SKU: 2419139437

Solving Kepler's Equation

Sale price$27.86 Regular price$30.95
Save 10%

Shipping Estimate
USA
  • USA
  • CAN

Ships within 48 hours · Estimated delivery Jul 12 - Jul 17

Promo Codes Available:

For Your Every Summer RSVP, with Code: SUMMER15

Description

Solving Kepler's EquationBy Colwell. Product Information: 6. 00" by 9. 00", 202 pages, hardbound, published 1993. The sole subject of Solving Kepler's Equation work is Kepler's Equation (KE) M = E e sin E . In its narrowest form, the Kepler problem is to solve KE for E , given M in the interval [0,p]and e in the interval [0,1]. In virtually every decade from 1650 to the present there have appeared papers devoted to the Kepler problem and its solution. We can see from a list

By Colwell.

Product Information: 6.00" by 9.00", 202 pages, hardbound, published 1993.

The sole subject of Solving Kepler's Equation work is Kepler's Equation (KE) M = E - e sin E . In its narrowest form, the Kepler problem is to solve KE for E , given M in the interval [0,p]and e in the interval [0,1]. In virtually every decade from 1650 to the present there have appeared papers devoted to the Kepler problem and its solution. We can see from a list of them that the problem has enticed a wide variety of scientists to comment on or involve themselves in its solution.

It is surely not unique in science for a specific problem to be given so much attention over so long a period—particularly if it resists solution, if its partial solutions are inadequate or unsatisfactory, or if it is recharged with new interpretations and new applications. Still, it is curious that the Kepler problem should have continued to be this interesting to so many for so long. Admittedly it is a problem central to celestial mechanics, but it is a technical little problem for which a number of satisfactory solutions are long known. With the advent of calculators and computers, there is no impediment to achieving quick solutions of great accuracy. The problem has neither the broad appeal of an Olbers Paradox, nor the depth and intractability of a many-body problem.

In common with almost any scientific problem which achieves a certain longevity and whose literature exceeds a certain critical mass, the Kepler problem has acquired an undeniable luster and allure for the modern practitioner. Any new technique for the treatment of transcendental equations should be applied to this illustrious test case; any new insight, however slight, lets its conceiver join an eminent list of contributors.

The Kepler problem has been “on the scene” in Western civilization science for over three centuries. To gather its story is to view this science through a narrow-band filter, and our goal is to make the picture at one wavelength instructive and interesting.

The idea to gather all the work on the Kepler problem is not new. Early work was surveyed in Melander,1767, Detmoldt,1798 and Brinkley,1803, and much of the recent work was described in Danby,1983, Burkhardt,1983 and Gooding,1985. In addition, various partial bibliographies have appeared which contain extensive references to the Kepler problem. Perhaps the most cited has been Radau,1900; others are Struve,1860, Houzeau,1882, Herglotz,1910, and Wood,1950.

Our concern will be almost exclusively for the elliptic case of Kepler's problem. What coverage we attempt of the hyperbolic case will appear in Chapter 8 when we look at universal forms of KE, and the parabolic case, e = 1, will be considered in Chapter 5, where treatments for high eccentricity (e near 1) cases are gathered. Related to KE and the Kepler problem is the subject of Lambert's theorem and the Lambert orbital problem. Except for a few bibliography entries, we won't describe this area at all, even though it has an extensive literature and independent interest. The references [Gooding,1988,1990] are to be recommended for a look at the subject.

In the language of the mathematician, there exists a unique solution of the Kepler problem, but there are many methods to describe or approximate it. It isn't feasible to say how many there are: the meaning of ""solution"" depends too much on the solver's motivations. In our classification of references bearing on KE which appear in the Bibliography, we have made seven primary categories and five secondary categories of methods of solution. These have been adequate to describe almost all our references.

