Answer:
[tex]m = 2.23 \times 10^{-32} kg[/tex]
Explanation:
Given data:
PERIOD OF MOTION IS T = 25.5 days
orbital speeds = 220 km/s
we know that
acceleration due to centripetal force is[tex] a = \frac{F}{m} = \frac{V^2}{r}[/tex]
Gravitational force[tex] F= \frac{Gm m}{d^2}[/tex]
we know that
[tex]v = \frac{2\pi R}{T}[/tex]
solving for
[tex]R = \frac{vT}{2\pi}[/tex]
[tex]F = \frac{Gm^2}{4(\frac{vT}{2\pi})^2}[/tex]
[tex]F = G\times \frac{\pi m}{(vT)^2}[/tex]
[tex]a = \frac{v^2}{\frac{vT}{2\pi}}[/tex]
[tex]a = \frac{2\pi v}{T}[/tex]
we know that
f =ma
[tex]G\times \frac{\pi m}{(vT)^2} = a = \frac{2\pi m v}{T}[/tex]
solving for m
[tex]m = \frac{2Tv^3}{\pi G}[/tex]
[tex]m = \frac{2\times 25.5 \times 86400 \times 220000^3\ m/s}{\pi \times 6.67\times 10^{-11}}[/tex]
[tex]m = 2.23 \times 10^{-32} kg[/tex]
Based on the calculations, the mass of each star is equal to [tex]2.24 \times 10^{26}\;kg[/tex]
Given the following data:
Period = 25.5 days.
Orbital speed = 220 km/s.
Scientific data:
Gravitational constant = [tex]6.67 \times 10^{-11}[/tex]
Conversion:
Period = 25.5 days to seconds = [tex]25.5 \times 24 \times 3600[/tex] = 2203200 seconds.
Orbital speed = 220 km/s to m/s = [tex]220\times 10^3[/tex] m/s.
From Newton's law of motion and the law of universal gravitation, the mass of a planetary object is given by this formula:
[tex]m=\frac{2TV^3}{\pi G}[/tex]
Where:
Substituting the given parameters into the formula, we have;
[tex]m=\frac{2 \times 2203200 \times (220\times 10^3)^3}{3.142 \times 6.67 \times 10^{-11}}\\\\m=\frac{469193472 \times 10^{14}}{2095714 \times 10^{-10}} \\\\m=2.24 \times 10^{26}\;kg[/tex]
Read more on orbital speed here: https://brainly.com/question/4854338
