## Relativistic Recoil

English Version
Yukterez
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Registriert: Mi 21. Okt 2015, 02:16

### Relativistic Recoil

This is the english version.   Deutschsprachige Version: hier entlang

without Gravity

Exercise: A projectile has a velocity of v0=0.9 (in natural units of c) when shot from a clamped in canon. If the canon is not clamped in but floating freely, and the mass of the canon is 10× that of the projectile, what would the velocity v1 of the projectile be, and how high the recoil velocity v2 of the canon?

1) Newton

2) Einstein

by Simon Tyran, Vienna @ youtube || rumble || odysee || minds || wikipedia || stackexchange || License: CC-BY 4 ▣ If images don't load: [ctrl]+[F5]

Yukterez
Beiträge: 272
Registriert: Mi 21. Okt 2015, 02:16

### Relativistic Recoil

with Gravity

Exercise: A satellite orbits around a black hole's ISCO. How much energy is required to launch a projectile with the required escape velocity to escape to infinity if the mass of the satellite is 10× higher than the mass of the projectile?

Calculation: vPro: prograde velocity of the satellite, vEsc: escape velocity (both measured in the frame of a locally stationary and angular momentum free observer), vDif: required projectile velocity, vRec: recoil (both in the satellite's frame of reference), Ek: required energy to launch the projectile (in natural units of mc², where m is the mass of the projectile).

Animation: on the left the projectile (red) is launched with the required escape velocity, and the satellite's orbital velocity is reduced by the recoil. On the right a second projectile (orange) is launched into the opposite direction to cancel out the recoil so the satellite can keep a constant velocity. Before the shot at t=0 the numerical display shows the orbital parameters of the satellite, and after t=0 those of the projectile.

1) Kepler

Simulation (click on the image to lower the frame rate):

Code: .txt, worksheet: .nb

2) Schwarzschild

Simulation (click on the image to lower the frame rate):

Code: .txt, worksheet: .nb

3) Kerr

Simulation (click on the image to lower the frame rate):

Code: .txt, worksheet: .nb

by Simon Tyran, Vienna @ youtube || rumble || odysee || minds || wikipedia || stackexchange || License: CC-BY 4 ▣ If images don't load: [ctrl]+[F5]