A moon is in orbit around a planet. The moon's orbit has a semimajor axis of 4.3 times 10 Superscript 8 Baseline m and has an orbital period of 1.516 days. Use these data …

Question

asked May 22, 2020 204k views

1 Answer

Somedirection · Answer 1 · 2020-05-26T17:34:23+0000

Answer:

The mass of the planet is
$2.7*10^(27)\ kg$ .

Step-by-step explanation:

Given that,

Semi major axis
a= 4.3*10^(8)

Orbital period T=1.516 days

Using Kepler's third law

$T^2=(4\pi^2)/(GM)a^3$

$M=(4\pi^2)/(GT^2)a^3$

Where, T = days

G = gravitational constant

a = semi major axis

Put the value into the formula

M=(4*(3.14)^2)/(6.67*10^(-11)(1.516*24*60*60)^2)(4.3*10^(8))^3

$M=2.7*10^(27)\ kg$

Hence, The mass of the planet is
$2.7*10^(27)\ kg$ .