Spaceship flying towards earth at relativistic speeds?

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Discussion Overview

The discussion revolves around the relativistic effects observed when a spaceship travels towards Earth at a significant fraction of the speed of light (0.5c). Participants explore the implications of time dilation and the perception of the spaceship's position from an Earth-based observer's perspective.

Discussion Character

  • Exploratory, Conceptual clarification

Main Points Raised

  • One participant describes a scenario where a spaceship approaches Earth at 0.5c from a distance of 1 light year, questioning how its position is perceived over time by an Earth observer.
  • Another participant asserts that the described effect is well-known and has been observed in phenomena such as quasar jets, suggesting that the initial participant's reasoning is correct.
  • A follow-up question is posed regarding the convergence of the real position of the ship and its trailing image as the observer gets closer.
  • A participant confirms the convergence of the ship's real position and its image only occurs when the observer is infinitely close.

Areas of Agreement / Disagreement

Participants appear to agree on the validity of the initial participant's reasoning regarding the relativistic effects, but the discussion does not resolve all aspects of the scenario, particularly regarding the nuances of perception and distance.

Contextual Notes

The discussion does not address potential limitations or assumptions regarding the observer's frame of reference or the effects of relativistic speeds on measurements.

Who May Find This Useful

This discussion may be of interest to those exploring concepts in relativity, particularly in relation to observational effects at relativistic speeds.

novop
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Here is something I thought about the other day that could use some clarification... say a spaceship starts its voyage towards the Earth at 0.5c at a distance of 1 light year away from the earth. All measurements are made from an observer on earth.

An observer on Earth only notices the ship after 1 year has passed, but at this time the spaceship is in reality halfway between it's starting position and the earth. After 1.5 years have passed, the ship appears to be at the halfway position but is in reality 3/4 between it's starting position and the earth. To an observer on earth, wouldn't the ship have appeared to be approaching at the speed of light? Only half a year has passed but the image of the ship appears to have traversed a distance of half a light year. Where am I going wrong here?
 
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I see... so it is only infinitely close to the observer that the real position of the ship and it's trailing image converge to the same point?
 
Yes.
 
Perfect thank you!
 

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