How is our planet and solar system different than others?

Introduction

What can solar systems look like?

We think of our solar system, with 1 star and 8 planets as the norm. But there are other solar systems out there with very different configurations than that with which we are familiar.

For example, it’s possible to have a multi-star system. Our nearest stellar neighbor, the Alpha Centauri system, includes three stars. This diagram illustrates what a 6-star system looks like, with the stars actually existing in pairs:

Sextuple Star system Image source

It’s also possible to have a planet that orbits more than 1 star, we call those planets Circumbinary: Circumbinary planetary system

Image reference: https://en.wikipedia.org/wiki/Circumbinary_planet

We see some of these depictions in Science Fiction, such as in the planet Tatooine in Star Wars with its “Twin suns”: Tatooine’s twin suns

The Data

NASA Exoplanets

NASA keeps a log of every discovered “exoplanet”. An exoplanet is a planet that is part of a solar system that is not our own.

The original Exoplanets dataset had 313 columns and 5438 observations.

In order to focus on the question of “How is our planet and solar system different than other planets and their solar systems?”, I pared down the dataset to only 16 columns with the same number of observations:

Univariate description of the variables

variable type na na_pct unique min mean max
PlanetName chr 0 0.0 5438 NA NA NA
HostName chr 0 0.0 4056 NA NA NA
PlanetLetter fct 0 0.0 8 NA NA NA
NumberOfStars int 0 0.0 4 1.00 1.10 4.0000e+00
NumberOfPlanets int 0 0.0 8 1.00 1.77 8.0000e+00
CircumbinaryFlag lgl 0 0.0 2 0.00 0.01 1.0000e+00
PlanetOrbitalPeriod_Days dbl 237 4.4 5191 0.09 82218.21 4.0200e+08
PlanetRadius_EarthRadius dbl 17 0.3 1642 0.31 5.67 7.7340e+01
PlanetMass_EarthMass dbl 24 0.4 2435 0.02 484.48 2.3900e+05
PlanetEquilibriumTemp_K int 1417 26.1 1506 34.00 914.66 4.0500e+03
StellarLuminosity_Solar dbl 223 4.1 1919 -6.09 -0.11 3.8000e+00
StellarEffectiveTemp_K dbl 207 3.8 2144 415.00 5443.26 5.7000e+04
StellarRadius_SolarRadius dbl 228 4.2 436 0.01 1.53 1.0946e+02
StellarMass_SolarMass dbl 4 0.1 239 0.01 0.96 1.0940e+01
StellarAge_Gyr dbl 1181 21.7 592 0.00 4.37 1.4900e+01
SystemDistance_Parsecs dbl 21 0.4 3982 1.30 701.91 8.5000e+03

Data Structure

So now we have 16 columns to focus on. Let’s first look at the structure of the data, including how many NA’s we should keep in mind.

We have:

  • 1 logical
  • 3 integers
  • 1 factor (aka categories)
  • 9 doubles (all which have NA’s)
  • 2 characters

Agenda

I’ll examine the variables at a solar system level first, then look at planets, stars, and then compare all the variables. Finally we’ll run one statistical test to answer a question about different types of solar systems.

1. Other Solar Systems

An exoplanet is a planet that is in another system. So let’s start by looking into the makeup of those other solar systems.

How far are these solar systems from us?

These distances are measured in parsecs which are used for distances above 3.26 light years. The sun is only 8.3 light minutes away from the earth, so even though Parsecs would not traditionally be used for such a small distance, the distance from the earth to the sun in parsecs is \(\ 4.84x10^{-6}\).

The closest solar system is 1.3 parsecs away which means it is about 4.2 light years away. And as a reminder, a light year is roughly 5.88 trillion miles!

This chart combines a violin plot that displays the density of the observations with a boxplot.

Solar system configuration

What are the number of stars and planets in other solar systems? Unlike our own system of only 1 star, some solar systems have two, three, even four stars! And also unlike our own 8-planet system, most other systems have only 1 planet (that we’ve discovered!).

2. Planet characteristics

Overview of planet data including:

  • Planet Orbital Period (in Days)
  • Planet Radius (in Earth Radius units, e.g. 2 means 2x the Earth’s radius)
  • Planet Mass (in Earth Mass units, e.g. 2 means 2x the Earth’s mass)
  • Planet Equilibrium Temperature (Kelvin)

How does earth compare to other planets?

