Mass-radius relationship of simulated two-layer planets

In many cases, astronomers can measure the radius of a planet, but not its mass. Our models of Earth-like planets give us an estimate of the mass of small exoplanets. We model our planets as spheres that contain multiple layers of differing composition. We simulate the mass, radius, and core mass fraction (CMF) of these planets by integrating equations of planetary structure over many time-steps. For two-layer planets, we optimize the pressure at the center of the planet and the radius of the core by comparing the simulated planetary radius and CMF to the expected radius and CMF of the planet. If the radius and/or the CMF of a simulation are off from the expected values, we use linear interpolation to home in on better guesses for the pressure and core radius. Keeping one of the independent variable constant, the other independent variable is optimized by using one of the dependent variables as a measure of fit. Once one of the independent variables is optimized, that variable is kept constant and the other independent variable is then optimized using the other dependent variable. A family of planets, all with the same CMF, can be produced by varying the expected radius of the planets. We plot the radius of these planets against their simulated mass to produce equations that relate the radius of a planet to its mass and CMF. The estimated mass of an Earth-like planet is dependent on the state of the planet’s core (liquid or solid). This theoretical uncertainty should be considered in estimating exoplanet masses. In cases where the mass can be measured to high precision, our models may constrain the nature of the planet\u27s core