Lesson test: Tycho and the price of precision

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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?

CorrectNot quite: 14

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?

CorrectNot quite: 1.72

3.[2p]
What did the comet of 1577 establish?

It moved above the moon and through the region assigned to the planetary spheres, so the solid spheres do not exist

Correct

That comets are burning vapours in the upper air

The answer is: It moved above the moon and through the region assigned to the planetary spheres, so the solid spheres do not exist

That the earth moves around the sun

The answer is: It moved above the moon and through the region assigned to the planetary spheres, so the solid spheres do not exist

That the heavens are made of an unchangeable fifth element

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?

CorrectNot quite: 1.0

5.[3p]
Why was Tycho's argument from stellar disc sizes wrong, despite being carefully measured?

The measured disc was an artefact of the eye and of diffraction, not a property of the star

Correct

His instruments were less accurate than he believed

The answer is: The measured disc was an artefact of the eye and of diffraction, not a property of the star

He used the wrong value for the earth's orbital radius

The answer is: The measured disc was an artefact of the eye and of diffraction, not a property of the star

Stars really are that large, but their distances are greater still

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.

True

Correct

False

The answer is: True

7.[3p]
Which of these were part of how Tycho reached arcminute accuracy?

Select all that apply

Instruments nearly two metres in radius, mounted so that wind could not disturb them

Correct

Transversal scales allowing a reader to interpolate within a division

Correct

A systematic table of atmospheric refraction

Correct

Repeated observation of the same object, and stating the size of the error

Correct

Early telescopes bought from Dutch spectacle makers

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.

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.

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

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?

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?

3.[2p] What did the comet of 1577 establish?

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?

5.[3p] Why was Tycho's argument from stellar disc sizes wrong, despite being carefully measured?

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.

7.[3p] Which of these were part of how Tycho reached arcminute accuracy?

8.[2p] Match each system to what it puts at the centre.

9.[2p] Put these events in the order they happened.

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?

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?

3.[2p]
What did the comet of 1577 establish?

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?

5.[3p]
Why was Tycho's argument from stellar disc sizes wrong, despite being carefully measured?

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.

7.[3p]
Which of these were part of how Tycho reached arcminute accuracy?

8.[2p]
Match each system to what it puts at the centre.

9.[2p]
Put these events in the order they happened.