Tip:
Highlight text to annotate it
X
in this lab, we wanna study a star orbiting
a black hole of unknown mass
we wanna determinate the mass of the black hole considerating
this initial values
using the Newton´s law
universal gravitatiton
the movement of a star orbiting is an eliptic trajectory
make change of momentum in time in this lab we separate the component
of the momentum parallel and perpendicular, ando the initial position of the values
of trajectory is considerating the mass of the black hole
in this case calculate this way using
gravitational law
the model relevant to physics is the next
fnet parallel, f net perpendicular
this is a code that i used
in the python, the mass of the star
the velocity, momentum
delta p, fnet parallel, f net perpendicular
black black hole and G
arrow one, arrow tho, arrow three, this is a simulation
we see the three vector: blue arrow, yellow arrow and black arrow
black arrow is a fnetparallel (not perpedicular)
the yellow arrow
is the sum of the blue arrow and the black arrow
this is a mass of the black hole
we need to find
a relation between
the Kepler's law and the Newton´s law
and the combinations of the both
way of thinking with the next
see the proportionality between the force
and that the 1/R^2
(distance squared) is the
next way to connection Newton
and Kepler´s Law. The star make an elliptic trajectory
with the vector fnet parallel a black arrow
the vector f net a yellow arrow
and the blue arrow fnet perpendicular.
the analysis of parallel moment is next. Fnet is opposite to the movement
and cause a change of directionof velocity
the star continues an elliptic movement
due inertia, even if the velocity parallel
in a certain point is opposite to the net force
as you see in this case, fnet
is yellow arrow
an in this case, the black arrow
are pointing in direction of this movement
and in this case is pointing in opposite direction
of the movement
this is because this expression is menor to zero
when this part of the equation is non zero, indicate
there is not(straight)...is a curve trajectory
and note the perpenducular (momentum) dependence
of the inverse of the distance 1/R
this is observed when the yellow
arrow and the blue arrow is very big
when the black hole is near to the star
when the back hole is far away from the star
the blue arrow is not too big
because the fnet parallel is not too big
the dp/dt is related
with the fnet, in this case
is a combination of parallel and perpendiular
fnet, when a star
is near of the black hole
we see a major velocity (increment)
this is
according to the Kepler´s law
fnet and dp/dt are not the same, (the momemtum) is caused
by the net force in this direction and not
in the opposite direction
if you imagine to place a different black hole
and the star remained unchanged the trajectory
we wanna find and explanation
there is the same (physics situation) the new mass is already know
and the mass of the old black hole
and nothing change, nothing different here
In summary, the object momentum is in continually changing
even if the star move with constant speed
a chhange of the direction means dp/dt is nonzero
Thanks you for watching
Thanks you for watching