Planet Mass Calculator

The calculator applies Kepler's Third Law in its Newtonian form:

$$T^2 = \frac{4\pi^2 a^3}{G(M_* + m_p)}$$

Solving for the total mass of the system:

$$M_* + m_p = \frac{4\pi^2 a^3}{G T^2}$$

The planet mass is then:

$$m_p = \frac{4\pi^2 a^3}{G T^2} - M_*$$

where $$T$$ is the orbital period in seconds, $$a$$ is the semi-major axis in meters, $$G = 6.674 \times 10^{-11}$$ N·m²/kg² is the gravitational constant, and $$M_*$$ is the star mass.

The orbital velocity is calculated as:

$$v = \frac{2\pi a}{T}$$

The Kepler consistency check computes $$a^3/T^2$$ in AU³/yr², which should equal the total system mass in solar masses for a valid orbit.

Note that for real exoplanet detection, the planet mass is typically much smaller than the star mass, so the measurement precision of $$a$$ and $$T$$ must be extremely high to extract $$m_p$$ from the difference.

The planet mass result represents the gravitationally inferred mass assuming a circular orbit. For Earth orbiting the Sun (T = 365.25 days, a = 1 AU, M* = 1 M☉), the calculator recovers Earth's mass. The Kepler consistency value should approximately equal the star mass in solar masses for planetary-mass companions.

If the computed planet mass is negative, it indicates the input parameters are inconsistent — the given period is too short for the specified semi-major axis and star mass, which is physically impossible. The orbital velocity gives the mean speed of the planet in its orbit, useful for understanding energy budgets and escape conditions.