Me yasa wani orbit yana da wata faduwa

Duk wani mai tafiyar sama da ka gani yana gudu a cikin tashar sararin samaniya ya faɗi ne. Wancan ne tsari da watã. Bãbu kõwa daga cikinsu “a saman nauyi”. Sunã kẽwayẽwa a kan ƙasa sau da yawa, kuma bã zã su iya sãduwa ba zuwa gare ta.

Wani taurari ne kawai mai fãɗuwa wanda bã ya ƙarewa.

Look

Ka yi jĩfa da ƙusa ga sãsanni kuma ta karkata zuwa ƙasa. Ka jẽfa ta da ƙarfi, zã ta fãɗi a wuri mai nĩsa. Now imagine throwing it so hard that, by the time it has fallen one metre, the ground beneath it has curved away by one metre too. Har yanzu yana faɗuwa. Kuma bã ya kusa.

A kan ƙasa wannan yana faruwa a cikin ~ 7.8 km/s kusa da fuskar (28,000 km/h). Babu wani abu a kan ƙasa da zai iya tafiya da sauri saboda iska za ta hana shi, don haka mu tafi sama da iska farko. Wannan shi ne abin da roketi ke yi: tana ɗaukar wani jirgin sama a saman yanayi kuma sa’an nan ta ja shi sideways, mai tsanani.

• Slower than orbital speed: the path curves into the ground.
• Exactly orbital speed: a circle.
• Mafi sauri: wani ellipse, swinging waje da baya.
• Mafi sauri fiye da gudun gudu (kamar 11 km/s daga orbit mai ƙaranci): hanya tana buɗewa kuma ba ta komawa ba.

Ka yi zaton farko: menene ƙarfin matsin tattalin ƙasa a tsayin Tashar Jirgin Sama ta Duniya, idan aka kwatanta da ƙasa?

A kan 90% kamar ƙarfi. Masu tafiyar sama ba sa tashi saboda babu matsa lamba, amma saboda su da tasharsu suna faduwa tare.

A cikin wani jirgin sama mai faduwa duk abin da yake fadowa tare a kan mataki guda, don haka babu wani abu da ke yin tasiri ga wani abu. Wannan shi ne dalilin da ya sa masu tafiyar sama suke gudu. Mikrogravitasiya.

Understand

A kusa da ƙasa, matsin lamba yana janwa tare da sauri na g = GM/r². Motsa cikin wani daki na radius r a sauri v yana buƙatar ya ja zuwa tsakiyar v²/r. A orbit ne inda gravity bayar da daidai wannan drag:

v²/r = GM/r²  →  v = √(GM / r)

Kuma da GM na ƙasa = 398,600 km³/s² da r = 6,371 + 200 = 6,571 km, v ≈ 7.79 km/s. A tsayin dutsen da Newton ya yi tunanin zai kai kilomita 600 a cikin fim din, r = kilomita 6,978 da v = kilomita 7.56/s.

Lokacin da ake tafiyar wata guda yana zuwa: T = 2πr / v, kusan minti 88 a kilomita 200. Higher orbits are slower and longer: the Moon, 384,400 km away, takes 27.3 days.

Master

Farawa a tsaye a cikin radius r₀ da sauri v kuma hanya ita ce wani ɓangare na conic tare da tsakiyar duniya a cikin mai hankali ɗaya. A power per kilogram,

ε = v²/2 − μ/r₀,

decides the shape: ε < 0 is an ellipse (including the circle and the paths that hit the ground, which are ellipses interrupted by the surface), ε = 0 a parabola, ε > 0 a hyperbola. Ƙara ε = 0 na ba da gudun gudu v_esc = √(2μ/r₀), daidai √2 sau na gudun juyawa a kan matsakaicin tsayi.

Farawa mai zurfi na koyaushe yana sanya maɓallin farawa a cikin apsis: mafi girman maɓallin orbit idan v ya fi sauri, mafi ƙasƙanci idan ya fi sama. Wannan shi ne dalilin da ya sa ƙananan ƙwallo a cikin fim ɗin ke faɗuwa daga dutsen, kuma waɗanda suke da sauri suna dawowa zuwa gare shi daga ƙasa.