Question

The orbital radius of the Earth (from Earth to Sun) is 1.496 x 10^11 m.

Mercury's orbital radius is 5.79 x 10^10 m and Pluto's is 5.91 x 10^12 m.
Calculate the time required for light to travel from the Sun to each of the
three planets.
a. Sun-Earth:_______
b. Sun-Mercury:________
c. Sun-Pluto:________​

Answer 1

Step-by-step explanation:

The orbital radius of the Earth is
`r_1=1.496* 10^(11)\ m`

The orbital radius of the Mercury is
`r_2=5.79 * 10^(10)\ m`

The orbital radius of the Pluto is
`r_3=5.91 * 10^(12)\ m`

We need to find the time required for light to travel from the Sun to each of the three planets.

(a) For Sun -Earth,

Kepler's third law :

`T_1^2=(4\pi ^2)/(GM)r_1^3`

M is mass of sun,
`M=1.989* 10^(30)\ kg`

So,

`T_1^2=(4\pi ^2)/(6.67* 10^(-11)* 1.989* 10^(30))* 1.496* 10^(11)\\\\T_1=\sqrt{(4\pi^(2))/(6.67*10^(-11)*1.989*10^(30))*1.496*10^(11)}\\\\T_1=2* 10^(-4)\ s`

(b) For Sun -Mercury,

`T_2^2=(4\pi ^2)/(6.67* 10^(-11)* 1.989* 10^(30))* 5.79 * 10^(10)\ m\\\\T_2=\sqrt{(4\pi^(2))/(6.67*10^(-11)*1.989*10^(30))* 5.79 * 10^(10)}\ m\\\\T_2=1.31* 10^(-4)\ s`

(c) For Sun-Pluto,

`T_3^2=(4\pi ^2)/(6.67* 10^(-11)* 1.989* 10^(30))* 5.91 * 10^(12)\\\\T_3=\sqrt{(4\pi^(2))/(6.67*10^(-11)*1.989*10^(30))* 5.91 * 10^(12)}\\\\T_3=1.32* 10^(-3)\ s`