No, it isn't. It's correct in the basic claim of the title. Scientists in 1863 who believed that no known source of energy was capable of powering the Sun were right. The Sun is not powered by any source of energy that was known in 1863.
> I would prefer if there was some more working shown to back up the article
Scientific American wasn't the place to show the details then any more than it is today. But the calculations are simple to do, and plenty of physicists had done them at the time of the article.
A summary of the calculations:
Chemical reactions, which is what burning coal is an example of, produce an energy per unit mass of fuel on the order of 10^8 Joules per kilogram. (That's actually on the high end, but it's fine for a rough calculation.) The Sun's mass is about 2 x 10^30 kilograms today; if we assume that half of that is burned as fuel, we get a total energy of 10^38 Joules. The Sun's power output is about 4 x 10^26 Watts, so 10^38 Joules will supply the Sun's power output for about 2 x 10^11 seconds, which is pretty close to 5,000 years (a year is about 3 x 10^7 seconds).
Meteorite impacts essentially convert gravitational potential energy to heat, so the energy per unit mass available is the change in gravitational potential energy from the average distance of a meteorite from the Sun when it starts falling in, to the radius of the Sun. That difference is GM/R - GM/r, where R is the Sun's radius and r is the distance from which the meteorite starts falling in. If we take the maximum possible change, that will be for r -> infinity, in which case our potential energy gain is just GM/R. G is about 7 x 10^-11, M we have from above, and R is about 7 x 10^8 meters. This works out to 2 x 10^11 Joules per kilogram. At that rate, to supply the Sun's power output for 100 million years (about 3 x 10^15 seconds) would take about 6 x 10^30 kilograms, or 3 times the Sun's mass.
That tells me that the article greatly overestimated the potential mass of meteorites available, since the Sun is something like 99 percent of the mass of the solar system, and even counting in the Oort cloud doesn't change that number appreciably. An optimistic upper limit based on current knowledge would be something like 0.1 percent of the Sun's mass (since most of the 1 percent of mass that is not the Sun is the planets, not meteorites), and even that is probably much too large. But taking that value gives an time of 1e12 seconds, or about 30,000 years.
(Note that later in the 1800s, someone--I think it was Lord Kelvin--calculated how long the Sun could be kept shining by gravitational contraction--i.e, by just contracting its own mass to a smaller radius and converting gravitational potential energy into radiation. He came up with a figure of something like 10 million years, which is about what you get if you take the potential energy change formula I gave above and plug in an r--the distance from which "falling in" starts--of something like twice the Sun's radius, and then multiply by the entire mass of the Sun. That's basically what Kelvin's calculation did.)
The article is using meteorites as an analogy; the model is of the Sun forming by gravitational contraction of a gas cloud, for which an r of infinity is appropriate.
What's interesting is that the power available from solar fusion is of a similar order of magnitude to that available from gravitational contraction. But of course it must be, because if fusion was too powerful medium-mass stars wouldn't be able to form to provide light and heat to habitable worlds, and if it was too weak then giant stars wouldn't be able to overcome their gravitational binding energy in supernovae to disperse the elements that form habitable worlds.
> What's interesting is that the power available from solar fusion is of a similar order of magnitude to that available from gravitational contraction.
No, it isn't; fusion provides much more energy per unit mass than gravitational contraction would for the Sun. As I calculated, gravitational contraction falling in from infinity to the current radius of the Sun provides about 2 x 10^11 Joules per kilogram. Fusion provides about 5 x 10^14 Joules per kilogram (the exact number depends on the particular fusion reaction).
No, it isn't. It's correct in the basic claim of the title. Scientists in 1863 who believed that no known source of energy was capable of powering the Sun were right. The Sun is not powered by any source of energy that was known in 1863.
> I would prefer if there was some more working shown to back up the article
Scientific American wasn't the place to show the details then any more than it is today. But the calculations are simple to do, and plenty of physicists had done them at the time of the article.
A summary of the calculations:
Chemical reactions, which is what burning coal is an example of, produce an energy per unit mass of fuel on the order of 10^8 Joules per kilogram. (That's actually on the high end, but it's fine for a rough calculation.) The Sun's mass is about 2 x 10^30 kilograms today; if we assume that half of that is burned as fuel, we get a total energy of 10^38 Joules. The Sun's power output is about 4 x 10^26 Watts, so 10^38 Joules will supply the Sun's power output for about 2 x 10^11 seconds, which is pretty close to 5,000 years (a year is about 3 x 10^7 seconds).
Meteorite impacts essentially convert gravitational potential energy to heat, so the energy per unit mass available is the change in gravitational potential energy from the average distance of a meteorite from the Sun when it starts falling in, to the radius of the Sun. That difference is GM/R - GM/r, where R is the Sun's radius and r is the distance from which the meteorite starts falling in. If we take the maximum possible change, that will be for r -> infinity, in which case our potential energy gain is just GM/R. G is about 7 x 10^-11, M we have from above, and R is about 7 x 10^8 meters. This works out to 2 x 10^11 Joules per kilogram. At that rate, to supply the Sun's power output for 100 million years (about 3 x 10^15 seconds) would take about 6 x 10^30 kilograms, or 3 times the Sun's mass.
That tells me that the article greatly overestimated the potential mass of meteorites available, since the Sun is something like 99 percent of the mass of the solar system, and even counting in the Oort cloud doesn't change that number appreciably. An optimistic upper limit based on current knowledge would be something like 0.1 percent of the Sun's mass (since most of the 1 percent of mass that is not the Sun is the planets, not meteorites), and even that is probably much too large. But taking that value gives an time of 1e12 seconds, or about 30,000 years.
(Note that later in the 1800s, someone--I think it was Lord Kelvin--calculated how long the Sun could be kept shining by gravitational contraction--i.e, by just contracting its own mass to a smaller radius and converting gravitational potential energy into radiation. He came up with a figure of something like 10 million years, which is about what you get if you take the potential energy change formula I gave above and plug in an r--the distance from which "falling in" starts--of something like twice the Sun's radius, and then multiply by the entire mass of the Sun. That's basically what Kelvin's calculation did.)