Answers: (A)
(B) 
(C)
(D)
Explanation:
<h2>(A) Gravitational force of one star on the other</h2>
According to the law of universal gravitation:
(1)
Where:
is the module of the gravitational force exerted between both bodies
is the universal gravitation constant.
and 
are the masses of both bodies.
is the distance between both bodies
In the case of this binary system with two stars with the same mass 
and separated each other by a distance 
, the gravitational force is:
(2)
(3) This is the gravitational force between the two stars.
<h2>(B) Orbital speed of each star</h2>
Taking into account both stars describe a circular orbit and the fact this is a symmetrical system, the orbital speed 
of each star is the same. In addition, if we assume this system is in equilibrium, <u>gravitational force must be equal to the centripetal force</u> 
(remembering we are talking about a circular orbit):
So: 
(4)
Where 
(5) Being 
the centripetal acceleration
On the other hand, we know there is a relation between and the velocity :
(6)
Substituting (6) in (5):
(7)
Substituting (3) and (7) in (4):
(8)
Finding :
(9) This is the orbital speed of each star
<h2>(C) Period of the orbit of each star</h2><h2 />
The period 
of each star is given by:
(10)
Substituting (9) in (10):
(11)
Solving and simplifying:
(12) This is the orbital period of each star.
<h2>(D) Energy required to separate the two stars to infinity</h2>
The gravitational potential energy 
is given by:
(13)
Taking into account this energy is always negative, which means the maximum value it can take is 0 (this happens when the masses are infinitely far away); the variation in the potential energy 
for this case is:
(14)
Knowing 
the total potential energy is 
and in the case of this binary system is:
(15)
Now, we already have the <u>potential energy</u>, but we need to know the kinetic energy 
in order to obtain the total <u>Mechanical Energy</u> 
required to separate the two stars to infinity.
In this sense:
(16)
Where the kinetic energy of both stars is:
(17)
Substituting the value of found in (9):
(17)
(18)
Substituting (15) and (18) in (16):
(19)
(20) This is the energy required to separate the two stars to infinity.
