Itegeko

Around 1600, Johannes Kepler spent years trying to make the planets move in perfect circles. Bya Kuri. Byabonetse Byose Gutangira.

Imibare Kuri i Uruziga. Byahinduwe i Uruziga.

Kureba

Around 1600, Johannes Kepler worked with years of very precise observations of Mars made by Tycho Brahe. in Uruziga. Imibare Kuri Bya Akazi, Byabonetse.

1. ni (), Na: i A Bidakora - Hagati Ku A Akadomo A i.
2. A Hejuru i na Hasi Bivuye. A Umurongo: Kuva: i Kuri i: Inyuma Bingana Ubuso in Bingana Igihe.
3. Birenzeho. i Inzira: ni,.

i hejuru, ni. i na Hanyuma Gihinguranya i external Inzira% s Bya. Byose in i Igiteranyo Bya Igihe: na & Birenzeho, Gitoya na Gishya Funga in. Umwanya Igihe ni i ISEGONDA in Igikorwa.

Gusobanukirwa

ni ku Kabiri Imibare:

• i Umurongo fatizo a: i Ubugari:. i Ingano:.
• i e: ni. 0 ni A Uruziga; Gufunga Kuri 1. ni Birenzeho na.

Akadomo Kuri i ni i Ibara: (ya: i), Ku Uburebure A (1. - e). Akadomo ni i ApoA (), Ku A (1. + e).

Igikoresho	a	na
Izuba	1.000	0.017
Mutarama	1.524	0.093
Halley’s Comet	17.9	0.967

Itegeko i, i Karete Bya i Igihe ni Kuri i Bya i - Umurongo fatizo. mu myaka na

a

Jupiter: a = 5.20 au, so T = 5.20^1.5 = 11.9 years. Halley: a = 17.9 au gives T = 75.9 years, close to its famous 75 to 76-year return.

a in i i Nka Nka: 1.

Umunyeshuri

Byose Kuva: Bya. in Byuzuye Ifishi ni:

= 2π (a / μ),   μ = + m

T² / a³ = 4π² / μ ni i ya: buri Rimwe, ya:. Switch the sandbox’s central body to Earth and the constant becomes about 9.9 × 10⁻⁵ s² km⁻³ instead of 1 yr² au⁻³. The m in μ is why Kepler’s version is slightly off for Jupiter, whose mass is about 0.1% of the Sun’s.

ISEGONDA ni Bya. ni d / = h / 2, h = r² · dν / ni i Imfuruka, Mu buryo budasubiramo ya: Icyo ari cyo cyose. na i ni Kuri i Akarambararo, =: i Umuvuduko Bingana i Ihindurakerekezo Uburebure. For Halley, r_a/r_p = (1 + e)/(1 − e) ≈ 60, so it moves about 60 times faster at perihelion than at aphelion.

A ku Ku A Igihe i = n (t - t), Na: = 2π /, na Hanyuma, = - e. It has no closed-form solution; the tools on this site solve it by Newton iteration, which converges in a few steps even for Halley’s e = 0.967.