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Chapter 23: Problem 17

How do astronomers determine how fast the Sun moves in its orbit around the Galaxy? How does this speed tell us about the amount of mass inside the Sun's orbit? Does this speed tell us about the amount of mass outside the Sun's orbit?

Short Answer

Expert verified
Astronomers determine the speed of the Sun by observing its motion relative to distant celestial objects and applying the formula for orbital speed, v = 2πR/P. This speed reveals the mass inside the Sun's orbit due to the gravitational law. However, it does not directly provide information about the mass outside the Sun's orbit, though mass outside affects the overall gravitational field and galactic geometry.

Step by step solution

01

Understanding the Concept of Orbital Motion

The Sun, like other stars, moves in an orbit around the center of the galaxy. Astronomers determine this speed by observing the motion of the Sun and other nearby stars relative to distant, 'fixed' celestial objects.
02

Calculating the Sun's Velocity

The velocity of the Sun around the center of the galaxy is calculated using the formula v = 2πR/P, where R is the distance from the Sun to the center of the galaxy and P is the orbital period.
03

Relating Velocity to Mass Inside the Sun's Orbit

The velocity of the Sun in its orbit provides information about the mass inside its orbit. This is based on the gravitational law, which states that the gravitational force (which causes the Sun to move in orbit) is directly proportional to the mass inside the orbit.
04

Understanding the Relation to Mass Outside the Sun's Orbit

The speed of the Sun in its orbit does not give direct information about the mass outside its orbit. Objects outside the Sun's orbit, however, do affect the overall gravitational field and therefore the geometry of the Galaxy.

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Most popular questions from this chapter

A gas cloud located in the spiral arm of a distant galaxy is observed to have an orbital velocity of \(400 \mathrm{~km} / \mathrm{s}\). If the cloud is \(20,000 \mathrm{pc}\) from the center of the galaxy and is moving in a circular orbit, find (a) the orbital period of the cloud and (b) the mass of the galaxy contained within the cloud's orbit.

The disk of the Galaxy is about \(50 \mathrm{kpc}\) in diameter and 600 pc thick. (a) Find the volume of the disk in cubic parsecs. (b) Find the volume (in cubic parsecs) of a sphere \(300 \mathrm{pc}\) in radius centered on the Sun. (c) If supernovae occur randomly throughout the volume of the Galaxy, what is the probability that a given supernova will occur within \(300 \mathrm{pc}\) of the Sun? If there are about three supernovae each century in our Galaxy, how often, on average, should we expect to see one within \(300 \mathrm{pc}\) of the Sun?

(a) Calculate the Schwarzschild radius of a supermassive black hole of mass \(3.7 \times 10^{6} \mathrm{M}_{\odot}\), the estimated mass of the black hole at the galactic center. Give your answer in both kilometers and astronomical units. (b) What is the angular diameter of such a black hole as seen at a distance of \(8 \mathrm{kpc}\), the distance from the Earth to the galactic center? Give your answer in arcseconds. Observing an object with such a small angular size will be a challenge indeed! (c) What is the angular diameter of such a black hole as seen from a distance of \(45 \mathrm{AU}\), the closest that the star SO-16 comes to Sagittarius \(A * ?\) Again, give your answer in arcseconds. Would it be discernible to the naked eye at that distance? (A normal human eye can see details as small as about 60 arcseconds.)

Sketch the rotation curve you would obtain if the Galaxy were rotating like a rigid body.

In a spiral galaxy, are stars in general concentrated in the spiral arms? Why are spiral arms so prominent in visible-light images of spiral galaxies?
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