How did the measured diameter of Ceres evolve over time?

Question

Based on the Wikipedia page of Ceres, Herschel measured a diameter of 260 kilometers for Ceres, and Schröter measured 2613 kilometers.

I do remember seeing at least a half-dozen estimates of the diameter of Ceres that were made over time, but I can't seem to put my hands on the source again. Which astronomers attempted to measure the diameter of Ceres, and what values did they find?

Answer 1

How did the measured diameter of Ceres evolve over time?

Which astronomers attempted to measure the diameter of Ceres, and what values did they find?

Background

If astronomers can see an object as a disc instead of point of light, they can measure the apparent diameter of the disc.

For example, they can have thin wires stretched across the telescope at regular intervals, and see how many of those intervals the object fills. Thus they can calculate how much of the diameter of their field of view the object occupied. And knowing the angular diameter of the field of view at he magnification used, they can calculate the angular diameter of the object. And knowing the distance to the object, and its angular diameter, they can calculate its physical diameter.

So as instruments to measure angular diameters of objects improved, and more accurate measurements and calculations of the distances of those objects were made, calculations of the physical diameters of those objects improved over time.

Using the heliocentric theory, the relative distances of the planets from the Sun were easy to calculate, and more and better observations of the apparent motions of the planets resulted in better calculations of their actual motions and better determinations of their relative distances from the Sun.

But until the absolute distance between two planets could be discovered, the absolute distances between all of the planets were unknown. Astronomers measured the relative distances between planets in Astronomical Units (AU). One AU was the distance between Earth and the Sun. So a major quest for astronomers was to estimate, calculate, or measure the value of an AU, and to do it more and more accurately over time.

Here:

https://en.wikipedia.org/wiki/Astronomical_unit#History[1]

is a link to a discussion of the history of the AU, with a table of various historical values for it. The first approximately correct values for the AU came in the 17th century, and today radar is used to measure the distance from Earth to other planets and thus find the value of an AU.

Of course some object are too small and distant to appear as measurable discs in Earthbound telescopes. The solution to the problem of measuring their diameters is to create better earthbound telescopes to view those objects, or to send small telescopes much, much closer to those objects in space probes, which has been done many times in the last 60 years.

Many astronomers had no belief that there would ever be a space age, or in some cases that it would arrive as soon as it did. So they looked for other ways to find the diameters of objects which were mere points of light in their telescopes.

If the brightness of an object's image could be estimated or measured by instruments, and its its distance known with greater or lesser accuracy, the total brightness of all the light reflected from its surface could be calculated with greater or lesser accuracy.

If an astronomer estimated what the albedo, or reflectivess of the object was, and knew the total amount of light it reflected, he could calculate the surface area and diameter of the object.

So that was one method which astronomers used to calculate the diameters of various solar system objects. The diameter of a particular object might be calculated many times over decades and centuries, with a somewhat different value each time. So different astronomy books published before space probes passed close to an object would have different values for its diameter.

I noticed, for example, that different books disagreed on whether Ganymede, Callisto, Titan, or Triton was the largest moon in the solar system.

My copy of Exploration of the Universe: Brief Edition, George Abell, 1964, 1969, has an Appendix 11, Satellites of Planets, on page 463. It give the diameters of Jupiter's moons Ganymede and Callisto as 4,900 kilometers (3,044.7 miles) and 4,570 kilometers (2,839.666 miles) respectively, and Saturn's Titan as 4,950 kilometers (3,075.7 miles) and Neptune's Triton as 4,000 kilometers (2,485.4 miles), thus making Titan the most titanic moon.

My copy of The Guinness Book of Astronomy Facts & Feats: Second Edition, Ptrick Moore, 1979, 1983 says that Ganymede has a diameter of 5,276 kilometers (3,278.3 miles), Callisto has a diameter of 4,820 kilometers (2,295 miles) on page 97, Titan has a diameter of 5,140 kilometers 3,193.8 (miles) on page 110, and Triton has a diameter of 6,000? kilometers (3,728.2 miles) on page 123, thus making Ganymede the largest unless Triton actually is about 6,000 kilometers in diameter.

My copy of Men of Other Planets Kenneth Heuer, 1951, 1954, has a table on page 156 listing the surface areas in square miles of the planets and other large bodies in the solar system.

It gives Ganymede a surface area of 33,576,000 square miles (86,961,440.781 square kilometers), Callisto 30,959,000 square miles (80,183,441.897 square kilometers), Titan 39,572,000 square miles (102,491,009.489 square kilometers), and Triton 105,630,000 square miles (273,580,444.059 square kilometers) - which is between the surface areas of Mars and Venus.

So the diameters would be Ganymede 3,269 miles (5,261 kilometers), Callisto 3,139 miles (5,052 kilometers), Titan 3,549 miles (5,711 kilometers), and Triton 5,560 miles (8,947.9 kilometers).

My guess is that this diameter of Triton was calculated from its brightnes and assuming it had an albedo similar to that of Earth's moon.

The first attempt to measure the diameter of Triton was made by Gerard Kuiper in 1954. He obtained a value of 3,800 km. Subsequent measurement attempts arrived at values ranging from 2,500 to 6,000 km, or from slightly smaller than the Moon (3,474.2 km) to nearly half the diameter of Earth.[73] Data from the approach of Voyager 2 to Neptune on August 25, 1989, led to a more accurate estimate of Triton's diameter (2,706 km).[74]

https://en.wikipedia.org/wiki/Triton_(moon)#Observation_and_exploration[2]

So presumably all figures for Triton's diameter before 1954 were calculated from it's brightness and assumed albedo.

As the Voyager 2 space probe approached Neptune in 1989, it observed Triton from closer and closer distances, and the measured diameter got smaller and smaller every time. So the project scientists joked that Triton would disappear before the probe reached it.

In 2021, Triton is listed as having a diameter of 1,680 miles (2,700 kilometers).

https://solarsystem.nasa.gov/moons/neptune-moons/triton/in-depth/[3]

Or a radius of about 1,358.4 kilometers, giving a diameter of about 2,716.8 kilometers, (1,688.59 miles).

https://en.wikipedia.org/wiki/Triton_(moon)[4]

So the diameter of Triton in Exploration of the Universe was about 1.47 times 2,716.8 kilometers, the diameter in Guinness Book of Astronomy Facts and feats was about 2.2 times that, and the diameter in Men of Other Planets was about 3.29 times that.

Ceres

Ceres is listed as having a mean radius of 469.73 kilometers,and thus a mean diameter of 939.46 kilometers.

https://en.wikipedia.org/wiki/Ceres_(dwarf_planet)[5]

So Herschel's diameter of 260 kilometers was 0.276 of the present value, and Schröter's diameter of 2,613 kilometers was 2.78 of the present value, as well as being 10.05 Herschel's.

And I think that the examples of the differing estimated diameters of the largest moons of the giant planets, made 150 years after Herschel and Schröter's estimates of the diameter of Ceres, show that such large discrepancies are not that odd.