Lab 3: Black Holes
Emiliano Larach
Professor: Dr. Flavio Fenton
Physics 2211M
Objectives
• Analize the trajectory of a star around a black hole to determine the mass of
the black hole using net force, and gravitational force equations.
• Find the initial velocity a ship needs to have, taking off from a planet, to
avoid crashing back again with the planet, or getting engulfed by the black
hole.
First part: calculating the mass of the black
hole
• We have the mass of the star
• Use
𝑑𝑝 𝐺𝑚1𝑚2
Fgrav(net)= =
𝑑𝑡
|𝑟 2 |
𝑑𝑝 2
∗𝑟
𝑑𝑡
• m2= 𝐺𝑚1
• Fnet=
𝑑𝑝
𝑑𝑡
⊥ +
𝑑𝑝
𝑑𝑡
∥
1st part
code: Initial
conditions
Initial Velocities
Momentum calculation
Change in velocity and momentum
Momentum principle
Change of variable from dpdt to Fnet
Net parallel force
Find net perpendicular force
While loop
Calculating the mass of the black hole
Results:
visualized
Orange: Fnet
Magenta: Fnet_paralell
Cyan: Fnet_perpendicular
Results: the numbers
|Fnet|= 9.02955e+28
|Fnet_par|= 1.42047e+28
|Fnet_perp|= 8.92464e+28
Mass of Black Hole= 1.33703e+34
Part 2: We know physics. Getting just close
enough to black holes is no danger.
• We have the mass of the Black hole
• Use
𝑑𝑝 𝐺𝑚1𝑚2
Fgrav(net)= =
𝑑𝑡
|𝑟 2 |
𝑑𝑝 2
∗𝑟
𝑑𝑡
• m2= 𝐺𝑚1
• Fnet=
𝑑𝑝
𝑑𝑡
⊥ +
𝑑𝑝
𝑑𝑡
∥
Black hole mass from previous part
Part 2: the
code
Planet’s initial conditions
Nesessary speeds to not crash in the black hole. Trial and error.
Fgrav on the planet by the black hole
Fgrav on the planet by the ship
Planet’s net force
Fgrav on the ship by the black hole
Fgrav on the ship by the planet
Fnet on the ship
Newton’s 2nd law! (position update)
The code:
While loop
Results: visualized
Discussion questions
• What does it mean? [Part 1 of the lab] In your analysis, you should discuss
how the net force and its parallel and perpendicular components are
different from the rate of change of momentum (dpdt) and its parallel and
perpendicular components.
Discussion questions
• What if...? [Part 2 of the lab] Instead of wanting to take a quick look at the
black hole and leave, you decide you want to enter into an orbit around the
black hole. What initial velocity would your spaceship need to have in order
to enter into some kind of orbit around the black hole? Your spaceship
should still not crash into the black hole, nor crash into the planet.
• I’m a physics master! I can calculate that.
Enter a circular orbit
Enter a
circular orbit