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Summary of Current Information
 A. The Parent Star B. The Exoplanet

### V. Calculating the Mass of the Exoplanet

The mass of the exoplanet can be determined from an estimate of its density. Plotting the densities of the planets in our solar system as a function of their radii may be informative.

 A. Model #1 A log-log plot of the densities and radii of the planets in our solar system produces the graph at right. The line indicates an approximate best fit. However, many of the planets do not fit the curve well. The average density of an object is defined by:   density = mass / volume. Since a planet is basically a sphere, its volume is:   V = (4/3) pi R3. Thus one can solve for the mass of the exoplanet if its density and radius are known. (See the formula below.)

To use the data from the graph, locate the radius of this exoplanet on the graph and read its associated density from the curve. Enter this density in the formula below.

(Data for Earth: density = 5500 kg/m3, mass = 5.98 X 1024kg, radius = 6.378 X 106m)

 mass of exoplanet = density * (4/3 * pi * radius3)
 Earth masses = kg/m3 * [Conversion from Earth radii to meters and from kilograms to Earth masses are done internally.] (Press the calculate button to estimate the mass of the exoplanet.)
 B. Model #2 A straight forward plot of the densities of the planets in our solar system with the average distance they are from the Sun produces the graph at right. The line indicates an approximate best fit. As before, not all of the planets fit well on this curve. To use this data locate the semi-major axis of this exoplanet on the graph and read its associated density from the curve. Enter this density in the formula below to calculate a second estimate of this exoplanet's mass.
 mass of exoplanet = density * (4/3 * pi * radius3)
 Earth masses = kg/m3 * [Conversion from Earth radii to meters and from kilograms to Earth masses are done internally.] (Press the calculate button to estimate the mass of the exoplanet.)

Press the "Next Page" button to continue your analysis.

### Explanations

Notes on Estimating the Mass of the Exoplanet

The models used here to estimate the density of a planet are very simplistic. It is assumed that the density depends only upon one variable (either the size, i.e., radisu, of the planet or its distance from the Sun. Even for our solar system, this cannot be the whole story, as it can be seen from the rough attempts to draw a best-fit line to the plots above.

A more complete model for the density of a planet should at least include:

• the size of the planet
• the distance the planet is from the parent star
• the spectral type of the parent star, and thus its size and surface temperature

Hints (Reminders)

• Use the appropriate buttons. Do not press the "Enter" key.
• Enter or change numbers only in the appropriate boxes.
• Complete all "calculations" in order from the top of the page to the bottom.