Isantya sokuhamba: i-equation ye-vis-viva

Ihamba njani ngokukhawuleza inqanawa yenqwelo-moya? Nceda ndixelele ukuba ibekwe kuphi kwiplanethi kwaye inkulu kangakanani indawo yayo yokuhamba, kwaye enye i-equation efutshane iza kuphendula umbuzo naphi na kwindawo ejikeleze indlela yayo. Abacwangcisi bemikhosi basebenzisa le nto yonke imihla.

I-equation efutshane enye inika isantya naphi na kujikelezo lweplanethi.

Bona

Nantoni na ejikeleza ilanga iyaqhubeka irhweba ubude besantya, njengento yokudada ngebhodi kwinxalenye yombhobho.

• Ukuwa phezulu kufutshane nombindi wesiqu, ikhawuleza.
• Ukunyuka kude, ihamba phantsi.

Kwibhokisi yesand isalathisi esimnyama sibonisa isantya: isalathisi eside, esikhawulezayo; isalathisi esifutshane, esicothayo. Bona ukuba ikhula xa umzimba ujikeleza ngaphakathi, kwaye ucinezele xa unyuka ngaphandle.

Ihlabathi liyenza into efanayo, kuphela ngokulula kuba i orbit yayo inokuba yindawo ejikelezayo: iyahamba malunga ne-30.3 km/s ekuqaleni kukaJanuwari kwaye malunga ne-29.3 km/s ekuqaleni kukaJulayi.

Ukuqonda

I vis-viva equation (“isandla esiphilayo”, igama elidala le-energy) inika isantya kwindawo nganye:

v = √( μ · (2/r − 1/a) )

• v: speed
• μ: iparamitha yoxinzelelo lwesiqu esisisiseko (GM)
• r: umgama okhoyo ukusuka kwisiqithi esiphakathi kwesiseko
• a: umgca ohamba ngaphaya kwe-orbit

Khangela:

• Isijikelezi (r = a): v = √(μ/a). Le yisantya esijikelezayo kwiNewton lesson.
• I-periapsis, r incinci kakhulu, ngoko ke 2/r inkulu kwaye v ikhawuleza.
• Kude kakhulu kwindlela yokuyeka (a → ∞): v = √(2μ/r). Le yisantya sokuphuma, esichazwe kwisifundo esilandelayo.

Umzekelo osebenza: Ihlabathi lijikeleze ilanga, μ = 1.327 × 10¹¹ km³/s², a = 149.6 yezigidi zeekhilomitha. Kwindawo ejikelezayo r = 152.1 yezigidi zeekhilomitha:

v = √(1.327 × 10¹¹ × (2/1.521 × 10⁸ − 1/1.496 × 10⁹)) ≈ 29.3 km/s.

Umphathi

I-vis-viva yinkqubo yokugcina amandla efihlakeleyo. Umbane othile we-orbit (umandla ngekilogram) yi

ε = v²/2 − μ/r = −μ / (2a)

Uxinzelelo olujikelezayo kunye ne-amandla anamandla ahlala njalo kufutshane nomjikelo weplanethi kwaye luxhomekeke kuphela kwi-a. I-v isolwa kwaye ufumana i-vis-viva. Iingxaki:

• I-iphawu le ε lihlalutya i orbit: e negativi kwi ellipses, isiphelo separabola, e positive ye hyperbola.
• Nakweyiphi na indawo enikezelweyo, isantya kuphela simisela i-a. Le nto ibangela ukuba i-injini enye itshise kwindawo enye itshintshe ubungakanani bendawo yokuhamba yonke, kwaye kutheni izifundo ezilandelayo zingathetha malunga ne-delta-v budgets.

Isantya se-apsis silandela ukusuka kwi-vis-viva nge r = a(1 ± e):

v_p = √(μ/a · (1+e)/(1−e)),   v_a = √(μ/a · (1−e)/(1+e))

Umkhiqizo wabo ngu v_p · v_a = μ/a = v_circ², ngoko ke isantya esijikelezayo si isimo segeometry esiphakathi kwezimbini, hayi isiqingatha sobalo. Oku kuphendula umbuzo wokuba Zama.