Question

always use significant figure rules. remember that these rules apply to all numbers that are measurements.
planet geos in orbit a distance of 1 a.u. (astronomical unit) from the star astra has an orbital period of 1 \year.\ if planet logos is 4 a.u. from astra, how long does logos require for a complete orbit?
tb =
years
8
64

Explanation:

Step1: Aplicar la tercera ley de Kepler

La tercera ley de Kepler establece que \( T^{2}\propto a^{3}\), donde \(T\) es el período orbital y \(a\) es la distancia media del planeta al sol. Entonces, \(\frac{T_{1}^{2}}{T_{2}^{2}}=\frac{a_{1}^{3}}{a_{2}^{3}}\).

Step2: Sustituir los valores dados

Dado que \(a_{1} = 1\) A.U., \(T_{1}=1\) año y \(a_{2} = 4\) A.U. Sustituyendo en la ecuación \(\frac{1^{2}}{T_{2}^{2}}=\frac{1^{3}}{4^{3}}\).

Step3: Resolver para \(T_{2}\)

Despejando \(T_{2}\), \(T_{2}^{2}=4^{3}\), \(T_{2}^{2} = 64\), \(T_{2}=\sqrt{64}=8\) años.

Answer:

8 años