Question

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

Answer 1

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 = 8 years

Answer 2

8 years

Step-by-step explanation:

Kepler's third law states that the ratio between the cube of the distance of a planet from its star and the square of its orbital period is constant for all the planets orbiting around that star:

`(d^3)/(T^2)=const.`

where d is the distance of the planet from the star and T is the orbital period.

By applying this law to the two planets of this problem, we can write

`(d_g^3)/(T_g^2)=(d_L^3)/(T_L^2)`

where
`d_g=1 AU` is the distance of geos from the star,
`T_g=1 y` is its orbital period,
`d_L=4 AU` is the distance of logos from the star. Re-arranging the equation , we can find
`T_L`, the orbital period of logos around the star:

`T_L=\sqrt{(T_g^2 d_L^3)/(d_Lg^3)}=\sqrt{((1 y)^2 (4 AU)^3)/((1 AU)^3)}=√(4^3)=8 years`