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28 votes
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Why do we use Chebyshev polynomials to predict positions of solar system bodies?

I'm also surprised that JPL uses a numerical model rather than doing a n-body physics simulation of the Solar System. JPL does use an n-body physics simulation of the solar system. It's a very ...
David Hammen's user avatar
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15 votes
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The Moon's shadow could not possibly look like this — could it?

The deviations are real and directly related to the size of valleys on the Moon. The simple calculation you do here does only work for a point-like light source that projects the shape of the Moon ...
asdfex's user avatar
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9 votes
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How does Curiosity know how to point and move it's high gain antenna in real time?

This answer is based on a book called "The Design and Engineering of Curiosity" https://doi.org/10.1007/978-3-319-68146-7 On chapter 6 it is mention that The Hazcams and Navcams are flight ...
Eviatar.E's user avatar
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9 votes

Is it possible to create an analytical ephemeris from raw position and velocity of a Body?

It's possible, because that's partly how VSOP was made, but the amount of effort involved is immense. What you are describing is at the very least a doctoral thesis, if not several of them. Why not ...
Ryan C's user avatar
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8 votes
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I've almost learned to spell Chebyshev, why has JPL switched to Hermite interpolation for DE438?

Not seeing that. I downloaded de438.bsp, and it in fact uses only Чебышёв position polynomials. (Or Chebyshev, Chebychev, Chebysheff, Chebychov, Chebyshov, Chebycheff, Chebyschev, Chebyschef, ...
Mark Adler's user avatar
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7 votes

The Moon's shadow could not possibly look like this — could it?

I'll add this to the other answers, which do a very good job of explaining why this very irregular shape is not inconsistent with the Moon's original much "rounder" shape. This could be done with ...
uhoh's user avatar
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7 votes
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How is the Chebyshev method used by JPL?

The $a_i$ are the coefficients for the Chebyshev approximation. As you say, NASA gives us those. That is what you find in the DE files, e.g. de430.bsp. (Don't click on that unless you want to download ...
Mark Adler's user avatar
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7 votes

Calculating the planets and moons based on Newtons's gravitational force

Aside from numerical issues, "With Sun as centre" may be part of your problem. Get all the data from Horizons relative to the Solar System Barycenter, not the Sun, which moves relative to the ...
Mark Adler's user avatar
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7 votes
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What happened to time in 1962? (JPL Horizons changes displayed time from UT1 to UTC for dates starting in 1962)

I recommend searching for the string 1962 in https://www.ucolick.org/~sla/leapsecs/timescales.html to see the list of changes that happened to the way time was reckoned as of 1962-01-01. To save you ...
Steve Allen's user avatar
6 votes
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How to choose between Hermite and Chebyshev interpolation for spacecraft trajectory?

SPICE has multiple tools for constructing and using piecewise Lagrange and Hermite polynomials because those techniques are textbook. In contrast, techniques for constructing piecewise Chebyshev ...
David Hammen's user avatar
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6 votes

Access to Chebyshev coefficients from JPL ephemerides

Your question is slightly ambiguous, a file containing the Chebyshev coefficients wouldn't be an ephemeris, but it's something you could use to generate an ephemeris. Regardless, the article Format ...
Greg Miller's user avatar
6 votes

Why does Earth's North Pole RA flip by ~180 deg around AD2000 relative to SSB? (JPL Horizons data)

Is this an artifact to do with J2000 and ICRF? It's an artifact of choosing to use right ascension and declination to describe the Earth's orientation. Right ascension is undefined at a declination ...
David Hammen's user avatar
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5 votes

How to obtain Chebyshev coefficients directly from the JPL Horizon's interface?

The best and most concise answer is here The "gold standard" is the SPICE toolkit. You can read more about using spice in this excellent answer. The JPL Development Ephemerides are lists of the ...
uhoh's user avatar
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5 votes

What format is a "TSA Ephemeris?"

