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Keplers Laws

Total questions: 105

Worksheet time: 53mins

Name
Class
Date
1.

Which beliefs were still held by most astronomers after Copernicus introduced heliocentrism?

a)

The planets are moved by crystalline spheres in which they are embedded

b)

Mars was the center of the universe

c)

The planets must move in perfectly circular paths

d)

The Earth is flat

2.

Tycho Brahe's most important contribution to astronomy:

a)

discovering that planets orbit the Sun in elliptical paths

b)

producing the best observational data for planets and stars ever seen before

c)

developing the geoheliocentric model

d)

the invention of the telescope

3.

Which event allowed Kepler to access data that led him to develop his laws?

a)

Copernicus died

b)

the telescope was invented

c)

Tycho died

d)

the spectroscope was invented

4.

Kepler discovered the elliptical shape of planetary orbits by studying the data for which planet?

a)

Earth

b)

Mars

c)

Venus

d)

Jupiter

5.

Which statements are true according to Kepler’s 1st Law?

a)

the Sun is not at the center of a planet's orbit, but rather sits at one of two foci of the planet's elliptical orbit

b)

the distance of a planet to the Sun and its distance to the orbit's empty focus will always add up to equal a constant

c)

the major planets have orbits that are elliptical, but still look a lot like circles (more round than flat)

d)

planets move in elliptical orbits, not circular orbits

e)

planets move in perfectly circular orbits

6.

The following are true of ellipses:

a)

they have two foci

b)

they are perfectly circular

c)

they have a center

d)

they are the conic section produced by slicing a cone at an angle

e)

all points are equally distant from the center

7.

What is the distance from one focus to the other through the center?

a)

semimajor axis (a)

b)

eccentricity (e)

c)

linear eccentricity (c)

d)

semiminor axis (b)

8.

What is the distance from one focus to the other through the center?

a)

semimajor axis (a)

b)

eccentricity (e)

c)

linear eccentricity (c)

d)

semiminor axis (b)

9.

What is the distance from one focus to the other through the center?

a)

semimajor axis (a)

b)

eccentricity (e)

c)

linear eccentricity (c)

d)

semiminor axis (b)

10.

What is the distance from one focus to the other through the center?

a)

semimajor axis (a)

b)

eccentricity (e)

c)

linear eccentricity (c)

d)

semiminor axis (b)

11.

Which equation best describes the semiminor axis?

a)

e → e = c/a

b)

b → b=a2−c2b = \sqrt{a^2 - c^2}

c)

c2=a2−b2c^2 = a^2 - b^2 or c=aec = ae

d)

a=b2+c2a = \sqrt{b^2 + c^2} or a=c/ea = c/e

12.

Which equation best describes the semimajor axis?

a)

e → e = c/a

b)

b → b=a2−c2b = \sqrt{a^2 - c^2}

c)

c2=a2−b2c^2 = a^2 - b^2 or c=aec = ae

d)

a=b2+c2a = \sqrt{b^2 + c^2} or a=c/ea = c/e

13.

Which equation best describes linear eccentricity?

a)

e → e = c/a

b)

b → b=a2−c2b = \sqrt{a^2 - c^2}

c)

c2=a2−b2c^2 = a^2 - b^2 or c=aec = ae

d)

a=b2+c2a = \sqrt{b^2 + c^2} or a=c/ea = c/e

14.

Which equation best describes eccentricity?

a)

e → e=c/ae = c/a

b)

b → b=a2−c2b = \sqrt{a^2 - c^2}

c)

c2=a2−b2c^2 = a^2 - b^2 or c=aec = ae

d)

a=b2+c2a = \sqrt{b^2 + c^2} or a=c/ea = c/e

15.

Linear eccentricity of Mars's orbit (semi-major = 1.524 AU, semi-minor = 1.517 AU)

a)

2.322 AU

b)

2.3018 AU

c)

0.0202 AU

d)

0.1423 AU

16.

Eccentricity of Mars's orbit

a)

10.71 AU

b)

10.71

c)

0.093

d)

0.093 AU

17.

Mars's orbit is closer to a flat line or a circle?

a)

equally similar to both

b)

flat line

c)

perfect circle

18.

The major planet with the most circular orbit:

a)

Jupiter

b)

Venus

c)

Uranus

d)

Saturn

19.

The major planet with the most elliptical orbit:

a)

Neptune

b)

Mars

c)

Jupiter

d)

Mercury

e)

Uranus

20.

Which non-major planet has a very elliptical orbit?

a)

Earth’s Moon

b)

Venus

c)

Pluto

21.

What was the Copernican Revolution?

a)

Pluto being reclassified as a dwarf planet instead of a major planet

b)

the change from a geocentric model of the universe to a heliocentric model

c)

the shift from believing the Earth was flat to it being a sphere

22.

During which historical period did the Copernican Revolution occur?

a)

the 20th century

b)

the Middle Ages

c)

the Enlightenment

d)

the European Renaissance

23.

What was Brahe able to accomplish?

a)

Discover a new planet

b)

Discover the moons of Jupiter

c)

Propose that the Sun was at the center of the Solar System

d)

Collect the best astronomical data at that point in history

24.

Copernicus (and pretty much everyone else) thought that the orbits of the planets…

a)

were perfect circles

b)

were ellipses

c)

were double circles — epicycles attached to circular main orbits

25.

Kepler used Brahe’s data to determine that the orbits of the planets…

a)

were perfect circles

b)

were double circles — epicycles attached to circular main orbits

c)

were ellipses

26.

Circles have one _______ and ellipses have two ________.

a)

focus; centers

b)

center; foci

c)

center; conic sections

27.

In the diagram of an elliptical orbit of the Earth (in the video), the sum of r1 and r2 is:

a)

always equal to the orbital velocity of the Earth

b)

always equal to the square of the ellipse’s area

c)

impossible to determine

28.

The closer the two foci of an ellipse are, the more that ellipse…

a)

resembles a sphere

b)

resembles a circle

c)

becomes flatter in appearance

29.

In Kepler’s model of planetary orbits, one focus of each elliptical orbit is occupied by:

a)

a planet other than Earth

b)

the Earth

c)

the Sun

30.

Perihelion is when a planet is:

a)

closest to the Sun

b)

closest to the Moon

c)

farthest from the Moon

31.

The fact that the orbits of the planets are ellipses with the Sun acting as one focus is also known as:

a)

Kepler’s 3rd Law

b)

Newton’s Universal Law of Gravitation

c)

Kepler’s 2nd Law

32.

According to Kepler’s 2nd Law, ________

a)

the orbital speed of a planet will remain constant, but planets closer to the Sun have a higher constant speed

b)

the orbital speed of a planet will remain constant, but planets farther from the Sun have a higher constant speed

c)

the orbital speed of a planet will vary depending on its distance from the Sun

33.

When would Earth experience its fastest orbital velocity?

a)

aphelion

b)

perigee

c)

apogee

34.

Another consequence of Kepler’s 2nd Law is that, as a planet moves across both blue-shaded areas shown in the image,

a)

there will be no way to predict how long it will take for the planet to move across either shaded area

b)

it will take the same amount of time to move across both

c)

it will move across the left shaded area faster than the right shaded area

35.

In Kepler’s 3rd Law, he relates the orbital period of a planet to the length of:

a)

the distance between both foci

b)

the semimajor axis

c)

the semiminor axis

36.

The cube of a planet’s semimajor axis is proportional to the ______ of the planet’s orbital period.

a)

square

b)

cube

c)

cube root

37.

What was one major early use of Kepler’s Laws?

a)

calculate the masses of the planets

b)

discover the first “new” planet: Uranus

c)

determine the size of the Sun

38.

Kepler’s Laws proved that:

a)

the orbits of the planets are complicated and hard to predict

b)

the Earth is a cube!

c)

things in space obey simple mathematical laws

39.

How did Kepler gain access to astronomical observational data that helped him formulate his laws?

a)

Kepler was Tycho’s assistant, so Tycho simply shared his findings.

b)

Tycho died and his family allowed Kepler access.

c)

Kepler had to do all of his own observations.

40.

The best naked-eye observational data of stars & planets was recorded:

a)

by Copernicus in the early 1500s

b)

in the earliest days of human prehistory

c)

in the decades leading up to the telescope’s invention (late 1500s–early 1600s)

41.

When reviewing Tycho’s data, Kepler focused on Tycho’s observations of:

a)

the Sun

b)

Jupiter

c)

Venus

42.

Kepler studied observations of Mars because:

a)

Tycho recommended it based on the observations of Mars being very difficult to match with a circular orbit

b)

Tycho told him that Mars’s observations should mean that it would have the most circular of all planetary orbits

c)

the orbit of Mars had never been accurately observed before

43.

Was Kepler able to match Tycho’s Martian observations with a circular orbit?

a)

no

b)

yes

44.

Which best describe Kepler’s discovery of elliptical orbits for planets? (select all that apply)

a)

Kepler was actively looking for proof for circular orbits

b)

The idea of elliptical orbits clashed with his ideas about God, faith and creation

c)

Kepler was actively looking for proof for elliptical orbits

45.

In Kepler’s elliptical model of planetary orbits, the Sun is located at:

a)

one of two foci of the elliptical orbit

b)

the very center of a circular orbit

46.

Which description correctly matches the fastest orbital velocity?

a)

planet is closest to the Sun

b)

planet is farthest from the Sun

47.

Which description correctly matches the slowest orbital velocity?

a)

planet is farthest from the Sun

b)

planet is closest to the Sun

48.

Which are true of Kepler’s 1st Law of Planetary Motion? (select all that apply)

a)

a planet moves around the Sun in a circle

b)

a planet moves around the Sun in an ellipse

c)

the Sun is located at one of two foci of a planet’s orbit

49.

Kepler was the first person to ________ use ________ to explain how the planets move and predict their motion.

a)

diagrams

b)

correctly

c)

inaccurately

d)

mathematical equations

50.

Problems After Copernicus — What problem remained in the Copernican model even after it replaced geocentrism?

a)

It used telescopes

b)

It excluded the Moon

c)

It still used perfect circles for planetary orbits

d)

It denied gravity

51.

Problems After Copernicus — What ancient idea did Copernicus and Galileo still believe in?

a)

Elliptical orbits

b)

Crystalline spheres and circular motion

c)

Flat Earth

d)

Parallax

52.

Problems After Copernicus — Why was it difficult to study Copernicus’s heliocentric model?

a)

Lack of printing

b)

The Christian Church considered it heretical

c)

It was written in Latin

d)

It had no support

53.

Tycho Brahe — Where was Tycho Brahe from?

a)

Germany

b)

Denmark

c)

Austria

d)

Sweden

54.

Tycho Brahe — What was Tycho Brahe’s greatest contribution to astronomy?

a)

Telescope invention

b)

Extremely accurate data on stars and planets

c)

Discovery of Neptune

d)

Proof of gravity

55.

Tycho Brahe — What made Brahe’s research possible?

a)

He built telescopes

b)

He was wealthy and had royal support

c)

He used satellites

d)

He worked in a university

56.

Tycho Brahe — Where did Brahe go after leaving Denmark?

a)

Berlin

b)

Prague

c)

Rome

d)

Vienna

57.

Tycho Brahe — What position did Brahe hold in Prague?

a)

Royal Astronomer of Austria

b)

Imperial Mathematician for the Holy Roman Emperor

c)

Pope’s Astronomer

d)

Dean of Prague Observatory

58.

Johannes Kepler — What was Kepler’s profession?

a)

Priest

b)

Mathematician and astronomer

c)

Navigator

d)

Explorer

59.

Johannes Kepler — How did Kepler become interested in heliocentrism?

a)

He read Aristotle

b)

Through his college professor Michael Maestlin

c)

From Galileo’s books

d)

By inventing a telescope

60.

Johannes Kepler — What religion did Kepler follow?

a)

Catholic

b)

Lutheran (Protestant)

c)

Muslim

d)

Orthodox

61.

Johannes Kepler — Why did Kepler leave Graz in 1600?

a)

He was exiled for science

b)

Protestants were forced to convert or flee

c)

He wanted to study with Galileo

d)

He was invited by Copernicus

62.

Johannes Kepler — How did Kepler gain access to Brahe’s data?

a)

He bought it

b)

He became Brahe’s assistant

c)

He hacked his notes

d)

He found it in a library

63.

Johannes Kepler — What role did Kepler assume after Brahe’s death?

a)

Royal cartographer

b)

Imperial Mathematician

c)

Astronomer General

d)

Professor of Astrology

64.

Kepler’s First Law — What planet’s data did Kepler focus on to discover his first law?

a)

Venus

b)

Mars

c)

Jupiter

d)

Mercury

65.

Kepler’s First Law — What did Kepler realize about Mars’s orbit?

a)

It was circular

b)

It was elliptical

c)

It was flat

d)

It was unpredictable

66.

Kepler’s First Law — What shape defines Kepler’s First Law of Planetary Motion?

a)

Circle

b)

Ellipse

c)

Spiral

d)

Triangle

67.

Kepler’s First Law — In an ellipse, where is the Sun located according to Kepler’s First Law?

a)

At the center

b)

At one of the two foci

c)

Outside the orbit

d)

At both foci

68.

Kepler’s First Law — What does the sum of distances from a planet to each focus of the ellipse equal?

a)

The eccentricity

b)

A constant

c)

The orbit time

d)

The planet’s speed

69.

Circles vs. Ellipses — What is true about all points on a circle?

a)

They are random

b)

They are the same distance from the center

c)

They move at different speeds

d)

They point to the Moon

70.

Circles vs. Ellipses — How is an ellipse different from a circle?

a)

It has one focus

b)

It has two foci

c)

It is a spiral

d)

It is square-shaped

71.

Circles vs. Ellipses — What shape results from slicing a cone at an angle not parallel to the base?

a)

Circle

b)

Ellipse

c)

Square

d)

Sphere

72.

Circles vs. Ellipses — What other conic sections exist besides ellipses and circles?

a)

Squares and triangles

b)

Parabolas and hyperbolas

c)

Cylinders and cubes

d)

Rectangles and ovals

73.

Ellipse Measurements — What is the major axis of an ellipse?

a)

The short diameter

b)

The long diameter through both foci

c)

The distance to the Sun

d)

The orbit speed

74.

Ellipse Measurements — What does the semimajor axis represent?

a)

Half of the major axis

b)

The shortest distance to the Sun

c)

A random line

d)

The orbit time

75.

Ellipse Measurements — What is the linear eccentricity (c)?

a)

The orbit speed

b)

Distance from the center to a focus

c)

The radius of a circle

d)

The age of the planet

76.

Ellipse Measurements — What does 1 AU equal?

a)

93 million meters

b)

~150,000,000 km or ~93,000,000 miles

c)

The Sun’s radius

d)

One light-year

77.

Eccentricity (e) — What does eccentricity (e) describe?

a)

The color of a planet

b)

How stretched or flat an ellipse is

c)

Planet temperature

d)

Number of moons

78.

Eccentricity (e) — What is the eccentricity of a perfect circle?

a)

1

b)

0

c)

0.5

d)

2

79.

Eccentricity (e) — Which major planet has the most eccentric orbit?

a)

Earth

b)

Venus

c)

Mercury

d)

Mars

80.

Eccentricity (e) — Which major planet has the least eccentric orbit?

a)

Mercury

b)

Venus

c)

Mars

d)

Jupiter

81.

Eccentricity (e) — What is the formula for finding eccentricity?

a)

e = a/c

b)

e = c/a

c)

e = a × b

d)

e = b − a

82.

If Mercury’s semimajor axis a=0.387 AUa = 0.387 \text{ AU} and semiminor axis b=0.3788 AUb = 0.3788 \text{ AU} , what is c2c^2 for its elliptical orbit using c2=a2−b2c^2 = a^2 - b^2 ?

a)

0.1435 AU^2

b)

0.0063 AU^2

c)

0.205 AU^2

d)

0.387 AU^2

83.

Using a = 0.387 AU and b = 0.3788 AU for Mercury’s orbit, what is the linear eccentricity c (in AU) computed from c=a2−b2c = \sqrt{a^2 - b^2} ?

a)

0.205 AU

b)

0.0794 AU

c)

0.387 AU

d)

0.3788 AU

84.

Given Mercury’s semimajor axis a = 0.387 AU and linear eccentricity c = 0.0794 AU, what is the orbital eccentricity e using e = c / a?

a)

0.0794

b)

0.205

c)

0.387

d)

0.0063

85.

Find Mercury’s orbital eccentricity if its semimajor axis is 0.387 AU0.387 \, \text{AU} and its semiminor axis is 0.3788 AU0.3788 \, \text{AU} . Use c2=a2−b2c^2 = a^2 - b^2 to determine cc , then e=cae = \frac{c}{a} .

a)

0.0794

b)

0.205

c)

0.387

d)

0.0063

86.

Section: Kepler’s 2nd Law – Equal Areas in Equal Time — What does Kepler’s 2nd Law state?

a)

Planets orbit in perfect circles

b)

A planet sweeps equal areas in equal time as it orbits the Sun

c)

Gravity keeps planets in motion

d)

All planets move at constant speed

87.

Section: Kepler’s 2nd Law – Equal Areas in Equal Time — What happens to a planet’s speed when it is closest to the Sun?

a)

It slows down

b)

It speeds up

c)

It stops

d)

It moves in a straight line

88.

Section: Kepler’s 2nd Law – Equal Areas in Equal Time — What is the name of the point where a planet is closest to the Sun?

a)

Apogee

b)

Perihelion

c)

Focus

d)

Zenith

89.

Section: Kepler’s 2nd Law – Equal Areas in Equal Time — What is the name of the point where a planet is farthest from the Sun?

a)

Perigee

b)

Zenith

c)

Aphelion

d)

Solstice

90.

Section: Kepler’s 2nd Law – Equal Areas in Equal Time — Why do planets move faster near the Sun?

a)

Solar wind pushes them

b)

Gravitational force is stronger

c)

The Sun heats them up

d)

Light pressure accelerates them

91.

Section: Kepler’s 2nd Law – Equal Areas in Equal Time — What traditional belief did Kepler’s 2nd Law challenge?

a)

Circular orbits

b)

Invisibility of stars

c)

Perfect and unchanging heavenly motion

d)

Flat Earth theory

92.

Section: Kepler’s 2nd Law – Equal Areas in Equal Time — Did Kepler know why the speed changed during orbit?

a)

Yes, he cited gravity

b)

No, he only observed the pattern

c)

Yes, he used calculus

d)

No, but Galileo explained it

93.

Section: Kepler’s 2nd Law – Equal Areas in Equal Time — In what book did Kepler publish both his 1st and 2nd laws?

a)

The Harmony of the World

b)

The New Astronomy

c)

The Starry Messenger

d)

The Almagest

94.

Section: Kepler’s 2nd Law – Equal Areas in Equal Time — When were Kepler’s 1st and 2nd laws published?

a)

1595

b)

1619

c)

1609

d)

1630

95.

Section: Kepler’s 3rd Law – The Harmonic Law — What does Kepler’s 3rd Law compare?

a)

Planet size and gravity

b)

A planet’s orbital period squared to its semimajor axis cubed

c)

Orbit speed and temperature

d)

Planet mass and distance

96.

Section: Kepler’s 3rd Law – The Harmonic Law — What is the formula for Kepler’s 3rd Law?

a)

P2=a3P^2 = a^3

b)

a2=p3a^2 = p^3

c)

P = a

d)

a = √p

97.

Section: Kepler’s 3rd Law – The Harmonic Law — What does P stand for in the formula P2=a3P^2 = a^3 ?

a)

Planetary mass

b)

Perihelion distance

c)

Orbital period (in Earth years)

d)

Planetary temperature

98.

Section: Kepler’s 3rd Law – The Harmonic Law — What does a stand for in the formula P2=a3P^2 = a^3 ?

a)

Average orbital speed

b)

Semimajor axis (distance from Sun in AUs)

c)

Aphelion distance

d)

Axis of rotation

99.

Section: Kepler’s 3rd Law – The Harmonic Law — What is the simplified meaning of Kepler’s 3rd Law?

a)

All orbits are slow

b)

Planets closer to the Sun orbit faster

c)

Bigger planets take longer

d)

Planets orbit in a spiral

100.

Section: Kepler’s 3rd Law – The Harmonic Law — What pattern did Kepler notice from data on all planets?

a)

Every planet orbited in 1 year

b)

P2/a3≈1P^2 / a^3 \approx 1 for all planets

c)

All orbits were circles

d)

Planet distances were equal

101.

Section: Kepler’s 3rd Law – The Harmonic Law — What did Kepler call this consistent ratio between planets?

a)

Gravity

b)

Harmony (resonance)

c)

Revolution

d)

Ellipse constant

102.

Section: Kepler’s 3rd Law – The Harmonic Law — In which book did Kepler publish his 3rd Law?

a)

The New Astronomy

b)

The Harmony of the World

c)

Principia Mathematica

d)

Dialogues on Motion

103.

Section: Kepler’s 3rd Law – The Harmonic Law — In what year was Kepler’s 3rd Law published?

a)

1609

b)

1619

c)

1630

d)

1596

104.

Section: From Kepler to Newton — What did Kepler not fully understand about his own laws?

a)

The shape of orbits

b)

Why planets sped up near the Sun or why closer planets orbited faster

c)

The structure of the universe

d)

How to use telescopes

105.

Section: From Kepler to Newton — Who eventually explained the causes behind Kepler’s laws?

a)

Galileo Galilei

b)

Isaac Newton

c)

Tycho Brahe

d)

Albert Einstein

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