Will Beers

Sarah Reising

Our Planetary Database

Background:

For years scientists have been dreaming about and searching for extrasolar planets. These are planets that remain outside of our solar system, orbiting stars other than our Sol. 80 such extrasolar planets have been discovered in the past 8 years. To find these stars, scientists noticed the “wobble” of nearby stars and discovered through radial velocity graphs that there is something else occupying the space, invisible to our technology. Using such properties as periods of revolution, luminosity of the star, parallax (and thus distance to the star itself), Doppler shift of light from the star, eclipses, and mass ratios astronomers can find other properties unobservable to us such as temperature of the planet, radius of the planet, and distance to the planet from the star. Various factors affect these calculations such as eccentricity of orbit of the planet and possible gravitational perturbations from other planets or discs.

From the data that was obtained from Extrasolar Planet Catalog, we began calculations to determine high, middle and low temperatures for each planet. To do this, we first had to determine albeidos for each planet. Albeido is a ratio of light reflected by an object over the amount of light that the object is exposed to. Planets such as Venus and Jupiter have extremely high albeidos because of the thorough cloud cover; while more rocky planets have lower albeidos. Since we don’t know the physical properties of the extrasolar planets, we don’t know the amount of cloud cover or the composition of the planets; therefore, we do not know appropriate albeidos for the planets. An educated guess has to be made, and the reasonable range for albeidos we used was .6 for a maximum, .35 for an intermediate value, and .05 for a low value. These were based on albeidos of planets in our solar system.

Another piece of information that we use to determine the temperature of the planets is the luminosity of the star that the planets revolve around. First, we found the apparent magnitude of the star from the database that we obtained all of the other information about the planets, then, using the distance modulus equation (), we solved for absolute magnitude of the star. We then used the equation for the luminosity of a star compared to that of our own sun to find the luminosity of each planet’s star (). After obtaining the values of luminosity of the star, we then began to calculate a range of temperatures for the extrasolar planets.

To calculate the range of temperatures for the extrasolar planets, we used the equation:

Using the values we predicted/calculated for albeido and luminosity along with documented distances, we determined high, middle, and low values for the temperature of each planet.

Using Microsoft Excel, we easily prepared a database of 75 extrasolar planets and their properties. To analyze these properties, we used a few different programs. We first used the JMP Intro 4 program. This is a program designed specifically for the study of statistics. We were able to make numerous graphs with this program to express our thoughts; we had a problem with the eccentricity data, though, so we had to also use Graphical Analysis to analyze properties. Both of these programs produce excellent graphs that are very useful in statistical analysis.

Using these methods we analyzed a few trends among the extrasolar planets. First, we analyzed how the distance from the star affects the temperature. As expected, the plot exhibited an inverse behavior, specifically very close to a ¼ power fit. Next we compared how the mass of the planet relates to the temperature. This also appeared to have an inverse behavior, but much more scattered than the distance plot. Now we decided to plot eccentricity related to the mass of the planet. There was no obvious correlation, but it did appear that most of the extrasolar planets are Jupiter mass and have a low eccentricity. Another plot we made was the eccentricity and the distance to the star from earth. This plot showed no correlation or trend. We did one more eccentricity plot, this time related to the distance of the planet from the star. The only thing apparent from this plot was that stars with low distances from their stars tend to be more likely to have a low eccentricity. Our next plot showed how the mass of the planet is related to the luminosity of the star. This only showed that more planets are found to be orbiting dimmer stars. Our final trend was between the mass of the planet and the distance of the planet from its star. We noticed a large portion of the planets possessed Jupiter class masses that were close to the star.

From the trends we noticed we could deduce three general conclusions. First, from the temperature vs. distance from star plot, we verify the Stefan-Boltzman law, relating the temperature and distance from star by a ¼ power. This is due to the fact that the amount of flux from the star reaching the planet decreases as the sphere about the star gets larger, and thus the temperature decreases by the fourth power of the distance from the star. From the luminosity vs. distance from star plot, we can conclude that very bright stars did not form planets as readily as dimmer stars. This can be attributed to the temperature of brighter stars being higher, and not allowing planets to condense. One more reason could be that brighter stars did not have a long enough lifetime to form planets. Our final conclusion is that many planets migrate over time. This can be seen in the final plot, of mass vs. distance, in the high portion of extrasolar planets that are of Jupiter mass with very small distances to their stars. Migration occurs when the star is rotating with a period greater than that of the revolution of the planet. This arises due to conservation of angular momentum of the planet/star system.

Middle Temperature Vs. Distance from Star

Middle Temperature Vs. Mass of Planet

M jup By Luminosity

M jup By Distance from Star