johnnydeep wrote: ↑Thu Aug 26, 2021 12:46 pm
In conclusion, when a 7 gm marshmallow falls from a height of 1 km and hits the surface of a neutron star, what is the energy released due to? Is it solely due to the kinetic energy of impact, or also the difference in gravitational potential energy? And since we're talking about a neutron star, I guess there might be relativistic effects as well?
Finally, in general, can a mass hitting something ever release more energy than you'd get by converting the mass to energy via e=mc
2? What if it hits at a large fraction of the speed of light? I would think so, since the effective mass would be greater (relativistic effect), so the energy release would also have to be greater.
I was doing a back of the envelope calculation based on the kinetic energy of impact = escape velocity energy based on the difference in gravitational potential energy. This formed the basis of my best guess as to
the local impact effect at the surface.
Known (non gravitational)
external energy releases of supernovas (e.g., collapse of a white dwarf to a black hole) or of kilonovas (e.g., merger of two neutron stars) amount to
less than 0.1% of mc2.
[Note: Since gravitational quadrupole radiation scales
as the square of the quadrupole moment small incoming objects (e.g., marshmallows) radiate a negligible percentage of their rest mass in gravitational radiation (... possibly not a single graviton).]
https://en.wikipedia.org/wiki/Foe_(unit) wrote:
<<A
foe is a unit of energy equal to 10
44 joules or 10
51 ergs, used to express the large amount of energy released by a supernova. An acronym for
"[ten to the power of] fifty-one ergs".
This unit of measure is convenient because a supernova typically releases about one foe of observable energy in a very short period (which can be measured in seconds). In comparison, if the Sun had its current luminosity throughout its entire lifetime, it would release ~1.2 foe.
- One solar mass has a rest mass energy of 1787 foe.>>
https://en.wikipedia.org/wiki/Kilonova wrote:
<<A kilonova (also called a macronova or r-process supernova) is a transient astronomical event that occurs in a compact binary system when two neutron stars or a neutron star and a black hole merge into each other. Kilonovae are thought to emit short gamma-ray bursts and strong electromagnetic radiation due to the radioactive decay of heavy r-process nuclei that are produced and ejected fairly isotropically during the merger process.
The term kilonova was introduced by Metzger et al. in 2010 to characterize the peak brightness, which they showed reaches 1000 times that of a classical nova. They are 1⁄10 to 1⁄100 the brightness of a typical supernova, the self-detonation of a massive star. The first kilonova to be found was detected as a short gamma-ray burst, SGRB 130603B, by instruments on board the Swift Gamma-Ray Burst Explorer and KONUS/WIND spacecraft and then observed using the Hubble Space Telescope 9 and 30 days after burst.
In October 2018, astronomers reported that GRB 150101B, a gamma-ray burst event detected in 2015, may be analogous to the historic GW170817, a gravitational wave event detected in 2017, and associated with the merger of two neutron stars. The similarities between the two events, in terms of gamma ray, optical and x-ray emissions, as well as to the nature of the associated host galaxies, are considered "striking", and this remarkable resemblance suggests the two separate and independent events may both be the result of the merger of neutron stars, and both may be a hitherto-unknown class of kilonova transients. Kilonova events, therefore, may be more diverse and common in the universe than previously understood, according to the researchers.>>
[quote=johnnydeep post_id=316126 time=1629981989 user_id=132061]
In conclusion, when a 7 gm marshmallow falls from a height of 1 km and hits the surface of a neutron star, what is the energy released due to? Is it solely due to the kinetic energy of impact, or also the difference in gravitational potential energy? And since we're talking about a neutron star, I guess there might be relativistic effects as well?
Finally, in general, can a mass hitting something ever release more energy than you'd get by converting the mass to energy via e=mc[sup]2[/sup]? What if it hits at a large fraction of the speed of light? I would think so, since the effective mass would be greater (relativistic effect), so the energy release would also have to be greater.[/quote]
I was doing a back of the envelope calculation based on the kinetic energy of impact = escape velocity energy based on the difference in gravitational potential energy. This formed the basis of my best guess as to [b][u][color=#0000FF]the local impact effect at the surface[/color][/u][/b].
Known (non gravitational) [b][u][color=#FF0000]external energy releases[/color][/u][/b] of supernovas (e.g., collapse of a white dwarf to a black hole) or of kilonovas (e.g., merger of two neutron stars) amount to [b][u][color=#FF0000]less than 0.1% of mc[/color][/u][sup]2[/sup][/b].
[Note: Since gravitational quadrupole radiation scales [b][u]as the square of the quadrupole moment[/u][/b] small incoming objects (e.g., marshmallows) radiate a negligible percentage of their rest mass in gravitational radiation (... possibly not a single graviton).]
[quote=https://en.wikipedia.org/wiki/Foe_(unit)]
<<A [size=135][b][color=#0000FF]foe[/color][/b][/size] is a unit of energy equal to 10[sup]44[/sup] joules or 10[sup]51[/sup] ergs, used to express the large amount of energy released by a supernova. An acronym for [b][i]"[ten to the power of] [b][color=#0000FF][size=155]f[/size][/color][/b]ifty-[b][color=#0000FF][size=155]o[/size][/color][/b]ne [b][color=#0000FF][size=155]e[/size][/color][/b]rgs"[/i][/b].
This unit of measure is convenient because a supernova typically releases about one foe of observable energy in a very short period (which can be measured in seconds). In comparison, if the Sun had its current luminosity throughout its entire lifetime, it would release ~1.2 foe.
[list][size=125][b][u][color=#FF0000]One solar mass has a rest mass energy of 1787 foe.[/color][/u][/b]>>[/size][/list][/quote][quote=https://en.wikipedia.org/wiki/Kilonova]
[float=left][img3=NGC 4993 kilonova fade over the course of six days ]https://upload.wikimedia.org/wikipedia/commons/f/fa/NGC_4993_and_GRB170817A_after_glow.gif[/img3][/float]
<<A kilonova (also called a macronova or r-process supernova) is a transient astronomical event that occurs in a compact binary system when two neutron stars or a neutron star and a black hole merge into each other. Kilonovae are thought to emit short gamma-ray bursts and strong electromagnetic radiation due to the radioactive decay of heavy r-process nuclei that are produced and ejected fairly isotropically during the merger process.
The term kilonova was introduced by Metzger et al. in 2010 to characterize the peak brightness, which they showed reaches 1000 times that of a classical nova. They are 1⁄10 to 1⁄100 the brightness of a typical supernova, the self-detonation of a massive star. The first kilonova to be found was detected as a short gamma-ray burst, SGRB 130603B, by instruments on board the Swift Gamma-Ray Burst Explorer and KONUS/WIND spacecraft and then observed using the Hubble Space Telescope 9 and 30 days after burst.
In October 2018, astronomers reported that GRB 150101B, a gamma-ray burst event detected in 2015, may be analogous to the historic GW170817, a gravitational wave event detected in 2017, and associated with the merger of two neutron stars. The similarities between the two events, in terms of gamma ray, optical and x-ray emissions, as well as to the nature of the associated host galaxies, are considered "striking", and this remarkable resemblance suggests the two separate and independent events may both be the result of the merger of neutron stars, and both may be a hitherto-unknown class of kilonova transients. Kilonova events, therefore, may be more diverse and common in the universe than previously understood, according to the researchers.>>[/quote]