SKU: 44603313571

Planetary Programs and Tables -4000 to +2800

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Description

Planetary Programs and Tables -4000 to +2800By Bretagnon and Simon with Foreword by Meeus. Product Information: 8. 50" by 11. 00", 165 pages, softbound, (see below for magnetic versions). The tables and computer programs detailed in Planetary Programs and Tables From 4000 to +2800 allow the computation of the positions of the Sun, and 7 planets with a precision better than 0. 01 degree over the period 4000, +2000 for Mercury, Venus, Mars, Jupiter and Saturn and +1600 to +2800 for Uranus and

By Bretagnon and Simon with Foreword by Meeus.

Product Information: 8.50" by 11.00", 165 pages, softbound, (see below for magnetic versions).

The tables and computer programs detailed in Planetary
Programs and Tables From -4000 to +2800 allow the computation of the positions of the Sun, and 7 planets with a precision better than 0.01 degree over the period -4000, +2000 for Mercury, Venus, Mars, Jupiter and Saturn and +1600 to +2800 for Uranus and Neptune.

Until now, the astronomical tables covering large historic and prehistoric periods give the geocentric positions of the planets for equidistant dates. As an example, the tables of B. Tuckerman give the positions of the Sun and planets at 5-(Mercury, Venus) or 10-day (Sun, Mars, Jupiter and Saturn) intervals over the -600 to +1649. Coordinates are the longitude of the Sun, the geocentric longitudes and the geocentric latitudes of the planets. Such tables, over the entire period from -4000 to +2600 would include over 3,700,000 numbers and would constitute a 3,000 page book.

Instead, compact tables and simple computations of the Sun and planets on a small computer are described in this book. Time-dependent expansions of the longitude and radius vector of the Sun as well as the heliocentric coordinates of the planets are provided. These coordinates refer to the mean equinox and ecliptic of date.

For the Sun, Mercury, Venus and Mars each coordinate is represented in Planetary Programs and Tables From -4000 to +2800 by only by one formula provided for the entire period -4000 to +2600. This formula includes between 5 and 60 terms depending on the coordinate and planet.

For Jupiter, Saturn, Uranus and Neptune the coordinates are expressed for time-spans of five years by power series with seven coefficients. The period -4000, +2600 is then constituted by 1320 time-spans of five years. In addition to the tables, formulae for corrections of aberration and nutation which allow you to compute apparent geocentric coordinates are provided.

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SKU: 44603313571

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4.7 ★★★★★
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K
KD
Houston, US
★★★★★ 5
Super entertaining toy if your dog likes balls and hunting
Color: Aqua
Love this! We got a similar ball for our dog about 6 months ago and she has been obsessed! We have 2 dogs, one hasa zero interest whatsoever in this toy (as expected) and the other will bark at it while its sitting on the charger so she can get it. Dogs, amirite? lol anyway, the issue we had with the previous one was that it was so loud on our wood floors because it was a solid plastic. The Cheerble ball has made a huge difference in sound for us! The ball itself is very quiet. When it rolls or bounces on something other than the floor you can barely hear it. With the previous ball we had, we couldn't be on the phone or watching a movie, etc if our dog was playing with the ball because it was so dang loud but this solves our problems! Its made of a hard silicone like material (thing a Nerf ball or something) so it remains quiet. The battery lasts as listed and its easy to charge. It took some time to figure out which setting our dog liked the best but after that it was smooth sailing. My only only negative to this is that the power on/off switch is inside so you have to twist it open to turn it off and on. The ball will naturally get some saliva on it so its kinda gross to put your hands all over it once its been played with and I'd prefer a button on the outside but understand why that isn't possible with this design. This ball is perfect if your dog is ball obsessed like ours. Shes a pitt/black lab/aussie mix so ball and hunting/chasing lizards are her favorite past times. If your dog prefers ripping toys apart to kill the squeaker (our other dog) or chewing bones, they may not take to this. Ball is life at our house and this ball is at the top of our pups list, there isn't a day that passes that she doesn't start her daily routine of seeking this out and begging us to turn it on. Highly recommend for the right pup!
WAS THIS REVIEW HELPFUL?YesReportShare
Reviewed in the United States on August 6, 2025
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Verified Purchase
Donna M.
Dallas, US
★★★★★ 5
Great toy
Color: Blue
Great toy, too bad my Shih Tzu is afraid of it. I love the way the movement is subtle and random.
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Reviewed in the United States on May 21, 2026
A
Verified Purchase
Amazon Customer
Bozeman, US
★★★★★ 5
Best toy for dogs
Color: Blue
My dog plays with this for hours!
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Reviewed in the United States on May 14, 2026
C
Chelsea H.
Chelsea, US
★★★★★ 4
I wouldn’t recommend this for strong chewers.
Color: Orange, Color: Orange
Is it fun? Sure. Was it easy to charge and set up? Yep. That being said, this toy kind of fell flat for me. It really didn’t do any big movements once charged that I expected it to, so that was a bummer. I initially got it for my dog, but my cats were more interested in this than my dog was. The battery does seem to last a long time and the motor is pretty quiet. I WOULD NOT recommend this toy for strong chewers as the material for this is a foam rubber and I don’t think it’s durable enough for strong chewers. While the material makes this ball extremely lightweight for more movement, a strong chewer would have this disintegrated in five minutes flat. My Dog is a super strong chewer. I don’t think I would feel comfortable leaving him unattended with this because I know he would destroy it.
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Reviewed in the United States on May 5, 2026
C
Verified Purchase
Charlie
Lowell, US
★★★★★ 5
Interactive puppy fun
Color: Blue
Pups love this and I enjoy watching them have so much fun. Serious playtime followed by a well earned nap!
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Reviewed in the United States on May 4, 2026

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