Concept explainers
(a)
The orbital period of the cloud, if a gas cloud located in the spiral arm of a distant galaxy has an orbital velocity of 400 km/s while moving in a circular orbit and the distance from the center of the galaxy is 20,000 pc.
(a)
Answer to Problem 26Q
Solution:
Explanation of Solution
Given data:
For a gas cloud located in the spiral arm of a distant galaxy, the orbital velocity is
Formula used:
The expression for time taken by an object in circular motion to complete an orbit is,
Here,
Conversion from km/s to m/s is performed as,
Conversion from pc to m is performed as,
Conversion from 1 s to 1 year is performed as,
Hence,
Explanation:
Write the expression for the period of the cloud’s orbit around the galactic center.
Substitute
Further, solve as,
Conclusion:
Therefore, the orbital period of the cloud is
(b)
The mass of the galaxy contained within the cloud’s orbit, if a gas cloud located in the spiral arm of a distant galaxy has an orbital velocity of 400 km/s while moving in a circular orbit and the distance from the center of the galaxy is 20,000 pc.
(b)
Answer to Problem 26Q
Solution:
Explanation of Solution
Given data:
For a gas cloud located in the spiral arm of a distant galaxy, the orbital velocity is
Formula used:
The expression for mass of our galaxy within the cloud is,
Here,
The value of
Conversion from km/s to m/s is performed as,
Conversion from pc to m is performed as,
Explanation:
Recall the expression for mass of our galaxy within the cloud.
Substitute
Conclusion:
Therefore, the mass of our galaxy within the cloud is
Want to see more full solutions like this?
Chapter 22 Solutions
Universe
- Observations indicate that each galaxy contains a supermassive black hole at its center. These black holes can be hundreds of thousands to billions of times more massive than the Sun. Astronomers estimate the size of such black holes using multiple methods. One method, using the orbits of stars around the black hole, is an application of Kepler's third law. The mass of the black hole can be found by using the given equation, where a is the semi-major axis in astronomical units, P is the period in years, and k is a constant with a value of 1 Mo X year²/ AU³. a³ M = k- p² What is the mass of a supermassive black hole if a star orbits it with a semimajor axis of 959 AU and a period of 13.3 years? mass: Another method measures the speed of gas moving past the black hole. In the given equation, v is the velocity of the gas (in kilometers per second), r is the distance of the gas cloud from the black hole (in kilometers), and G is Newton's gravitational constant. In this equation, G = 1.33 ×…arrow_forward(a) Estimate the height (z) above or below the Galactic plane for the globular cluster M13 (1,b = 59°, 40.9°) and the Orion Nebula (1,b = 209°, -19.4°). M13 and the Orion Nebula are 7 kpc and 450 pc away from Earth respectively. (b) To which components of the Galaxy do these objects probably belong? Explain your answers.arrow_forwardA star is 1.0 x 104 ly (light-years) from the center of its galaxy and is moving in a circle around that center at a speed of 110 km/s. (a) How long does it take the star to make one revolution about the galactic center? (b) How many revolutions has the star completed since it was formed about 5.6 x 109 years ago?arrow_forward
- Figure 2 shows the "rotation curve" of NGC 2742. It plots the “radial velocity (V)" (how fast material is moving either toward or away from us) that is measured for objects at different distances (R = radius") from the center of the galaxy. The center of the galaxy is at 0 kpc (kiloparsecs) with a speed of 9 km/sec away from us. (These velocities have been corrected for the observed tilt of the galaxy and represent true orbital velocities of the stars and gas.) 200 100 U4779 -100 As you can see, one side of the galaxy is moving with a negative velocity (spinning toward us), while the other side has a positive velocity (spinning away from us). Using Newton's gravity equation, we will be able to determine the gravitational mass of the entire galaxy and how the mass varies versus distance from the galaxy's center. -200 -8 8 -4 Radius (kpc) Read the following text carefully and follow the instructions: Select five radii spaced evenly from 0-10 kpc across the galaxy. Your selections should…arrow_forwardThe gas in the outer region of the Andromeda galaxy is found to be orbiting the galaxy with a velocity of 250 km/s. The gas is at a distance of 35 kpc from the center of the galaxy. The total mass of the galaxy is _______ solar masses.arrow_forwardA Cepheid variable in the Andromeda galaxy has a period of 22 days and a mean apparent magnitude of19.5.(a) Calculate the distance modulus of the Andromeda galaxy.(b) Given that the Andromeda galaxy is approaching the Milky Way with a velocity of 119 km/s, roughlyestimate how long before these two galaxies collide? Provide your answer in years.arrow_forward
- n(r) = 1ge where r represents the distance from the centre of the Galaxy, Ro is the distance of the Sun from the centre of the Galaxy, Ra is the typical size of disk and no is the stellar density of disk at the position of the Sun. All distances are expressed in kpc. An astronomer observes the center of the Galaxy within a small field of view. We take a particular type of Red giant stars as the standard candles for the observation with approximately constant absolute magnitude of M = -0.2, (a) A telescope has a limiting magnitude of m = 18. Calculate the maximum distance to which this telescope can detect these red giant stars. For simplicity we ignore the presence of interstellar medium so there is no extinction. (b) Assume an extinction of 0.7 mag/kpc for the interstellar medium. Repeat the calculation as done in the part 5a and obtain a rough number for the maximum distance these red giant stars can be observed. (c) Give an expression for the number of these red giant stars per mag-…arrow_forwardIf astronomers find they have made a mistake and our Solar System is actually 7,350 pc rather than 8,300 pc from the center of the Milky Way Galaxy, but the orbital velocity of the Sun is still 225 km/s, what is the minimum mass (in solar masses, MSun) of the Galaxy within the orbit of the Sun?arrow_forwardYou observe the H-alpha line of Hydrogen in a distant galaxy to have a wavelength of 918.4 nm. What is the radial velocity of the galaxy?arrow_forward
- If a planet was located approximately 32 thousand light-years from the center of a galaxy and orbits that center once every 313 million years, how fast is the planet traveling around the galaxy in km/hr? If needed, use 3.0 × 108 m/s for the speed of light.arrow_forwardThe Sun is at a distance of about 8 kpc from the galactic center and moves around the galactic center in a circular path with a velocity of about 220 km s. Make a rough estimate of the mass of the Galaxy.arrow_forwardIf the active core of a galaxy contains a black hole of 106 MSun , what will the orbital distance be (in km) for matter orbiting the black hole with an orbital period of 1 hour?arrow_forward