Lesson test: Eight minutes of arc

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Eight minutes of arc

1.[3p]
Why were 8 arcminutes of residual error decisive for Kepler when the same residual would have meant nothing in 1550?

Tycho's observations were good to 1 or 2 arcminutes, so the residual was several times the uncertainty rather than inside it

Correct

Astronomers had agreed on 5 arcminutes as the limit of an acceptable theory

The answer is: Tycho's observations were good to 1 or 2 arcminutes, so the residual was several times the uncertainty rather than inside it

The residual was visible to the naked eye as a gap between two stars

The answer is: Tycho's observations were good to 1 or 2 arcminutes, so the residual was several times the uncertainty rather than inside it

Earlier astronomers had never observed Mars near opposition

The answer is: Tycho's observations were good to 1 or 2 arcminutes, so the residual was several times the uncertainty rather than inside it

2.[3p]
What made Kepler refuse the standard remedy of adding another small circle?

He wanted a physical cause, and an extra circle describes a residual without explaining it

Correct

Extra circles had been forbidden by the Church

The answer is: He wanted a physical cause, and an extra circle describes a residual without explaining it

The extra circle would have made the fit worse

The answer is: He wanted a physical cause, and an extra circle describes a residual without explaining it

He could not calculate with more than one circle at a time

The answer is: He wanted a physical cause, and an extra circle describes a residual without explaining it

3.[3p]
Mars has an eccentricity of 0.0934. What is the ratio of its semi-minor to its semi-major axis?

CorrectNot quite: 0.9956

4.[3p]
With the same eccentricity, how many times faster does Mars move at perihelion than at aphelion?

CorrectNot quite: 1.21

5.[3p]
Saturn's sidereal period is 29.457 years. What does the third law give for its semi-major axis, in astronomical units?

CorrectNot quite: 9.54

6.[2p]
Kepler found the area law before he found the ellipse, and originally regarded it as an approximate device standing in for a simpler rule about speed and distance.

True

Correct

False

The answer is: True

7.[3p]
Match each of Kepler's laws to what it states.

First law
Second law
Third law

the line from the sun to the planet sweeps equal areas in equal times
the square of the period is proportional to the cube of the semi-major axis
each planet moves on an ellipse with the sun at one focus

Show the answer

First law: each planet moves on an ellipse with the sun at one focus Second law: the line from the sun to the planet sweeps equal areas in equal times Third law: the square of the period is proportional to the cube of the semi-major axis

8.[3p]
Which of these did Kepler's three laws leave unexplained?

Select all that apply

Why an orbit should be an ellipse rather than some other closed curve

Correct

Why equal areas rather than equal arcs are swept in equal times

Correct

Why the exponent relating period to distance is three halves

Correct

Where a planet will be on a given date

The answer is: Why an orbit should be an ellipse rather than some other closed curve, Why equal areas rather than equal arcs are swept in equal times, Why the exponent relating period to distance is three halves

9.[2p]
What actually persuaded working astronomers to use Kepler's system?

The Rudolphine Tables of 1627, accurate to arcminutes where earlier tables were wrong by degrees

Correct

His argument that the sun sweeps the planets round magnetically

The answer is: The Rudolphine Tables of 1627, accurate to arcminutes where earlier tables were wrong by degrees

The polyhedra of the Mysterium Cosmographicum

The answer is: The Rudolphine Tables of 1627, accurate to arcminutes where earlier tables were wrong by degrees

Galileo's public endorsement of elliptical orbits

The answer is: The Rudolphine Tables of 1627, accurate to arcminutes where earlier tables were wrong by degrees

1.[3p] Why were 8 arcminutes of residual error decisive for Kepler when the same residual would have meant nothing in 1550?

2.[3p] What made Kepler refuse the standard remedy of adding another small circle?

3.[3p] Mars has an eccentricity of 0.0934. What is the ratio of its semi-minor to its semi-major axis?

4.[3p] With the same eccentricity, how many times faster does Mars move at perihelion than at aphelion?

5.[3p] Saturn's sidereal period is 29.457 years. What does the third law give for its semi-major axis, in astronomical units?

6.[2p] Kepler found the area law before he found the ellipse, and originally regarded it as an approximate device standing in for a simpler rule about speed and distance.

7.[3p] Match each of Kepler's laws to what it states.

8.[3p] Which of these did Kepler's three laws leave unexplained?

9.[2p] What actually persuaded working astronomers to use Kepler's system?

1.[3p]
Why were 8 arcminutes of residual error decisive for Kepler when the same residual would have meant nothing in 1550?

2.[3p]
What made Kepler refuse the standard remedy of adding another small circle?

3.[3p]
Mars has an eccentricity of 0.0934. What is the ratio of its semi-minor to its semi-major axis?

4.[3p]
With the same eccentricity, how many times faster does Mars move at perihelion than at aphelion?

5.[3p]
Saturn's sidereal period is 29.457 years. What does the third law give for its semi-major axis, in astronomical units?

6.[2p]
Kepler found the area law before he found the ellipse, and originally regarded it as an approximate device standing in for a simpler rule about speed and distance.

7.[3p]
Match each of Kepler's laws to what it states.

8.[3p]
Which of these did Kepler's three laws leave unexplained?

9.[2p]
What actually persuaded working astronomers to use Kepler's system?