Mission 01 — In development

The interior of every
small body, mapped from orbit.

Mathilde recovers the interior density distribution of asteroids and comet nuclei from satellite-to-satellite tracking — the same physics that mapped the Earth's gravity field with GRACE, scaled down to a single small body and a constellation of cubesats.

Request the deck See the approach

The problem

Asteroids are economically and scientifically opaque.

We can image an asteroid's surface from a flyby. We can sometimes infer its bulk mass from a tracking arc. But the interior — whether it is a coherent monolith, a rubble pile bound by friction, or a differentiated body with a denser core — remains a guess.

That guess is everything. It determines whether a body can be safely deflected, whether a sample-return mission can anchor to it, whether prospective resources are concentrated or diffuse, and how the body formed in the first place.

Today, the only way to peek inside a small body is to send a flagship mission costing north of a billion dollars and wait a decade. That doesn't scale to a Solar System with hundreds of thousands of catalogued near-Earth and main-belt objects.

The approach

Borrow the physics that mapped Earth's gravity. Adapt it to a body the size of a city.

The principle is older than the satellites that carry it: a constellation in orbit is itself a gravity instrument. As the body's mass distribution bends the orbits, the inter-spacecraft ranges record the signal. The inversion problem — turning ranges back into densities — is what we do.

STEP 01 ◆

Constellation

Three or more cubesats co-orbit the body in the rotating frame. Each pair exchanges inter-satellite range measurements continuously.

STEP 02 ◆

Range observable

Sub-millimeter range and range-rate signals encode every inhomogeneity in the body's gravity field — exactly what GRACE and GRAIL exploited.

STEP 03 ◆

Mascon model

We discretize the body into mass concentrations. The forward model is a linear sum of point-mass potentials over the constellation's orbits.

STEP 04 ◆

Bayesian inversion

A JAX-differentiable forward model feeds a NUTS sampler. Out comes a posterior over densities — uncertainty included, not just a point estimate.

Capabilities

An end-to-end pipeline, today.

Forward model

Mascon gravity + spherical harmonics

Point-mass superposition for arbitrary geometries; fully-normalized harmonic expansion as a cross-check. JAX mirror for end-to-end differentiability.

Dynamics

Rotating-frame propagator

RK45 integration in the body-fixed frame with Coriolis and centrifugal terms. Energy and Jacobi-integral diagnostics for trustworthy long arcs.

Rotation

Tumbling rigid bodies

Torque-free Euler equations and quaternion kinematics — the body's spin state is part of the model, not an idealization.

Instruments

Realistic ranging models

Single-link SST and dual one-way ranging (DOWR) with imperfect clocks: bias, drift, white frequency noise.

Estimation

Joint EKF over states + clocks

Extended Kalman filter that recovers spacecraft trajectories and clock parameters from inter-satellite ranges alone.

Inversion

NUTS sampler over densities

Hamiltonian Monte Carlo on the JAX forward model produces a calibrated posterior over interior density — not a single fit.

Visualizations

Every claim, a figure you can run.

The figures below come straight from the simulation pipeline that produces our results. No marketing renders.

Interactive

Tumbling shape

Generated live in your browser using the same spherical-harmonic perturbation model the inversion uses.

Time series

Inter-satellite range signal

A J₂+J₃ gravity field fingerprints itself in the range derivative. Real signal, simulated.

Sensitivity

EKF localization scaling

Filter accuracy as a function of constellation size. More baselines, better state recovery.

Posterior

Mascon density posterior

Posterior draws over interior density from NUTS. Where the data does and doesn't constrain the body.

// Live figures rendered from examples/ coming soon

Founders

Built by the people who write the math.

Mathilde is engineered, not pitched. Every line of the inversion pipeline comes from the same hand.

Meet the founders

Logbook

Working notes from the bench.

Every design decision in Mathilde started as a discussion. We keep them — equations, dead ends, derivations and all — in the open.

All entries

Currently raising

We're talking to investors who think on a decade horizon.

If asteroid prospecting, planetary defense, or in-orbit science is on your thesis, we'd like to share the deck and walk you through the model.

hello@mathilde.space Read the logbook