Oberth Effect Near Sag A*

  • Context: High School 
  • Thread starter Thread starter Devin-M
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Discussion Overview

The discussion revolves around the feasibility of achieving a final velocity of 0.95c for a spacecraft using the Oberth effect near Sagittarius A* (Sag A*), a supermassive black hole. Participants explore the implications of relativistic speeds, delta-v calculations, and orbital mechanics in the context of a hypothetical Falcon 9-sized craft with specific thrust and velocity parameters.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • Some participants propose that the Oberth effect could allow a spacecraft to reach 0.95c with a delta-v of 0.23c near Sag A*, while others question the feasibility of this claim.
  • One participant suggests treating the thrust as a semi-instantaneous impulse to simplify calculations, while another emphasizes the need for a sustained burn.
  • Equations from general relativity and Schwarzschild black hole dynamics are referenced to analyze the energy and velocity changes during the burn.
  • There is a discussion about the differences in velocity gain when comparing the black hole scenario to a flyby of Jupiter, with some participants noting that relativistic effects complicate the calculations.
  • Participants express confusion regarding the optimal periapsis altitude and its impact on the velocity gain, with one stating that they have not calculated this yet.
  • One participant corrects their earlier calculation of the final velocity at infinity, indicating the complexity of the computations involved.
  • Another participant suggests that a detour to Sag A* could potentially yield a faster arrival at Andromeda compared to a direct route, despite the extra distance involved.

Areas of Agreement / Disagreement

There is no consensus on whether achieving 0.95c is possible with the given parameters. Multiple competing views remain regarding the effectiveness of the Oberth effect in this scenario, the necessary calculations, and the assumptions made about the spacecraft's trajectory.

Contextual Notes

Participants note that the calculations depend on specific assumptions about the spacecraft's trajectory, the nature of the burn, and the relativistic effects involved. There are unresolved questions about the optimal periapsis altitude and how it influences the velocity gain.

  • #31
PeterDonis said:
Heuristically, at periapsis it's going to slightly squeeze the ship, since the ship will be oriented tangentially.
"Slightly" depends on ship size and black hole size, so if @Devin-M is considering a flight path via other BHs then that might affect his thinking. That's the only point I was making.
 
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  • #32
Ibix said:
E is the kinetic energy at infinity
kinetic energy per Kg?
 
  • #33
Devin-M said:
kinetic energy per Kg?
My apologies - it's the total energy per kilogram.

I'll edit my post above.
 
  • #34
Sorry it’s taken me so long. I’m planning to run the numbers with a 5 solar mass black hole and a 1 solar mass black hole - in a conversation I had with Grok, it told me that the 5 solar mass BH could give 0.95c and the solar mass black hole could give 0.99c at a large distance in this scenario (with a .1c approach speed and 0.23c burn). Does that seem reasonable? I’m very curious if when I run the numbers that will indeed be the case.
 
  • #35
Devin-M said:
in a conversation I had with Grok, it told me that the 5 solar mass BH could give 0.95c and the solar mass black hole could give 0.99c at a large distance in this scenario (with a .1c approach speed and 0.23c burn). Does that seem reasonable?
Not even close, based on calculations posted earlier in this thread.
 
  • #36
Devin-M said:
I’m planning to run the numbers with a 5 solar mass black hole and a 1 solar mass black hole
Note that in the calculations posted earlier in the thread, the mass of the central object (whether it's a black hole or the planet Jupiter or anything in between) doesn't matter in itself. All that matters is the ratio ##M / r## at periapsis.
 

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