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!
