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ELEN [110]
2 years ago
11

A star near the visible edge of a galaxy travels in a uniform circular orbit. It is 41,200 ly (light-years) from the galactic ce

nter and has a speed of 275 km/s. Estimate the total mass of the galaxy based on the motion of the star.
Gravitational constant is 6.674×10−11 m3/(kg·s2) and mass of the Sun Ms=1.99 × 1030 kg.
*Answer in billion solar mass
Physics
1 answer:
Ronch [10]2 years ago
6 0

The total mass of the galaxy is 443.4 Solar mass

Orbital velocity (v) = \sqrt{\frac{MG}{R} }

where M= weight of galaxy

G= gravitational constatnt = 6.674*10^-^1^1 (given)

R = distance from centre = 41200 Light years (given)= 4.12*9.5*10^1^6  km (1 ly= 9.5*10^3 billion km)

v= orbital velocity = 275  km/s (given)

∴ According to the formula

(2.75*10^2)^2 = \frac{M*6.674*10^-^1^1}{4.12*9.5*10^1^6}

⇒ 7.56*10^4*4.12*9.5*10^1^6=M*6.674*10^-^1^1 (cross multiplying and expanding)

⇒ 29.59*10^2^1=M*6.674*10^-^1^1

⇒ \frac{29.59*10^2^1*10^1^1}{6.674}=M

⇒ 4.434*10^3^2=M

1 solar mass = 1.989*10^3^0 kg

⇒ Mass in solar mass =443.4 Solar mass

⇒ M = 443.4 Solar mass

Learn more about Orbital velocity here :

brainly.com/question/22247460

#SPJ10

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