The discussion revolves around how an observer moving at relativistic speeds perceives a pulsar, particularly focusing on the effects of time dilation and the relativistic Doppler effect. Participants explore the implications of these effects on the observed rotation speed of a neutron star and the frequency of its emitted pulses.
Participants do not reach a consensus on the observed speed of rotation for the neutron star, with multiple competing views and interpretations remaining unresolved throughout the discussion.
Participants express uncertainty regarding the application of time dilation and the Doppler effect, and there are unresolved mathematical steps in the calculations presented. The discussion also highlights the complexity of transforming velocities between different frames of reference.
https://www.astronomy.com/science/weird-object-neutron-star-psr-j1748-2446/PeterDonis said:I don't see the point of switching scenarios if you haven't even gotten the original one right. The solution of both is the same in any case since we were only concerned with the equatorial plane of the rotating neutron star, which is the same as the rotating disk in your new scenario. So you've already been given the answer to your new scenario anyway.
It’s hard to visualize. In everyday life, the fastest-spinning thing we might see is the blade on a kitchen blender or a circular saw. But those never rotate more than a few hundred times a second. This star’s equator moves at one-quarter the speed of light. This rotation of 43,000 miles (70,000km) per second would be like Earth’s equator completing nearly two spins a second instead of one a day.
Neither. Do the math. I've already pointed you at it.King Solomon said:So now we start moving towards PSR J1748−2446ad at 0.995c, does the 70,000km remain the same or to the speed of light (minus a very small number).
Note that this is a speed in the pulsar's rest frame, and you are asking for a speed in the observer's frame. But this speed is not something the observer directly observes. They have to calculate it. Actually, two ways of making that calculation have been given in this thread. One of them just uses the direct velocity addition formula. The other starts with the Doppler factor, which is directly observed (the pulsar's frequency is 20 times faster) and then corrects for the change in light travel time due to the shortening distance between the pulsar and the observer. The two methods will both give the same answer if done correctly.King Solomon said:the 70,000km