Question

The planet Jupiter revolves around the Sun in a period of about 12 years (3.79 × 108 seconds). What is its mean distance from the center of the Sun? The mass of the Sun is 1.99 × 1030 kilograms.

A. 1.1 × 10^11 meters
B. 1.5 × 10^11 meters
C. 2.3 × 10^11 meters
D. 5.8 × 10^11 meters
E. 7.8 × 10^11 meters

Answer 1

As we know that gravitational force of Sun will provide the centripetal force to all planets

so here we will have

`F_g = F_c`

`(GMm)/(r^2) = m\omega^2 r`

here we know that

`\omega = (2\pi)/(T)`

`\omega = (2\pi)/(3.79 * 10^8)`

`\omega = 1.66 * 10^(-8)`

now from above equation

`(GM)/(r^2) = \omega^2 r`

`(GM)/(\omega^2) = r^3`

`((6.67 * 10^(-11))(1.99* 10^(30)))/((1.66* 10^(-8))^2) = r^3`

`r = 7.8 * 10^(11) m`