Misalai 3 na dokokin Kepler
1. Matsakaicin nisan da ke tsakanin duniyar Duniya zuwa rana shine 149,6 x 106 km kuma lokacin juyin juya halin Duniya shekara 1 ne. Menene rabon da ya dace na murabba'in lokacin zuwa kubiyar matsakaicin nisan daga Duniya zuwa Rana?
Tattaunawa
Wannan tambayar tana da alaƙa da Dokokin Kepler.
An san cewa:
T = shekara 1, r = 149,6 x 106 km
An tambaya: T2 /r3 = …?
Amsa:
k = T 2 / r 3 = 1 2 / (149,6 x 10 6 ) 3 = 1 / (3348071,9 x 10 18 ) = 2,98 x 10 -25 shekaru 2 / km 3
2. Daidaiton rabon lokacin juyin juya halin duniya zuwa kubiyar matsakaicin nisan da duniyar ke da shi daga rana iri ɗaya ne ga dukkan duniyoyi. Ana iya ƙididdige daidaiton ta amfani da dabarar:
Daga ina wannan dabara ta fito? Koyi game da ita a cikin kayan da ke kan dokokin Kepler.
Bayani:
G = ma'aunin nauyi na duniya = 6,67 x 10-11 Nm2/ kg2
m = nauyin rana = 1,99 x 1030 kg
pi = 3,14
Lissafin daidaiton daidaito ta amfani da dabarar da ke sama. Yi amfani da naúrar lokaci = shekaru da naúrar nisa = kilomita.
Tattaunawa
3. Matsakaicin nisan da ke tsakanin duniyar Duniya zuwa rana shine 149,6 x 106 km kuma matsakaicin nisan duniyar Mercury shine 57,9 x 106 km. Lokacin juyin juya halin duniya shekara 1 ne, menene lokacin juyin juya halin duniyar Mercury?
Tattaunawa
An san cewa:
r na ƙasa = 149,6 x 106 km
r na mercury = 57,9 x 106 km
Duniya T = shekara 1
An tambaya: T mercury?
Amsa:
T2 = Shekarun duniya 0,24
Shekarar duniya 1 = kwanaki 365
Lokacin juyin juya halin Mercury = (0,24)(kwanaki 365) = kwanaki 87,6.
Tambayoyin Dokar Kepler
1. Matsakaicin nisan da duniyar Venus ke da shi daga rana shine kilomita 108,2 x 10 6 , kuma lokacin juyin juya halin Venus shine shekaru 0,615. Menene rabon da ke tsakanin murabba'in lokacin da kubik na matsakaicin nisan Venus daga rana?
2. Matsakaicin nisan da duniyar Venus ke da shi zuwa rana shine 108,2 x 10 6 km kuma matsakaicin nisan da duniyar Mars ke da shi shine 227,9 x 10 6 km. Lokacin juyin juya halin Venus shine shekaru 0,615, menene lokacin juyin juya halin duniyar Mars?
