The observation point on Earth and the two stars form a triangle. The two sides of the triangle are 23.3 ly and 34.76 ly and their included angle is 76.04°. We can use the cos rule to find the third side, which is the distance between the two stars.
c² = a² + b² - 2abCos(C)
c² = (23.3)² + (34.76)² - 2(23.3)(34.76)Cos(76.04)
c = 36.88 light years.
Wat does that mean I don't understand this
The gravitational force would be <u>180,000 N</u> if the distance is reduced by one- half.
According to Newton's law of gravitation, the force of attraction between two objects is proportional to the product of their masses and inversely proportional to the square of the distance between them.
Therefore, the force <em>F</em> between the two masses when they are at a distance <em>d</em> apart can be written as
........(1)
When the distance between the two objects is reduced to one- half, then the new force F₁ is given by,

Divide equation (2) by equation (1)

Substitute 45,000 N for <em>F</em>.

If the distance between the two objects is reduced by one- half, the force between them has a value <u>180,000 N.</u>
Answer:
angular acceleration = 209.44 [rad/s^2]
Explanation:
First we have to convert the velocities which are in revolutions per minute to radians on second.
where:
![w_{0} = 1000 [\frac{rev}{min}]*[\frac{2\pi rad }{1rev}] * \frac{1min}{60s} = 104.7[\frac{rad}{s} ]\\w = 2000 [\frac{rev}{min}]*[\frac{2\pi rad }{1rev}] * \frac{1min}{60s} = 209.4[\frac{rad}{s} ]](https://tex.z-dn.net/?f=w_%7B0%7D%20%3D%201000%20%5B%5Cfrac%7Brev%7D%7Bmin%7D%5D%2A%5B%5Cfrac%7B2%5Cpi%20rad%20%7D%7B1rev%7D%5D%20%20%2A%20%5Cfrac%7B1min%7D%7B60s%7D%20%3D%20104.7%5B%5Cfrac%7Brad%7D%7Bs%7D%20%5D%5C%5Cw%20%3D%202000%20%5B%5Cfrac%7Brev%7D%7Bmin%7D%5D%2A%5B%5Cfrac%7B2%5Cpi%20rad%20%7D%7B1rev%7D%5D%20%20%2A%20%5Cfrac%7B1min%7D%7B60s%7D%20%3D%20209.4%5B%5Cfrac%7Brad%7D%7Bs%7D%20%5D)
Now we can find the angular acceleration:
![w=w_{0} + \alpha *t\\\alpha =\frac{w-w_{0} }{t} \\\alpha =\frac{209.43-104.71}{\0.5 } \\\alpha = 209.44[\frac{rad}{s^{2} } ]](https://tex.z-dn.net/?f=w%3Dw_%7B0%7D%20%2B%20%5Calpha%20%2At%5C%5C%5Calpha%20%3D%5Cfrac%7Bw-w_%7B0%7D%20%7D%7Bt%7D%20%5C%5C%5Calpha%20%3D%5Cfrac%7B209.43-104.71%7D%7B%5C0.5%20%7D%20%5C%5C%5Calpha%20%3D%20209.44%5B%5Cfrac%7Brad%7D%7Bs%5E%7B2%7D%20%7D%20%5D)