Measuring the Astronomical Unit - part ii

Updated 29 May 26

Introduction

Here's a summary of two (identical!) estimates of the AU made in 1672, based on telescopic observations of Mars at or near opposition. They are remarkably accurate for the time, being well within 10% of the accepted figure.

With these estimates, for the first time the terrestrial scale could be connected to the astronomical, via the radius of the Earth, the size of which had been known since the time of the Ancient Greeks. 

(True, the Earth-Moon distance had also been fairly accurately known, but that was a dead-end as a unit of measurement).

Summary

i. Flamsteed (Britain)

Method: diurnal parallax, i.e. non-simultaneous observations made at the same location

Location: Greenwich (51.5 N)

Baseline not known by me, but:

• if observations were made at 9 pm then 3 am (90° Earth rotation later), then 

        baseline = radius of circle of latitude x √ 2 = Rₑ x cos 51.5° x √ root 2: ~ 0.9 Rₑ

• if observations were made at 8 pm then 4 am (120° Earth rotation later), then

        baseline = radius of circle of latitude' x 2 x sin 60°  =  cos 51.5° x 2 x sin 60 ~ 1.1 Rₑ

(where Rₑ is the mean radius of the Earth)

Pros:

• no travel involved
• no need to determine longitude
• one observer - consistency of observation

Cons: 

• need to allow for relative movement of Mars between observations

Result: 92.5 % actual

ii. Cassini, Richer (France)

Method: 'standard' parallax, i.e. simultaneous observations at distant locations

Locations: Paris (49N,2E), Cayenne (5N, 52W), separation 63° of arc (from here).

Baseline: ~ 1 Rₑ 

Cons:

• (very) long-distance travel involved
• need to determine longitude accurately*
• two observers needed - inconsistency of observation?

Result: 92.5 % actual

* In 1668 Cassini himself had produced astronomical tables in order to do just that.

Sources: wikipedia plus links above.

Comments

These estimates of the AU are remarkable achievements for the time - a mere 60 or so years after the invention of the telescope and a similar number of years since Kepler's theories.

However, it is inconceivable that two independent estimates using different methods should be in exact agreement! 

Flamsteed's method is ingenious, but I wonder how easy it would have been to achieve in practice. It surely must have occurred to Cassini also.

Further investigation is needed! 

Further reading

Six stages in the history of the astronomical unit, David. W. Hughes

The Mars Parallax Project, John J. McCarthy Observatory