Question

A satrun year is $29.5$ times the earth year. How far is the Saturn from the sun if the earth is $1.5 \times 10 ^ { 8 }$ away from the sun?

• A. $1.4 \times 10 ^ { 6 } \mathrm {~km}$
• B. $1.4 \times 10 ^ { 7 } \mathrm {~km}$
• C. $1.4 \times 10 ^ { 8 } \mathrm {~km}$
• D. $1.4 \times 10 ^ { 9 } \mathrm {~km}$

Answer 1

Answer: (D)

$1.4 \times 10 ^ { 9 } \mathrm {~km}$

Answer 2

Here,

$\mathrm { T } _ { \mathrm { s } } = 29.5 \mathrm {~T} _ { \mathrm { E } } , \mathrm { R } _ { \mathrm { E } } = 1.5 \times 10 ^ { 8 } \mathrm {~km} , \mathrm { R } _ { \mathrm { s } } = ?$

According to Kepler’s third law,

$\therefore \frac { \mathrm { T } _ { \mathrm { S } } ^ { 2 } } { \mathrm {~T} _ { \mathrm { E } } ^ { 2 } } = \frac { \mathrm { R } _ { \mathrm { S } } ^ { 3 } } { \mathrm { R } _ { \mathrm { E } } ^ { 3 } }$