Isibonelo semithetho kaKepler

Izibonelo ezi-3 zemithetho kaKepler

1. Ibanga elijwayelekile ukusuka eplanethini yoMhlaba ukuya elangeni lingu-149,6 x 10⁶ km kanti isikhathi sokuguquka koMhlaba singunyaka owodwa. Iyini isilinganiso esingaguquki sesikwele sesikhathi ne-cube yebanga eliphakathi ukusuka eMhlabeni kuya eLangeni?
Ingxoxo

Lo mbuzo uhlobene no Imithetho kaKepler.
Kuyaziwa ukuthi:
T = unyaka ongu-1, r = 149,6 x 10⁶ km
Kubuziwe: T² /r³ = … ?
Impendulo:

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

2. Isilinganiso esingaguquki sesikhathi sokuguquka kweplanethi kuya ku-cube yebanga elimaphakathi leplanethi ukusuka elangeni liyafana kuwo wonke amaplanethi. Isilinganiso singabalwa kusetshenziswa ifomula:

Ivelaphi le fomula? Funda ngayo ezintweni eziphathelene nemithetho kaKepler.

Imininingwane:
G = ukungaguquguquki komhlaba wonke = 6,67 x 10^-11 I-Nm²/ kg²
m = isisindo selanga = 1,99 x 10³⁰ kg
ipi =3,14
Bala i-proportionality constant usebenzisa ifomula engenhla. Sebenzisa i-period unit = iminyaka kanye ne-distance unit = amakhilomitha.
Ingxoxo

3. Ibanga elijwayelekile ukusuka eplanethini yoMhlaba ukuya elangeni lingu-149,6 x 10⁶ km kanti ibanga elimaphakathi leplanethi iMercury lingu-57,9 x 10⁶ km. Isikhathi sokuguquka koMhlaba singunyaka owodwa, siyini isikhathi sokuguquka kweplanethi iMercury?
Ingxoxo
Kuyaziwa ukuthi:
r womhlaba = 149,6 x 10⁶ km
r ye-mercury = 57,9 x 10⁶ km
I-T yoMhlaba = unyaka ongu-1
Kubuziwe: I-T mercury?
Impendulo:

T₂ = 0,24 Iminyaka Yomhlaba
1 Unyaka womhlaba = izinsuku ezingu-365
Isikhathi sokuguquka kukaMercury = (0,24)(izinsuku ezingu-365) = izinsuku ezingu-87,6.

Imibuzo Yomthetho KaKepler

1. Ibanga elimaphakathi leplanethi iVenus ukusuka elangeni lingu-108,2 x 10 ⁶ km kanti isikhathi sokuguquka kweVenus siyiminyaka engu-0,615. Iyini isilinganiso esingaguquki sesikwele sesikhathi kuya ku-cube yebanga elimaphakathi leVenus ukusuka elangeni?

2. Ibanga elimaphakathi leplanethi iVenus nelanga lingu-108,2 x 10 ⁶ km kanti ibanga elimaphakathi leplanethi iMars lingu-227,9 x 10 ⁶ km. Isikhathi sokuguquka kweVenus siyiminyaka engu-0,615, yisiphi isikhathi sokuguquka kweplanethi iMars?