Shipping Notes
  • Free Standard Shipping on $100+ Orders to the USA.
  • Except Preorder products are shipped in 48 hours.
  • Delivery to the USA:
  1. Standard Shipping : 3-10 business days
  • If time is of the essence, please consider selecting expedited delivery for faster service.
Exchange/Return Notes
  • We offer a 30-day return/exchange service after receiving.
  • Final sale items are not eligible for returns or exchanges.
  • To process your return/exchange, please contact us at [email protected]
  • Please click here for more details>>> Return & Exchange Policy
SKU: 2419139437

Discover Niche Categories That Outsell

Top-Converting Item to Boost Your Average Order

4.3 ★★★★★
Based on 279 reviews
Sort
Highest Rating
Newest First
Oldest First
Product Reviews
C
Verified Purchase
Cindy N.
Louisville, US
★★★★★ 4
Great quality ball
Color: Green, Size: Medium (2-1/2 in (Pack of 2))
The product is great no issues. It’s very durable. All of this brands products are strong and durable. The only reason I gave it a four star is I think my dogs prefer more the blue round balls. So that being said, I won’t buy these anymore, but they love the blue ones whether they’re the recycled or not. Great company!
WAS THIS REVIEW HELPFUL?YesReportShare
Reviewed in the United States on May 26, 2025
B
Verified Purchase
Brandie Luvlee
Pawtucket, US
★★★★★ 5
Unique bouncing
Color: Green, Size: Medium (2-1/2 in (Pack of 2))
Outside of many my kids🐶 balls this one his best favorite for than the others as the bounce is high and unpredictable that makes it more intellectual and exciting for him
WAS THIS REVIEW HELPFUL?YesReportShare
Reviewed in the United States on May 24, 2026
S
Verified Purchase
SH18750
Whiting, US
★★★★★ 5
Pups Love
Color: Green, Size: Medium (2-1/2 in, (Pack of 1)), Color: Green, Size: Medium (2-1/2 in, (Pack of 1))
As you can see from the photo, my pup absolutely loves it! It’s the perfect size for him and for reference he’s 25 pounds. It’s got a nice weight to it, but it’s soft enough to be able to throw and not worry about damaging the walls. We just started playing with it today, but it seems very durable.
WAS THIS REVIEW HELPFUL?YesReportShare
Reviewed in the United States on March 27, 2026
R
Verified Purchase
Randy Brock
Massapequa, US
★★★★★ 3
Fun for the first day, but just get the round balls.
Color: Green, Size: Medium (2-1/2 in (Pack of 2))
These balls do work, but they bouncy pretty much like a regular chuck it ball. They do NOT fit in the chuck it handheld ball launcher, which makes them a pain to throw. The green color also makes them somewhat challenging to find when the grass is long. That said, they do work as intended, and the dogs like them the same as all the other chuck it balls we own. As the person who had to throw them, my advice would be to just get the round balls that fit in the ball launcher. Durability: 9/10 they hood together better than the traditional balls without the hole (that crack down the seam over time). These have yet to crack despite the same wear and tear. Pros: durable, dogs like them, they do sink in water Cons: green color, hard to fit in handheld ball launcher
WAS THIS REVIEW HELPFUL?YesReportShare
Reviewed in the United States on June 3, 2023
S
Verified Purchase
Shopaholic
Dallas, US
★★★★★ 5
Winner!
Color: Green, Size: Medium (2-1/2 in (Pack of 2))
I recently got the BOUNCY DOG BALL TOY for my fur baby, and I'm thrilled to say that it's a total winner! The best feature of this interactive dog toy is its erratic bounce, which keeps my pup on their toes and makes every playtime session full of surprises. The squared corners of the ball cause it to bounce every which way when thrown, making it an exciting challenge for my dog to catch. And because it's compatible with the Chuckit! Ball Launchers, we can play fetch for hours on end without ever getting bored. One thing I love about this fetch toy is its durability. It's made of tough rubber that can withstand even the most aggressive chewers, and it's super easy to clean after a long day of play. Plus, with two balls included, we always have a backup when one inevitably gets lost.
WAS THIS REVIEW HELPFUL?YesReportShare
Reviewed in the United States on February 24, 2023

recommand products