Download the App!

Get 24/7 study help with the Numerade app for iOS and Android! Enter your email for an invite.

Astronomers have observed an otherwise normal star, called $S 2,$ closely orbiting an extremely massive but small object at the center of the Milky Way Galaxy called SgrA. S2 moves in an elliptical orbit around SgrA with a period of 15.2 yr and an eccentricity $e=0.87$ (Fig. $16 ) .$ In $2002, \mathrm{s} 2$ reached its closest approach to SgrA, a distance of only 123 AU $(1 \mathrm{AU}=1.50 \times 10^{11} \mathrm{m})$ is the mean Earth-Sun \right. distance). Determine the mass $M$ of SgrA, the massive compact object (believed to be a supermassive black hole) at the center of our Galaxy. State $M$ in kg and in terms of the mass of our Sun.

Get the answer to your homework problem.

Try Numerade free for 7 days

Like

Report

$7.4 \times 10^{36} \mathrm{kg}$$3.7 \times 10^{6}$

Physics 101 Mechanics

Chapter 6

Gravitation and Newton's Synthesis

Physics Basics

Newton's Laws of Motion

Applying Newton's Laws

Gravitation

Rutgers, The State University of New Jersey

Simon Fraser University

McMaster University

Lectures

03:43

In physics, dynamics is the branch of physics concerned with the study of forces and their effect on matter, commonly in the context of motion. In everyday usage, "dynamics" usually refers to a set of laws that describe the motion of bodies under the action of a system of forces. The motion of a body is described by its position and its velocity as the time value varies. The science of dynamics can be subdivided into, Dynamics of a rigid body, which deals with the motion of a rigid body in the frame of reference where it is considered to be a rigid body. Dynamics of a continuum, which deals with the motion of a continuous system, in the frame of reference where the system is considered to be a continuum.

03:55

In physics, orbital motion is the motion of an object around another object, which is often a star or planet. Orbital motion is affected by the gravity of the central object, as well as by the resistance of deep space (which is negligible at the distances of most orbits in the Solar System).

06:45

Astronomers have observed …

02:29

Observations of galaxy far…

06:47

Our Sun orbits a supermass…

03:28

06:13

At the Galaxy's Core.…

05:29

08:53

02:13

A star near the visible ed…

02:44

Mass of the Milky Way The …

03:54

The Sun orbits the center …

6.61. So there is a star Cold s too. Maybe make this up a little bit more like it, too. That orbits the center of the Milky Way galaxy with a period of 15 and a bit years. And, uh, the object at the center that it orbits is called sanitary iss A, which is believed to be a supermassive black hole. And given the orbital period, the eccentricity of the orbit and the that close this distance that s two gets to sanitary. It's a we want to estimate its mass where the massive secretary is hated. It's not a mess, too. So, um, in the in the chapter, it describes how Kepler's third law is valid If the sort of, uh, radius are, you know, mean distance A r r. Rather is replaced with the semi major axis s. So our men is s minus the eccentricity times s or s, times one minus. He and so the semi major axis, which we can then use in Kepler's third Law, is our men over one minus the ex interested. And this is also just a geometric fact about ellipses that you couldn't check in any number of ways. So with that, I can take Templars Law he's played over s cubed is equal to four pi square over the gravitational constant times. The mass of sanitary is a which is what we'd like to know which is the equal four times pi squared times the semi major axis squared. I'm sorry. So many Drax is huge. Invited by gravitational, constant times, the period squared. And so then this is 7.4. I must tend to the 36 kilograms, which is very gigantic. This is also equal 23 point 7,000,000 solar masses. So it's almost four times 4,000,000 times more massive than the sun is that, uh, gives a bit more of a sense of scale because, like, Okay, 10 to the 36 kilograms. What does that even mean? But, you know, it means that if you had 4,000,000 of our sons sitting there in the middle of the galaxy than that one be the equivalent mass

View More Answers From This Book

Find Another Textbook

Numerade Educator