We can conclude that star A is closer to us than star B.
In fact, the absolute magnitude gives a measure of the brightness of the star, if all the stars are placed at the same distance from Earth. So, it's a measure of the absolute luminosity of the star, indipendently from its distance from us: since the two stars have same absolute magnitude, it means that if they were at same distance from Earth, they would appear with same luminosity. Instead, we see star A brighter than star B, and the only explanation is that star A is closer to Earth than star B (the closer the star A, the brigther it is)
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
![a_g = \frac{GM}{R^2}](https://tex.z-dn.net/?f=a_g%20%3D%20%5Cfrac%7BGM%7D%7BR%5E2%7D)
Here
![M = \text{Mass inside the Orbit of the star}](https://tex.z-dn.net/?f=M%20%3D%20%5Ctext%7BMass%20inside%20the%20Orbit%20of%20the%20star%7D)
![R = \text{Orbital radius}](https://tex.z-dn.net/?f=R%20%3D%20%5Ctext%7BOrbital%20radius%7D)
![G = \text{Universal Gravitational Constant}](https://tex.z-dn.net/?f=G%20%3D%20%5Ctext%7BUniversal%20Gravitational%20Constant%7D)
Mass inside the orbit in terms of Volume and Density is
![M =V \rho](https://tex.z-dn.net/?f=M%20%3DV%20%5Crho)
Where,
V = Volume
Density
Now considering the volume of the star as a Sphere we have
![V = \frac{4}{3} \pi R^3](https://tex.z-dn.net/?f=V%20%3D%20%5Cfrac%7B4%7D%7B3%7D%20%5Cpi%20R%5E3)
Replacing at the previous equation we have,
![M = (\frac{4}{3}\pi R^3)\rho](https://tex.z-dn.net/?f=M%20%3D%20%28%5Cfrac%7B4%7D%7B3%7D%5Cpi%20R%5E3%29%5Crho)
Now replacing the mass at the gravitational acceleration formula we have that
![a_g = \frac{G}{R^2}(\frac{4}{3}\pi R^3)\rho](https://tex.z-dn.net/?f=a_g%20%3D%20%5Cfrac%7BG%7D%7BR%5E2%7D%28%5Cfrac%7B4%7D%7B3%7D%5Cpi%20R%5E3%29%5Crho)
![a_g = \frac{4}{3} G\pi R\rho](https://tex.z-dn.net/?f=a_g%20%3D%20%5Cfrac%7B4%7D%7B3%7D%20G%5Cpi%20R%5Crho)
For a rotating star, the centripetal acceleration is caused by this gravitational acceleration. So centripetal acceleration of the star is
![a_c = \frac{4}{3} G\pi R\rho](https://tex.z-dn.net/?f=a_c%20%3D%20%5Cfrac%7B4%7D%7B3%7D%20G%5Cpi%20R%5Crho)
At the same time the general expression for the centripetal acceleration is
![a_c = \frac{\Theta^2}{R}](https://tex.z-dn.net/?f=a_c%20%3D%20%5Cfrac%7B%5CTheta%5E2%7D%7BR%7D)
Where
is the orbital velocity
Using this expression in the left hand side of the equation we have that
![\frac{\Theta^2}{R} = \frac{4}{3}G\pi \rho R^2](https://tex.z-dn.net/?f=%5Cfrac%7B%5CTheta%5E2%7D%7BR%7D%20%3D%20%5Cfrac%7B4%7D%7B3%7DG%5Cpi%20%5Crho%20R%5E2)
![\Theta = (\frac{4}{3}G\pi \rho R^2)^{1/2}](https://tex.z-dn.net/?f=%5CTheta%20%3D%20%28%5Cfrac%7B4%7D%7B3%7DG%5Cpi%20%5Crho%20R%5E2%29%5E%7B1%2F2%7D)
![\Theta = (\frac{4}{3}G\pi \rho)^{1/2}R](https://tex.z-dn.net/?f=%5CTheta%20%3D%20%28%5Cfrac%7B4%7D%7B3%7DG%5Cpi%20%5Crho%29%5E%7B1%2F2%7DR)
Considering the constant values we have that
![\Theta = \text{Constant} \times R](https://tex.z-dn.net/?f=%5CTheta%20%3D%20%5Ctext%7BConstant%7D%20%5Ctimes%20R)
![\Theta \propto R](https://tex.z-dn.net/?f=%5CTheta%20%5Cpropto%20R)
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
<span>Force = Work done / distance = 4Nm / 2m = 2N</span>
Answer:
They developed during the Cambrian time period, which was around 530 million years ago.
Explanation:
Hope this Helps!
In an Internal Combustion Engine, the fuel is singed in the chamber or vessel. Example: Diesel or Petrol motor utilized as a part of Cars.
The internal engine has its vitality touched off in the barrel, as 99.9% of motors today. In an External Combustion Engine, the inner working fuel is not consumed. Here the liquid is being warmed from an outer source. The fuel is warmed and extended through the interior instrument of the motor bringing about work. Eg. Steam Turbine, Steam motor Trains. An outer burning case is a steam motor where the warming procedure is done in a kettle outside the motor.