Planets that orbit two stars

Circumbinary planets orbit two stars, as shown in the diagram in the introduction. How common is this?

The majority of planets are not circumbinary, with only 0.8% of planets in this data set being circumbinary. So now we know that earth is in the majority, with the other 90.2% of planets in this data set that are not circumbinary.

Circumbinary Flag by Planet Characteristics

Now we can look at the Planet variables and see how they differ on planets that are and aren’t circumbinary.

For example, here we can see that circumbinary planets tend to have a higher mass than planets that are not circumbinary.

Orbital Period

We know that the orbital period of the earth around its sun is 365 days. How does that compare with other suns in our solar system?

  • Earth’s orbital period is marked in blue
  • Mean is a dashed black line
  • Median is a dashed green line

Bivariate: Orbital Period vs. Temperature

We can also look at the relationship between a planet’s orbital period (in days) and it’s Equilibrium Temperature. This looks negatively correlated, which make sense intuitively: As a planet gets further from its sun, it gets colder.

Bivariate: Mass vs. Radius

There is a general positive correlation between a planet’s mass and it’s radius.

3. Star characteristics

What are the characteristics of the stars in this dataset?

Some interesting things emerge, such as a strong positive correlation between Mass and Luminosity.

Note: Luminosity is the “Amount of energy emitted by a star per unit time, measured in units of solar luminosities”

How does our sun/solar system compare to the suns of other solar systems?

Bivariate: Stellar Mass vs. Stellar Luminosity

Let’s take a look at our sun relative to some of those dimensions - in this case, I’ll pick the strongest positive correlation of Stellar Mass vs. Stellar Luminosity. I also added a linear regression model line marked in red.

Univariate: Age of our sun vs other stars in other solar systems

4. Correlation

A large correlation matrix of all the measured numerical variables for Planets and Stars.

5. Hypothesis Testing

What are the differences between “one-star” solar systems or “multiple star” solar systems?

First I started by creating groups that separated solar systems into 2 types: Single star systems and Multi-star systems.

Solar system groups

##  Multi-Star Single-Star 
##         489        4949

Then I created two equal sized random samples with 400 observations each.

From this I now had a categorical variable to measure against a variety of numeric continuous variables, including:

  • Number of Planets in a System
  • Planet Orbital Period Days
  • Planet Radius
  • Planet Mass
  • Planet Equilibrium Temperature
  • Solar system distance

Let’s focus on Planet Mass.

Do the number of stars in a solar system predict the mass of planets in that system?

So from this, I have a hunch that planets in Multi-star Solar Systems have a different mean mass than planets in a Single-star Solar System.

T-test

Our confidence interval is 95%, and our signficance level (or alpha) is 0.05.

Null Hypothesis (H0)

H0: The true difference between these group means is zero.

Alternate Hypothesis (H1)

H1: The true difference between these group means is not zero.

We will treat the types of solar systems as two different groups/samples. So we’ll use an Independent Samples T-test to test if this hunch is true and statistically significant.

## 
##  Welch Two Sample t-test
## 
## data:  sample_multi_star_systems$PlanetMass_EarthMass and sample_single_star_systems$PlanetMass_EarthMass
## t = 4.0449, df = 780.55, p-value = 5.754e-05
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  162.9601 470.2663
## sample estimates:
## mean of x mean of y 
##  664.9497  348.3365

Interpreting our T-test result

Our p-value of \(5.754e^{-5}\) is smaller than our alpha of 0.05, therefore we can say with 95% confidence that planets in Multi-star systems have a different mean mass than planets in Single-star system.

Takeaways

Some fun facts you can take with you today:

  • 91% of solar systems are made up of just 1 star, like our solar system
  • Only 1 other solar system has the same number of planets (8) as ours
  • There ARE planets that orbit 2 stars (e.g. Circumbinary) but only 45 that we know of
  • Our sun’s age (4.6 billion years) is close to the average age of other suns!

Next steps

There is so much more to explore! It was fascinating to learn so much about exoplanets.

Other things to dig into:

  • More statistical tests!
    • Do number of stars predict number of planets?
    • Do number of stars predict other planet characteristics?
  • Bring in more columns, such as data about Discovery methods, tools, and dates