Question

the radius of venus's orbit around the sun is 1.08x10^8 km. If earths orbital radius is 1.5x10^8 km then what is earth's Period in Venus years?

Answer 1

here,

mass of sun , M = 2 * 10^30 kg

for Venus

radius of orbit , Rv = 1.08 * 10^11 m

time period , Tv = sqrt(4*pi^2*Rv^3 /( G * M))

Tv = sqrt(4*pi^2*(1.08 * 10^11)^3 /( 6.67 * 10^-11 * 2 * 10^30))

Tv = 1.93 * 10^7 s

for Earth

radius of orbit , Re = 1.5 * 10^11 m

time period , Te = sqrt(4*pi^2*Re^3 /( G * M))

Te = sqrt(4*pi^2*(1.5 * 10^11)^3 /( 6.67 * 10^-11 * 2 * 10^30))

Te = 3.16 * 10^7 s

Te = 3.16 * 10^7 /( 1.93 * 10^7) * Tv

Te = 1.64 * Tv

so, the time peiod of earth is 1.64 times the year of Venus