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Shailesh Pincha
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There are 2 unknowns in the formula. The time period of rotation and the mass enclosed by orbit is Star. So how could we calculate the expected time period of rotation of stars in a galaxy and thus velocity of stars.
D H said:The title of this thread, "Rotation curve of galaxy Keplerian method," hints at a big misunderstanding. Stars in a spiral galaxy do not have Keplerian orbits. The concept of a Keplerian orbit implicitly assumes a spherical mass distribution. Normal matter in a spiral galaxy does not have anything close to a spherical mass distribution. Instead, there's a central bulge that contains a tiny fraction of the galaxy's mass. Most of the normal matter is in a fairly thin disk. The gravitational potential of that central bulge + disk is not anything close to the conditions for Keplerian orbits.
What can be done is to assume that the concentration of stars hints at the total mass of the galaxy. (A good portion of normal matter is in interstellar gas clouds rather than stars, but presumably the concentration of stars is an indicator of the concentration of those gas clouds.) From this, one can calculate how fast a star in a roughly circular orbit should be going. It's more complex than simple Keplerian orbits, but it is doable.
This is where the problem arises. No matter how much fudging one does regarding the amount of normal matter in those interstellar gas clouds, the numbers don't add up. Stars + gas clouds + dust don't explain the observations. There are only two explanations. One is that our concept of gravitation is fundamentally incorrect at the galactic levels and larger. The other is that our concept of gravitation is correct, but that some other form of mass exists that we can't see in galaxies and that isn't distributed the way stars are (hence the term "dark matter").
There are very few indicators that we don't know how gravity works at galactic scales. There are a large number of indicators that the second explanation is the correct one.
That is not what is done. Kepler's laws derive from Newtonian gravitation assuming a very, very large central mass. Kepler's laws don't quite work even in the solar system. Jupiter's mass is about 1/1000th of that of the Sun. This means that deviations from Keplerian orbits are easily observable even in the solar system because scientists do much better than three place accuracy nowadays.Shailesh Pincha said:That is precisely my question. We hypothesise the existence of dark matter or some new gravitational theory based on the deviation of rotation curve from what we expect from Kepler's III Law. But how do we formulate the Kepler's law to be applicable in that condition?
The rotation curve of a galaxy refers to the plot of the orbital velocity of stars or gas as a function of their distance from the center of the galaxy. It helps us understand the distribution of mass within the galaxy.
The Keplerian method is a technique used to study the rotation curve of a galaxy by observing the Doppler shift of spectral lines from stars or gas as they orbit around the center of the galaxy. This allows us to measure their velocities and map out the rotation curve.
In a planetary system, the orbital velocity of objects decreases as their distance from the central object increases. However, in a galaxy, the orbital velocity remains constant or even increases as distance from the center increases, indicating the presence of dark matter.
Studying the rotation curve of a galaxy allows us to determine the distribution of mass within the galaxy. This can help us understand the dynamics of the galaxy and also provide evidence for the existence of dark matter.
Yes, the rotation curve of a galaxy can change over time as the distribution of mass within the galaxy changes. This can happen due to interactions with other galaxies, star formation, or mergers with other galaxies.