Uniform approximation of planetary ephemerides

Gravity tests with INPOP planetary ephemerides

In this paper, we present several gravity tests made in using the last INPOP08 planetary ephemerides. We first propose two methods to estimate the PPN parameter β and its correlated value, the Sun J2 and we discuss the correlation between the Sun J2 and the mass of the asteroid ring. We estimate possible advance in the planet perihelia. In the end we show that no constant acceleration larger th...

An approximation to the errors in the planetary ephemerides of the Astronomical Almanac

Errors in the planetary coordinates of the Astronomical Almanac are approximated by comparing their fundamental ephemerides, upon which they are based, with a more recent ephemeris. JPL’s DE200 provided the fundamental planetary and lunar ephemerides of the Astronomical Almanac for the years, 1984–2002, and DE405 has replaced DE200 in that role, starting in 2003. Recently, new observational mea...

Hexadecapole Approximation in Planetary Microlensing

The frequency of microlensing planet detections, particularly in difficult-tomodel high-magnification events, is increasing. Their analysis can require tens of thousands of processor hours or more, primarily because of the high density and high precision of measurements whose modeling requires time-consuming finitesource calculations. I show that a large fraction of these measurements, those th...

On Constrained Uniform Approximation

Weierstrass and Uniform Approximation

We present the theorem of uniform approximation of continuous functions by polynomials in the Weierstrass framework for the construction of analysis based on the representation of functions by sums of power series and analytic functions, and his effort to bring new standards of rigor to analysis that accompanied his differences with Riemann. We also describe the most original proofs of the appr...