EED (Exoplanet Entropic Dataset)

This dataset brings together measured masses and radii for exoplanets in the DACE PlanetS catalog with derived surface accelerations and quantities calculated from Newtonian and entropic-gravity equations. The current release contains 1,008 planet records and is provided as tabular data for analysis, plotting, and scientific exploration.

Source and sample

The source is the PlanetS Exoplanet Catalog, maintained by the Data & Analysis Center for Exoplanets (DACE) at the University of Geneva. DACE describes the PlanetS catalog as a compilation of transiting planets with robust mass and radius measurements. See the DACE mass–radius catalog tutorial for field definitions and example use.

Each record represents one planet entry. A host name may appear in multiple records for multi-planet systems. The last_updated field records catalog update dates for individual entries; in this release those dates range from 2014-05-14 to 2026-10-08.

Data fields

The dataset includes these groups of values:

Group	Fields and units
Identifiers	Planet name and host-star name
Catalog measurements	Planet mass in Jupiter masses and kilograms; planet radius in Jupiter radii and meters; asymmetric upper and lower uncertainties
Catalog provenance	Mass-times-sine-of-inclination value (Msin(i)) as a separate field, literature reference, ADS link, and catalog update date
Surface gravity	gravity_from_GM_over_R2_m_s2, the positive magnitude (GM/R^2) at the catalog radius
Force values	Newtonian force, entropic screen force, and force from the Unruh-temperature relation, all in newtons for a 1 kg test mass
Temperatures	Screen/equipartition temperature and Unruh temperature, in kelvin
Other derived values	Holographic bit count, reduced Compton displacement, entropy change over one reduced Compton displacement, and relative equation-comparison differences

For a spherical Newtonian potential, the acceleration vector and its surface magnitude are:

$$\mathbf{g}=-\mathrm{\nabla }\varphi =-\frac{GM}{r^2}\widehat{\mathbf{r}},g(R)=\frac{GM}{R^2}\mathrm{.}\backslash mathbf\{g\}=-\backslash nabla\backslash phi=-\backslash frac\{GM\}\{r^2\}\backslash ,\backslash hat\{\backslash mathbf\; r\},\; \backslash qquad\; g(R)=\backslash frac\{GM\}\{R^2\}.$$

The data table stores the scalar magnitude $g(R)$; the inward vector direction is not stored.

Calculations

Mass and radius values are converted from Jupiter units using the factors in the DACE tutorial:

• 1 Mjup = 317.828 Mearth, with Mearth = 5.9722e24 kg.
• 1 Rjup = 11.209 Rearth, with Rearth = 6.371e6 m.
• G = 6.67430e-11 m^3 kg^-1 s^-2.

The Jupiter-radius convention affects SI radius and derived acceleration values slightly; the original catalog-unit values are retained for reference. The gravity calculation uses the catalog planet mass, not the separate Msin(i) field. Derived quantities use catalog point estimates. Source uncertainties are included, but are not propagated through the derived calculations.

The equations below follow Section 3, “Emergence of the Laws of Newton,” in Erik Verlinde's 2011 paper, “On the Origin of Gravity and the Laws of Newton”. Equation numbers refer to that paper.

Equations stated in the paper

The paper postulates that a particle of mass $m$, displaced toward a holographic screen by one reduced Compton wavelength, changes the screen entropy by $2\pi k_B$, Eq. (3.5). It writes the entropy change for a general small displacement as Eq. (3.6):

$$\mathrm{\Delta }x=\frac{\mathrm{\hslash }}{mc},\mathrm{\Delta }S=2\pi k_B\frac{mc}{\mathrm{\hslash }}\mathrm{\Delta }x\mathrm{.}\backslash Delta\; x\; =\; \backslash frac\{\backslash hbar\}\{mc\},\; \backslash qquad\; \backslash Delta\; S\; =\; 2\backslash pi\; k\_B\backslash frac\{mc\}\{\backslash hbar\}\backslash Delta\; x.$$

