, it was actually orbiting the SSB.

The radius of the orbit is small in an astronomical sense, which is why it is often ignored in simple calculations. But when performing scientific observations or experiments which are impacted by the position of the Sun, even minor changes might be significant.

Moreover, this wobbling movement has been used to detect the presence of planets around other stars as well. When a star has a planetary system, it wobbles just like our Sun. The wobbling is detected through its light spectrum that shifts between blue and red colours due to the minor differences in its distance from us.

Let us visualise the movement of the Sun by making SSB as the fixed reference instead of the Sun. The below figure plots the daily position of the centre of the Sun wrt SSB over the same 30 years.

This project has brought some astounding observations to our view. It has taken us a step deeper into the science behind celestial movements. In the next update, we shall increase our time period to include the past, present and future positions of the Sun. We shall also attempt a visualization of the wobbling Sun. Later we will see how much The Earth's orbit is affected by changing our reference point from the Sun to SSB.