This presentation takes data from NASA’s Exoplanet archive, specifically their “TESS Confirmed Planets” dataset. https://exoplanetarchive.ipac.caltech.edu/

## `geom_smooth()` using method = 'gam' and formula = 'y ~ s(x, bs = "cs")'

This slide shows the relationship between orbital period and semi major axis for exoplanets. In general, because of Kepler’s Law the relationship should be equal to p^2 = a^3.

As stated earlier, a key part of the last slide is Kepler’s third law, which states p^2 = a^3. (p being the period, how long it takes to orbit, and a being the semi major axis, which is about their average distance from their star).

The values, however, have a bit of variance to them, and this is most likely because the extended version of the Kepler’s third law is p^2 = (4 pi^2 / GM) a^3. What this really means is that the mass of the star can also affect the overall equation.

## `geom_smooth()` using formula = 'y ~ x'

This graph shows the idea that a bigger solar mass can increase solar temperature. The higher mass makes nuclear fusion more frequent and thus higher temperatures.

Strangely enough, even though the full formula for Kepler’s third law, p^2 = (4 pi^2 / GM) a^3 also accounts for M, the mass of the star, it overall doesn’t seem to affect the data much, since most of it is clumped together as can be seen from the 3d model.

#First chart (Kepler 2d)
ggplot(exoplanets, aes(x = pl_orbper, y = pl_orbsmax)) +
  geom_point(na.rm = TRUE) +
  geom_smooth(na.rm = TRUE) +
  xlab("Orbital Period (days)") +
  ylab("Orbital Semi-Major Axis (AU)")

#Second chart (Solar mass and temp)
ggplot(exoplanets, aes(x = st_mass, y = st_teff)) +
  geom_point(na.rm = TRUE) +
  geom_smooth(na.rm = TRUE, method = "lm") +
  xlab("Solar Mass") +
  ylab("Solar Effective Temperature (K)")

#Third chart (3d plotly)
fig <- plot_ly(exoplanets, x = ~pl_orbper,
y = ~pl_orbsmax, z = ~st_mass, text = ~pl_name,
type = "scatter3d", mode = "markers")
fig

In the end, it was interesting to see how the rule of Kepler’s third law applies to exoplanets as well as relationships such as star mass and temperature. Even after seeing a relationship between orbital period and semi major axis, star mass didn’t seem to affect much.