♞ Kepler's Three Fundamental Laws of Planetary Motion

Tycho Brahe’s accurate observations of planetary positions provided the data used by Johannes Kepler to derive his three fundamental laws of planetary motion.
Kepler’s laws describe the behavior of planets in their orbits as follows:

(1) planetary orbits are ellipses with the Sun at one focus;

(2) in equal intervals, a planet’s orbit sweeps out equal areas; and

(3) the relationship between the orbital period (P) and the semimajor axis (a) of an orbit is given by 

P² = a³ 

(when a is in units of AU and P is in units of Earth years).

☀️ The Stars: A Celestial Census - Key Terms

 

binary stars

two stars that revolve about each other

brown dwarf

an object intermediate in size between a planet and a star; the approximate mass range is from about 1/100 of the mass of the Sun up to the lower mass limit for self-sustaining nuclear reactions, which is about 1/12 the mass of the Sun

eclipsing binary

a binary star in which the plane of revolution of the two stars is nearly edge-on to our line of sight, so that the light of one star is periodically diminished by the other passing in front of it

H–R diagram

(Hertzsprung–Russell diagram) a plot of luminosity against surface temperature (or spectral type) for a group of stars

main sequence

a sequence of stars on the Hertzsprung–Russell diagram, containing the majority of stars, that runs diagonally from the upper left to the lower right

mass-luminosity relation

the observed relation between the masses and luminosities of many (90% of all) stars

selection effect

the selection of sample data in a nonrandom way, causing the sample data to be unrepresentative of the entire data set

spectroscopic binary

a binary star in which the components are not resolved but whose binary nature is indicated by periodic variations in radial velocity, indicating orbital motion

visual binary

a binary star in which the two components are telescopically resolved

white dwarf

a low-mass star that has exhausted most or all of its nuclear fuel and has collapsed to a very small size; such a star is near its final state of life

👕 Life in the Universe. Key Terms

 

organic compounds that are the molecular building blocks of proteins	amino acids
the multidisciplinary study of life in the universe: its origin, evolution, distribution, and fate; similar terms are exobiology and bioastronomy	astrobiology
evidence of the presence of life, especially a global indication of life on a planet that could be detected remotely (such as an unusual atmospheric composition)	biomarker
a molecule that stores information about how to replicate a cell and its chemical and structural components	DNA (deoxyribonucleic acid)
a formula for estimating the number of intelligent, technological civilizations in our Galaxy, first suggested by Frank Drake	Drake equation
an organism (usually a microbe) that tolerates or even thrives under conditions that most of the life around us would consider hostile, such as very high or low temperature or acidity	extremophile
the basic functional unit that carries the genetic (hereditary) material contained in a cell	gene
an environment capable of hosting life	habitable environment
the region around a star in which liquid water could exist on the surface of terrestrial-sized planets, hence the most probable place to look for life in a star’s planetary system	habitable zone
a compound containing carbon, especially a complex carbon compound; not necessarily produced by life	organic compound
a combination of carbon and other atoms—primarily hydrogen, oxygen, nitrogen, phosphorus, and sulfur—some of which serve as the basis for our biochemistry	organic molecule
a complex sequence of chemical reactions through which some living things can use sunlight to manufacture products that store energy (such as carbohydrates), releasing oxygen as one by-product	photosynthesis
a key biological molecule that provides the structure and function of the body’s tissues and organs, and essentially carries out the chemical work of the cell	protein
a molecule that aids in the flow of genetic information from DNA to proteins	RNA (ribonucleic acid)
the search for extraterrestrial intelligence; usually applied to searches for radio signals from other civilizations	SETI
solid, layered rock formations that are thought to be the fossils of oxygen-producing photosynthetic bacteria in rocks that are 3.5 billion years old	stromatolites
an organism that can tolerate high temperatures	thermophile

Calculate Given Mathematical Expression

Calculate given mathematical expression and input result in scientific notation using 3 significant figures:

 sin 40° + cos 129° / (sin -92° - tan 210° ) 

 Method of the calculation 

 In your internet browser make the copy of the text of the formula. 

Then paste the text to the google search of your internet browser. 

Replace the degree angle symbols with the word "degrees": 

 sin 40degrees + cos 129degrees / (sin -92degrees - tan 210degrees ) 

Click "enter". 

 The Google will give you following result: 

 1.04191489353 

Transform this number from normal notation to scientific notation for computers with 3 significant figures: 

 1.04E0

Formation of the Solar System 🔭

23) Based on our current theory of Earth's formation, the water we drink comes from 

A) ice that condensed in the solar nebula in the region where Earth formed. 

B) chemical reactions that occurred in Earth's crust after Earth formed. 

C) chemical reactions that occurred in Earth's core after Earth formed. 

D) material left behind during the giant impact that formed the Moon. 

E) comets that impacted Earth. 

Answer:  E

24) The heavy bombardment phase of the solar system lasted 

A) several million years. 

B) several tens of millions of years. 

C) several hundreds of millions of years. 

D) about a billion years. 

E) to the present time. 

Answer:  C

25) Which of the following is not evidence supporting the giant impact theory for the formation of the Moon? 

A) Computer simulations show that the Moon could really have formed in this way. 

B) The composition of the Moon is similar to that of Earth's outer layers. 

C) The Moon is depleted of easily vaporized materials, as we would expect from the heat of an impact. 

D) Scientists have found several meteorites that appear to be the remains of the object that caused the giant impact. 

E) We see signatures of giant impacts on other planets.

Answer:  D

26) Which of the following puzzles in the solar system cannot be explained by a giant impact event? 

A) the formation of the Moon 

B) the large metallic core of Mercury 

C) the backward rotation of Venus 

D) the extreme axis tilt of Uranus 

E) the orbit of Triton in the opposite direction to Neptune's rotation 

Answer:  E

27) The nebular theory of the formation of the solar system successfully predicts all but one of the following. Which one does the theory not predict? 

A) Planets orbit around the Sun in nearly circular orbits in a flattened disk. 

B) the compositional differences between the terrestrial and jovian planets 

C) the equal number of terrestrial and jovian planets 

D) asteroids, Kuiper-belt comets, and the Oort cloud 

E) the craters on the Moon 

Answer:  C

🕮 These are the asteroids to worry about!

Chapter 3 Key Terms

 

angular momentum

the measure of the motion of a rotating object in terms of its speed and how widely the object’s mass is distributed around its axis

aphelion

the point in its orbit where a planet (or other orbiting object) is farthest from the Sun

apogee

the point in its orbit where an Earth satellite is farthest from Earth

asteroid belt

the region of the solar system between the orbits of Mars and Jupiter in which most asteroids are located; the main belt, where the orbits are generally the most stable, extends from 2.2 to 3.3 AU from the Sun

astronomical unit (AU)

the unit of length defined as the average distance between Earth and the Sun; this distance is about 1.5 × 108 kilometers

density

the ratio of the mass of an object to its volume

eccentricity

in an ellipse, the ratio of the distance between the foci to the major axis

ellipse

a closed curve for which the sum of the distances from any point on the ellipse to two points inside (called the foci) is always the same

escape speed

the speed a body must achieve to break away from the gravity of another body

focus

(plural: foci) one of two fixed points inside an ellipse from which the sum of the distances to any point on the ellipse is constant

gravity

the mutual attraction of material bodies or particles

Kepler’s first law

each planet moves around the Sun in an orbit that is an ellipse, with the Sun at one focus of the ellipse

Kepler’s second law

the straight line joining a planet and the Sun sweeps out equal areas in space in equal intervals of time

Kepler’s third law

the square of a planet’s orbital period is directly proportional to the cube of the semimajor axis of its orbit

major axis

the maximum diameter of an ellipse

mass

a measure of the amount of material within an object

momentum

the measure of the amount of motion of a body; the momentum of a body is the product of its mass and velocity; in the absence of an unbalanced force, momentum is conserved

Newton’s first law

every object will continue to be in a state of rest or move at a constant speed in a straight line unless it is compelled to change by an outside force

Newton’s second law

the change of motion of a body is proportional to and in the direction of the force acting on it

Newton’s third law

for every action there is an equal and opposite reaction (or: the mutual actions of two bodies upon each other are always equal and act in opposite directions)

orbit

the path of an object that is in revolution about another object or point

orbital period (P)

the time it takes an object to travel once around the Sun

orbital speed

the speed at which an object (usually a planet) orbits around the mass of another object; in the case of a planet, the speed at which each planet moves along its ellipse

perigee

the point in its orbit where an Earth satellite is closest to Earth

perihelion

the point in its orbit where a planet (or other orbiting object) is nearest to the Sun

perturbation

a small disturbing effect on the motion or orbit of a body produced by a third body

satellite

an object that revolves around a planet

semimajor axis

half of the major axis of a conic section, such as an ellipse

velocity

the speed and direction a body is moving—for example, 44 kilometers per second toward the north galactic pole