Please Show ALL the Steps! The Milky Way Galaxy is a spiral galaxy with most of
ID: 1591846 • Letter: P
Question
Please Show ALL the Steps!
The Milky Way Galaxy is a spiral galaxy with most of the stars, such as the Sun, moving on circular orbits around the center. The centripetal force acting upon them is gravity and from measuring their speeds we can determine the amount of matter within the orbit. It was noticed in 1932 that the speed of the stars was larger than the total matter visible inside the orbit which lead to the idea that there might also be "dark matter" in the Galaxy. Dark matter is so-named because it contributes to the gravity but is not visible (i.e. does not absorb or emit radiation). The rotational velocity of our sun around the Galaxy is about 230 km/s, the visible mass contained inside of the sun's orbit is about 2 Times 10^40 kg, and the radius of the orbit is about 2.5 Times 10^20 m. Estimate the amount of dark matter within the Sun's orbit.Explanation / Answer
For circular motion we know that centripetal accleration = pull of gravity
hence Ms*Vs2 / Ro = GMsMt / Ro2 where Ms - mass of sun, Vs = rotational velocity Ro = radius of orbit G- universal gravity constant and Mt = visible mass + dark matter
subsituting vales we get Mt = Vs2 * Ro /G = 230000^2 * 2.5*10^20 / (6.674 * 10^-11) = 19.815 * 1040 Kg
Hence weight of dark matter = total mass - visible mass = (19.815-2) * 1040 = 17.815 * 1040 Kg