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?
Why were 8 arcminutes of residual error decisive for Kepler when the same residual would have meant nothing in 1550?
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 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 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?
What made Kepler refuse the standard remedy of adding another small circle?
The answer is: He wanted a physical cause, and an extra circle describes a residual without explaining it
The answer is: He wanted a physical cause, and an extra circle describes a residual without explaining it
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?
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?
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?
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.
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.
The answer is: True
7.[3p] Match each of Kepler's laws to what it states.
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?
Which of these did Kepler's three laws leave unexplained?
Select all that apply
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?
What actually persuaded working astronomers to use Kepler's system?
The answer is: The Rudolphine Tables of 1627, accurate to arcminutes where earlier tables were wrong by degrees
The answer is: The Rudolphine Tables of 1627, accurate to arcminutes where earlier tables were wrong by degrees
The answer is: The Rudolphine Tables of 1627, accurate to arcminutes where earlier tables were wrong by degrees