The associated script, mcc.py, appears to get the reference frame wrong but does get the units correct. An imperial foot and a US customary foot are the same unit. (This is not the case for all ...
David Hammen's user avatar
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5 votes
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How to calculate position of GPS Satellite with transmitted ephemeris data?

You can find a C++ method contained in the source code of Andrew Holme homemade GPS receiver project. The method is called GetXYZ and is the EPHEM (ephemeris) namespace and looks as the following: <...
cy8berpunk's user avatar
5 votes

Change frame center definition of Chebyshev coefficients

I want to have all coefficients defined in the same frame center. That's not a good ask, for many reasons (see below). For example is it possible to have Chebyshev coefficients of the Earth w.r.t ...
David Hammen's user avatar
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4 votes
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How to convert a SPICE SPK kernel into human-readable data using SPICE toolkit and utilities

So I am using the following layout for my SPICE kernels (not essential but matches tutorial recommendations, adjust paths in the spm2oek input file as needed) ...
astrosnapper's user avatar
  • 2,506
4 votes

How to calculate position of GPS Satellite with transmitted ephemeris data?

The required equations and much more are contained in the GPS Interface Control Document (IS-GPS-200L Table 20-IV. Broadcast Navigation User Equations), available on the GPS Website: https://www.gps....
Rob's user avatar
  • 141
4 votes

The Moon's shadow could not possibly look like this — could it?

The outline of the lunar umbra on Earth (shadow of totality) will be defined by those rays of light emanating from the very edge of the solar disk as seen from Earth which just miss the surface ...
Anthony X's user avatar
  • 17.6k
4 votes

Access to Chebyshev coefficients from JPL ephemerides

The best method I've found is to use Brandon Rhodes' Python "jplephem" from here, specifically using the _load() function of an SPK segment. You get a ...
ChrisR's user avatar
  • 6,230
3 votes

Calculating positions of Moon's ascending and descending nodes from ephemeris files

The answer using SPICE is excellent! A short cut is to use the JPL Horizons interface in ORBITAL ELEMENTS mode, download a table and use OM or $\Omega$, the ...
uhoh's user avatar
  • 149k
3 votes

What is the exact format of the JPL ephemeris files?

The exact format of the SPICE Toolkit SPK files (also called BSP files) is called DAF (Double-precision Array File). It is a binary format made up of consecutive blocks of 1,024 bytes. The first ...
Escualo's user avatar
  • 534
3 votes

Ground longitude/latitude under a satellite (cartesian coordinates) at a specfic epoch

From the point you are, you need to: Calculate the XYZ coordinates of your ground station Find the line in space between the satellite and the ground station Find the XYZ coordinates of the point at ...
Camilo Rada's user avatar
3 votes

Comparing results with Pyephem

I figured out,It was something wrong in the code: The function observer.next_pass(sat), return a vector of 5 values 0 Rise time 1 Rise azimuth 2 Maximum ...
mikesneider's user avatar
3 votes

Difficulty trying to use the SPK file ast343de430.bsp

The ast343de430.bsp file looks to be fine. There is only one thing of note - all bodies in this file are referenced to the sun (...
Kaushik Ghose's user avatar
3 votes
Accepted

JPL ephemerides: effect of Saturn, Uranus and Neptune

The equations of motion for how bodies move in the Solar System, which are then fitted to the observational data of positions and ranges to provide the ephemeris, involve a nested set of effects which ...
astrosnapper's user avatar
  • 2,506
3 votes

How to convert a SPICE SPK kernel into human-readable data using SPICE toolkit and utilities

Found another method/tool: "spy" from SPICE utilities, available for Windows (actually DOS), Unix and Mac. User manual: link Copy these data into a text file named "command.txt": <...
jumpjack's user avatar
  • 3,043
3 votes

Access to Chebyshev coefficients from JPL ephemerides

Update : I have found a way to extract Chebyshev coefficients at a requested date for a particular body using CSPICE. Here the program that allows to do this : ...
GuillaumeJ's user avatar

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