To solve this problem we will use the concepts related to gravitational acceleration and centripetal acceleration. The equality between these two forces that maintains the balance will allow to determine how the rigid body is consistent with a spherically symmetric mass distribution of constant density. Let's start with the gravitational acceleration of the Star, which is

Here



Mass inside the orbit in terms of Volume and Density is

Where,
V = Volume
Density
Now considering the volume of the star as a Sphere we have

Replacing at the previous equation we have,

Now replacing the mass at the gravitational acceleration formula we have that


For a rotating star, the centripetal acceleration is caused by this gravitational acceleration. So centripetal acceleration of the star is

At the same time the general expression for the centripetal acceleration is

Where
is the orbital velocity
Using this expression in the left hand side of the equation we have that



Considering the constant values we have that


As the orbital velocity is proportional to the orbital radius, it shows the rigid body rotation of stars near the galactic center.
So the rigid-body rotation near the galactic center is consistent with a spherically symmetric mass distribution of constant density
Answer:
It corresponds to a distance of 100 parsecs away from Earth.
Explanation:
The angle due to the change in position of a nearby object against the background stars it is known as parallax.
It is defined in a analytic way as it follows:

Where d is the distance to the star.
(1)
Equation (1) can be rewritten in terms of d:
(2)
Equation (2) represents the distance in a unit known as parsec (pc).
The parallax angle can be used to find out the distance by means of triangulation. Making a triangle between the nearby star, the Sun and the Earth (as is shown in the image below), knowing that the distance between the Earth and the Sun (150000000 Km), is defined as 1 astronomical unit (1AU).
For the case of (
):


Hence, it corresponds to a distance of 100 parsecs away from Earth.
<em>Summary:</em>
Notice how a small parallax angle means that the object is farther away.
Key terms:
Parsec: Parallax of arc second
Answer:
It would be 2.2 if you have to round the five to the one but if your not rounding the number, it'd be 2.1.
Explanation: