Question

A binary star system consists of two stars, each of mass 2 * 10^30 ??. The initial positions of Star A and Star B are ?⃗?? = 〈−3, −4, 0〉 * 10^9 ? and ?⃗?? = 〈3, 4, 0〉 * 10^9 ? respectively. The magnitude of the gravitational force that one star exerts on another is about 2.7 * 10^30 N.

The initial velocity of Star B is ?⃗?? = 〈−6.5,4.9,0〉*10^4 ? ? . What is the approximate velocity of Star B after a time step of about 1 hour (∆? = 3.6*10^3 ?)?

What is the approximate new position of Star B after a time step of about 1 hour (∆? = 3.6*10^3 ?)?

Answer 1

For any change of position, we can define that for going from point A to point B, the direction of the movement is:

Using th concept of gravitational force:

stands for the force that exerts star A over star B.

For stars of equal mass, and applying Newton´s second law:

For a "small" displacement, we can define final velocity and position as function of time as a rectilinear motion with constant acceleration:

Then, for star B:

Finally, the final velocity:

and final displacement: