Tycho and the price of precision
1.[3p] The moon's diurnal parallax reaches 57 arcminutes. Tycho found the new star of 1572 shifted by less than 4 arcminutes. How many lunar distances away is it, at least?
The moon's diurnal parallax reaches 57 arcminutes. Tycho found the new star of 1572 shifted by less than 4 arcminutes. How many lunar distances away is it, at least?
2.[3p] An arc is engraved with divisions 0.5 mm apart. What radius, in metres, does the instrument need for each division to be 1 arcminute?
An arc is engraved with divisions 0.5 mm apart. What radius, in metres, does the instrument need for each division to be 1 arcminute?
3.[2p] What did the comet of 1577 establish?
What did the comet of 1577 establish?
The answer is: It moved above the moon and through the region assigned to the planetary spheres, so the solid spheres do not exist
The answer is: It moved above the moon and through the region assigned to the planetary spheres, so the solid spheres do not exist
The answer is: It moved above the moon and through the region assigned to the planetary spheres, so the solid spheres do not exist
4.[3p] A star appears as a disc 1 arcminute across and lies at the Copernican minimum of 3438 AU. What is its diameter, in astronomical units?
A star appears as a disc 1 arcminute across and lies at the Copernican minimum of 3438 AU. What is its diameter, in astronomical units?
5.[3p] Why was Tycho's argument from stellar disc sizes wrong, despite being carefully measured?
Why was Tycho's argument from stellar disc sizes wrong, despite being carefully measured?
The answer is: The measured disc was an artefact of the eye and of diffraction, not a property of the star
The answer is: The measured disc was an artefact of the eye and of diffraction, not a property of the star
The answer is: The measured disc was an artefact of the eye and of diffraction, not a property of the star
6.[3p] The Tychonic system is geometrically equivalent to the Copernican one for every angle observed in the sky, so no measurement of position can tell them apart.
The Tychonic system is geometrically equivalent to the Copernican one for every angle observed in the sky, so no measurement of position can tell them apart.
The answer is: True
7.[3p] Which of these were part of how Tycho reached arcminute accuracy?
Which of these were part of how Tycho reached arcminute accuracy?
Select all that apply
The answer is: Instruments nearly two metres in radius, mounted so that wind could not disturb them, Transversal scales allowing a reader to interpolate within a division, A systematic table of atmospheric refraction, Repeated observation of the same object, and stating the size of the error
8.[2p] Match each system to what it puts at the centre.
Match each system to what it puts at the centre.
Ptolemaic
Copernican
Tychonic
the sun, with the earth one planet among six
the earth, circled by the sun, which carries the five planets round with it
the earth, with the sun and all five planets circling it
Show the answer
Ptolemaic: the earth, with the sun and all five planets circling it Copernican: the sun, with the earth one planet among six Tychonic: the earth, circled by the sun, which carries the five planets round with it
9.[2p] Put these events in the order they happened.
Put these events in the order they happened.
Tycho publishes his own arrangement of the world
Tycho is granted the island of Hven
The new star appears in Cassiopeia
Kepler joins Tycho in Prague
The great comet crosses the planetary region
Show the answer
a, b, c, d, e