Solar system model was originally fitted to basic astrometry (phases and relative sky position records, with scale by lunar parallax) [Kepler, early 1600's, Newton 1680's]. Distances within the solar system are now tracked by radar and telemetry.
Finite speed of light measured (relative to planetary orbital speeds) from Doppler shift in a signal (Io's stages) from Jupiter [Roemer, 1676] and annual aberration of stellar directions [Bradley, 1720's]. Direct local measurements are now trivial (e.g., modern computers can perform an instruction in a light handspan).
Lab measurements [Cavendish, 1798] of the gravitational constant permit the mass of astronomical bodies to be determined from the scale of orbital motions.
Relative molecular weights, along with the concept that ordinary matter is composed from elementary atoms, were inferred from the integer proportions in which chemicals react [Dalton, ~1805]. Absolute atomic masses (or Boltzmann's constant) were deduced from the behaviour of gasses [Loschmidt, 1865]. (A modern method would be crystal diffraction.)
Stellar parallax is the primary method for determining distance to stars in the nearby regions of the galaxy. [Bessel, 1838; Gaia, 2010's?].
Charge to mass ratios are found by mass spectroscopy, particularly for cathode rays and ions (permitting observation of distinct isotopes) [Thomson, c.1900]. The quantisation of electric charge can be measured directly [Millikan, ~1910].
Penetrating rays (that may trigger photochemical reactions or fluorescence) can be produced by cathode tubes [Roentgen, 1895]. Some substances spontaneously produce radiations [Becquerel, 1896], commonly of three types discernible by mass spectroscopy. The radioactivity process is atomic transmutation [Rutherford 1901; Curie], occurring randomly (to decay exponentially) [Geiger & Rutherford].
The nucleus of the atom was discovered by scattering [Rutherford, 1910].
Relativity [Einstein, 1905 & 1915].
The brightness of standard candles (Cepheid variable stars, having pulsation correlated to luminosity) identified in some extended astronomical objects showed that these are in fact separate galaxies (far more distant than the stars of our milky way galaxy), and furthermore their distance is roughly proportional with red-shift. That is, on the intergalactic scale everything is moving apart (at such a rate as if everything were together around 13 billion years ago) [Hubble, 1920's].
Understanding of life, mainly through fossil record [Darwin, 1859], DNA [1950's] and molecular biology.
Rotation curves, determined from the variation in red-shift across each galaxy, appear inconsistent with the visible distribution of matter (as though the motion of stars were influenced by large halos of invisible mass) . Gravitational lensing patterns around colliding (clusters of) galaxies appear to demonstrate electromagnetically observable matter becoming well separated from this dark matter [Bullet cluster, 2006].
Very distant standard candles are less red-shifted than would be extrapolated from their faintness, as though the universe is accelerating in its expansion. In General Relativity theory, this equates with the presence of a previously unobserved ("dark") form of energy. [Type Ia Supernovae, 1998]