Question

You are the science officer on a visit to a distant solar system. Prior to landing on a planet you measure its diameter to be 1.8 × 107 m and its rotation period to be 22.3 hours. You have previously determined that the planet orbits from its star with a period of 402 earth days. Once on the surface you find that the acceleration due to gravity is 59.7 m/s2. What are the mass of (a) the planet and (b) the star?

Answer 1

Part a)

`M = 7.25 * 10^(25) kg`

Part b)

`M = 2* 10^(30) kg`

Step-by-step explanation:

Part a)

As we know that the diameter of the planet is given as

`d = 1.8 * 10^7 m`

now the radius of the planet is given as

`r = 9 * 10^6 m`

now we know that the acceleration due to gravity of the planet is given by the equation

`g = (GM)/(r^2)`

here we know that

`g = 59.7 m/s^2`

now from above equation we have

`59.7 = ((6.67 * 10^(-11))M)/((9* 10^6)^2)`

now we have

`M = 7.25 * 10^(25) kg`

Part b)

Now by kepler's law we know that

time period of revolution of planet about the star is given as

`T = 2\pi \sqrt{(r^3)/(GM)}`

so we have

`(T_1^2)/(T_2^2) = (r_1^3)/(r_2^3)`

now we have

`(1^2)/(402^2) = ((1.5 * 10^11)^3)/(r^3)}`

`rr = 8.17 * 10^(12) m`

mula of time period

`402* (365* 24 * 3600) = 2\pi \sqrt{((8.17* 10^12)^3)/((6.67* 10^(-11))M)}`

Now we have

`M = 2* 10^(30) kg`