The entropic-force work relation is Eq. (3.7), and the Unruh temperature relation is Eq. (3.8):

$$F\mathrm{\Delta }x=T\mathrm{\Delta }S,k_{B}T=\frac{\mathrm{\hslash }a}{2\pi c}\mathrm{.}F\backslash Delta\; x\; =\; T\backslash Delta\; S,\; \backslash qquad\; k\_BT\; =\; \backslash frac\{\backslash hbar\; a\}\{2\backslash pi\; c\}.$$

Combining these with the entropy relation gives Newton's second law, Eq. (3.9):

$$F=ma\mathrm{.}F\; =\; ma.$$

For a spherical screen around enclosed mass $M$, the paper gives the bit count in Eq. (3.10), equipartition in Eq. (3.11), and mass-energy in Eq. (3.12):

$$N=\frac{A{c}^3}{G\mathrm{\hslash }},E=\frac{1}{2}N{k}_{B}T,E=M{c}^2\mathrm{.}N\; =\; \backslash frac\{Ac^3\}\{G\backslash hbar\},\; \backslash qquad\; E\; =\; \backslash frac\{1\}\{2\}Nk\_BT,\; \backslash qquad\; E\; =\; Mc^2.$$

Using the sphere area $A=4\pi R^2$ and the entropy relation, the paper derives Newton's gravitational force, Eq. (3.13):

$$F=\frac{GMm}{R^2}\mathrm{.}F\; =\; \backslash frac\{GMm\}\{R^2\}.$$

Expressions derived from those equations

Some quantities calculated for the dataset are rearrangements or combinations of the numbered equations rather than separate equations in the paper.

Entropy gradient. Differentiating Eq. (3.6) with respect to displacement gives the entropy-gradient term used in both entropic-force calculations:

$$\frac{dS}{dx}=2\pi k_B\frac{mc}{\mathrm{\hslash }}\mathrm{.}\backslash frac\{dS\}\{dx\}\; =\; 2\backslash pi\; k\_B\backslash frac\{mc\}\{\backslash hbar\}.$$

Screen temperature. Solving Eqs. (3.11) and (3.12) for temperature gives:

$$T_{\mathrm{s}\mathrm{c}\mathrm{r}\mathrm{e}\mathrm{e}\mathrm{n}}=\frac{2M{c}^2}{N{k}_B}\mathrm{.}T\_\{\backslash mathrm\{screen\}\}\; =\; \backslash frac\{2Mc^2\}\{Nk\_B\}.$$

Substituting Eq. (3.10) and the spherical area $A=4\pi R^2$ gives:

$$T_{\mathrm{s}\mathrm{c}\mathrm{r}\mathrm{e}\mathrm{e}\mathrm{n}}=\frac{GM\mathrm{\hslash }}{2\pi R^{2}c{k}_B}\mathrm{.}T\_\{\backslash mathrm\{screen\}\}\; =\; \backslash frac\{GM\backslash hbar\}\{2\backslash pi\; R^2\; c\; k\_B\}.$$

Screen-force calculation. Multiplying the screen temperature by the entropy gradient for a test mass $m$ recovers Eq. (3.13):

$$F_{\mathrm{s}\mathrm{c}\mathrm{r}\mathrm{e}\mathrm{e}\mathrm{n}}=T_{\mathrm{s}\mathrm{c}\mathrm{r}\mathrm{e}\mathrm{e}\mathrm{n}}\frac{dS}{dx}=\frac{GM\mathrm{\hslash }}{2\pi R^{2}c{k}_B}\left(2\pi k_B\frac{mc}{\mathrm{\hslash }}\right)=\frac{GMm}{R^2}\mathrm{.}F\_\{\backslash mathrm\{screen\}\}\; =\; T\_\{\backslash mathrm\{screen\}\}\backslash frac\{dS\}\{dx\}\; =\; \backslash frac\{GM\backslash hbar\}\{2\backslash pi\; R^2\; c\; k\_B\}\; \backslash left(2\backslash pi\; k\_B\backslash frac\{mc\}\{\backslash hbar\}\backslash right)\; =\; \backslash frac\{GMm\}\{R^2\}.$$

