Muenzaniso wemitemo yaKepler

Mienzaniso mitatu yemitemo yaKepler

1. Avhareji yedaro kubva pasi pano kuenda kuzuva i149,6 x 10⁶ km uye nguva yekuchinja kwenyika igore rimwe chete. Ndeipi chiyero chisingachinji chesikweya yenguva kusvika kucube yeavhareji yedaro kubva kuNyika kuenda kuZuva?
Kukurukurirana

Mubvunzo uyu une chekuita ne Mitemo yaKepler.
Zvinozivikanwa kuti:
T = gore 1, r = 149,6 x 10⁶ km
Akabvunzwa: T² /r³ = … ?
Mhinduro:

k = T ² / r ³ = 1 ² / (149,6 x 10 ⁶ ) ³ = 1 / (3348071,9 x 10 ¹⁸ ) = 2,98 x 10 ^-25 makore ² /km ³

2. Chiyero chenguva yekuchinja kwenyika kusvika kuchikamu cheavhareji yedaro repasi kubva kuzuva chakafanana kumapuraneti ese. Chiyero chinogona kuverengerwa uchishandisa fomura iyi:

Fomura iyi inobva kupi? Dzidza nezvayo muzvinyorwa zviri pamitemo yaKepler.

Information :
G = simba rinokwevera pasi rose = 6,67 x 10^-11 Nm²/ makirogiramu²
m = huremu hwezuva = 1,99 x 10³⁰ kg
pi = 3,14
Verengai chiyero chekuenzanisa uchishandisa fomura iri pamusoro. Shandisai chikamu chenguva = makore uye chikamu chedaro = makiromita.
Kukurukurirana

3. Avhareji yedaro kubva pasi pano kuenda kuzuva i149,6 x 10⁶ km uye avhareji yedaro repasi rose reMercury i57,9 x 10⁶ km. Nguva yekuchinja kwenyika igore rimwe chete, chii chinonzi nguva yekuchinja kwenyika yeMercury?
Kukurukurirana
Zvinozivikanwa kuti:
r yenyika = 149,6 x 10⁶ km
r ye mercury = 57,9 x 10⁶ km
T yePasi = gore rimwe chete
Akabvunzwa: T mercury?
Mhinduro:

T₂ = 0,24 Makore epasi
Gore rePasi 1 = mazuva 365
Nguva yekuchinja-chinja kweMercury = (0,24) (mazuva 365) = mazuva 87,6.

Mibvunzo yeMutemo waKepler

1. Avhareji yedaro repasi reVenus kubva kuzuva i108,2 x 10 ⁶ km uye nguva yekuchinja kweVenus imakore 0,615. Ndeipi ratio yenguva yechikwere chenguva iyoyo kusvika kucube yedaro repakati peVenus kubva kuzuva?

2. Avhareji yedaro repasi reVenus kuenda kuzuva i108,2 x 10 ⁶ km uye avhareji yedaro repasi reMars i227,9 x 10 ⁶ km. Nguva yekuchinja kweVenus imakore 0,615, inguvai yekuchinja kwepasi reMars?