Respuesta :
Answer: 5.55*10^29kg
Explanation:
To start, let us say, F(c) = F(g)
F(c) = m.4.π².r(1/2)/T²
F(g) = Gm1m2/r²
since, F(c) = F(g), then
m.4.π².r(1/2) / T² = Gm1m2/r², so that
4π²r(1/2)/T² = Gm2/r²
Since we're after m2, we make it the subject of formula. So that
m2 = 4π²r(1/2).r²/T²G
m = 4π²(1.8*10^11)(3.6*10^11²)/(1.5768*10^8²)(6.67*10^-11)
m = 4π² * (1.8*10^11)(1.296*10^23) / 2.487*10^16
m = 4π² * 2.333*10^34 / 1.658*10^6
m = 9.212*10^35/1.658*10^6
m = 5.56*10^25kg
Mass of the each binary-stars separated by 360 million km is [tex]\bold { 5.56x10^2^5\ kg}[/tex].
Kepler's third law of planetary motion,
F(c) = F(g)
[tex]\bold {F(c) = m 4\pi^2r \dfrac{1}{2}T^2}[/tex]
[tex]\bold {F(g) = G\dfrac {m_1m_2 }{r^2}}[/tex]
Since, F(c) = F(g), then
[tex]\bold { m 4\pi^2r \dfrac{1}{2}T^2 = G\dfrac {m_1m_2 }{r^2}}[/tex]
[tex]\bold { 4\pi^2r \dfrac{1}{2}T^2 = G\dfrac {m2 }{r^2}}[/tex]
[tex]\bold {m2 = 4\pi^2r\dfrac 1{2} \dfrac {r^2}{T^2G}}[/tex]
put the values in the formula,
[tex]\bold {m = 4\pi ^2\dfrac {(1.8x10^1^1)(3.6x10^1^1)^2}{(1.5768x10^8)^2(6.67x10^-^1^1)}}\\\\\bold {m = 4\pi ^2\dfrac {2.333x10^3^4}{(1.658x10^6)}}\\\\ \bold {m= 5.56x10^2^5\ kg}[/tex]
Therefore, mass of the each binary-stars separated by 360 million km is [tex]\bold { 5.56x10^2^5\ kg}[/tex].
To know more about Kepler's Law,
https://brainly.com/question/1086445