Unruh-force calculation. Using Eq. (3.8) for temperature and the entropy gradient from Eq. (3.6) gives:

$$F_{\mathrm{U}\mathrm{n}\mathrm{r}\mathrm{u}\mathrm{h}}=T_{\mathrm{U}\mathrm{n}\mathrm{r}\mathrm{u}\mathrm{h}}\frac{dS}{dx}=\frac{\mathrm{\hslash }a}{2\pi k_{B}c}\left(2\pi k_B\frac{mc}{\mathrm{\hslash }}\right)=ma\mathrm{.}F\_\{\backslash mathrm\{Unruh\}\}\; =\; T\_\{\backslash mathrm\{Unruh\}\}\backslash frac\{dS\}\{dx\}\; =\; \backslash frac\{\backslash hbar\; a\}\{2\backslash pi\; k\_B\; c\}\; \backslash left(2\backslash pi\; k\_B\backslash frac\{mc\}\{\backslash hbar\}\backslash right)\; =\; ma.$$

Entropy over one reduced Compton displacement. Substituting the reduced Compton displacement into Eq. (3.6) gives:

$$\mathrm{\Delta }x=\frac{\mathrm{\hslash }}{mc},\mathrm{\Delta }S=2\pi k_B\mathrm{.}\backslash Delta\; x\; =\; \backslash frac\{\backslash hbar\}\{mc\},\; \backslash qquad\; \backslash Delta\; S\; =\; 2\backslash pi\; k\_B.$$

In this dataset the entropy-change field uses the 1 kg test mass; the planet-mass reduced Compton displacement is also recorded separately.

How these map to the dataset

For each planet, M is its catalog mass and R is its catalog radius. The surface acceleration is calculated as:

$$g=\frac{GM}{R^2}\mathrm{.}g\; =\; \backslash frac\{GM\}\{R^2\}.$$

The runner uses a 1 kg test mass. The Newtonian force is:

$$F_N=\frac{GM{m}_t}{R^2},m_t=1\mathrm{k}\mathrm{g}\mathrm{.}F\_N\; =\; \backslash frac\{GMm\_t\}\{R^2\},\; \backslash qquad\; m\_t\; =\; 1\backslash ,\backslash mathrm\{kg\}.$$

The entropic screen force is calculated from the screen temperature and entropy gradient. The Unruh-force calculation multiplies the Unruh temperature by the same entropy gradient:

$$F_{\mathrm{U}\mathrm{n}\mathrm{r}\mathrm{u}\mathrm{h}}=T_{\mathrm{U}\mathrm{n}\mathrm{r}\mathrm{u}\mathrm{h}}\frac{dS}{dx}\mathrm{.}F\_\{\backslash mathrm\{Unruh\}\}\; =\; T\_\{\backslash mathrm\{Unruh\}\}\backslash frac\{dS\}\{dx\}.$$

The bit count uses Eq. (3.10) with the spherical area:

$$A=4\pi R^2\mathrm{.}A\; =\; 4\backslash pi\; R^2.$$

Interpretation

The sample focuses on transiting exoplanets with measured masses and radii. It is a curated observational sample, so its population does not represent every known exoplanet or planetary system. Measurements and uncertainty estimates originate in the cited literature and can use different methods and conventions; consult the per-record references when comparing individual planets.

The Newtonian and entropic-gravity force columns are calculated from their respective equations using the same planetary inputs and assumptions. The comparison values are useful for exploring the equations and their numerical behavior alongside the catalog data.

Citation and attribution

Please cite the DACE PlanetS catalog and the original literature reference listed for each planet. Relevant catalog papers include:

• Otegi et al. (2019), arXiv:1911.04745.
• Parc et al. (2024), arXiv:2406.04311.
• Verlinde (2011), arXiv:1001.0785, for the entropic-gravity equations used in the derived fields.

License

The applicable redistribution license for the source catalog export has not yet been confirmed. Please check the DACE terms for the specific catalog data before public redistribution, and set the Hugging Face license metadata only after confirming the data license. Preserve DACE attribution and the per-planet literature references.