Answer:
5.9x10³⁰ kg = 2.97 solar mass.
Explanation:
The mass of Sirius can be calculated using Kepler's Third Law:
[tex]P^{2} = \frac{4 \pi^{2}}{G (M_{1} + M_{2})} \cdot a^{3}[/tex]
where P: is the period, G: is the gravitational constant = 6.67x10⁻¹¹ m³kg⁻¹s⁻², a: is the size of the orbit, M₁: is the mass of the Earth-like planet = 5.97x10²⁴ kg, and M₂: is the mass of Sirius.
Firts, we need to convert the units:
P = 7 months = 1.84x10⁷ s
a = 1 AU = 1.5x10¹¹ m
Now, from equation (1), we can find the mass of Sirius:
[tex] M_{2} = \frac{4 \pi^{2} a^{3}}{P^{2} G} - M_{1} [/tex]
[tex] M_{2} = \frac{4 \pi^{2} (1.5 \cdot 10^{11} m)^{3}}{(1.84\cdot 10^{7} s)^{2} \cdot 6.67 \cdot 10{-11} m^{3} kg ^{-1} s^{-2}} - 5.97 \cdot 10^{24} kg = 5.9 \cdot 10^{30} kg = 2.97 solar mass [/tex]
Therefore, the mass of Sirius is 5.9x10³⁰ kg = 2.97 solar mass.
I hope it helps you!
Answer: 2.94kg
Explanation: Using Kepler's law of planetary motion which states that, the square of the orbital period of a planet is proportional to the cube of the semi major axis of it's orbit.
Sirius is the name given to the brightest star in the sky
It could be literally interpreted as;
1/mass of planet = (orbital period in years^2 ÷ semi major axis in AU^3)
Orbital period = 7months is equivalent to 7/12 = 0.5833 years
Semi major axis = 1AU
Therefore, mass of Sirius is given by:
1/Mass = (orbital period^2 ÷ semi major axis^3)
1/Mass = (0.5833^2 ÷ 1^3)
1/Mass = 0.3402 ÷ 1
1/Mass = 0.3402
Therefore,
Mass = 1/0.3402 = 2.94kg
