Astr ch 1-16

2. Define a light-year.

A light-year is the distance that light travels (in vacuum) over 1 Earth year. It is an immense distance and is measured as 9.46 trillion kilometers (or 5.88 trillion miles). The nearest star to the Sun is Proxima Centauri, which is approximately 4.25 light-years away.

9. Describe the elements of a wave and their units of measure. What makes a light wave different than a water wave?

A wave has a wavelength (measured in meters) that describes the distance between wave crests (or troughs), frequency (measured in 1/s or Hz) that describes how many waves pass a point for a unit of time, and a wave speed (measured in m/s) that describes how fast the wave travels through a medium. A water wave is a disturbance within the water itself and thus needs water to propagate, where a light wave can travel in vacuum (without a medium) because it propagates in 2 dimensions using electric and magnetic fields.

11. An astronomer discovers a new star and wants to measure its temperature. How can the astronomer do this without using a thermometer?

An astronomer can measure a star's temperature using the star's apparent brightness and its color. The star's brightness is directly related to its temperature through the Stefan-Boltzmann Law, where the color is related to the temperature through Wien's law.

4. Describe how astronomers are like police detectives.

Astronomers are like police detectives because of the finite speed of light in vacuum, where events in the cosmos reach us many years after they have actually occurred. Police detectives are unable to arrest or charge someone with a crime until after it has been committed and this is only accomplished after careful observation of the crime scene.

3. A star is 40 light-years away.

Describe how we interpret the light coming from the star. What would happen if the star was instantaneously removed from the universe? The speed of light is a constant (in vacuum) and astronomers interpret the light coming from a star as how the star appeared in the past. The star is in the past due to the travel time required by light to cross the distance between the star and us. If a star that is 40 ly away was instantaneously removed from the universe, we wouldn't know it was gone until 40 years later.

13. Explain what dispersion is and how astronomers use this phenomenon to study a star's light.

Dispersion is the separation of white light into its colors. This occurs using a prism because the light bends differently depending on the wavelength as it passes through the glass. Astronomer's use dispersion to obtain a star's spectra, which informs the astronomer about the chemical composition of the star.

15. Explain how electrons use light energy to move among energy levels within an atom.

Electrons "orbit" the nucleus of an atom and require energy to change between levels. Light energy or photons contain discrete (or specific) packets of energy that correspond to the exact energy that electrons need to move. An electron can absorb a photon's energy to move up a level, but has to give it back (emit) to go down a level.

15. How did Eratosthenes measure the size of the Earth?

Eratosthenes used the geometry of the sun's rays to measure the circumference of the Earth. His calculation required a measurement of the shadow cast in Alexandria on the same day when no shadow was visible in Syene. He chose Syene because the distance between Alexandria and Syene was already known. His calculations roughly match the modern values.

5. According to Kepler's second law, where in a planet's orbit would it be moving fastest? Where would it be moving slowest?

From Kepler's second law, we know that a planet sweeps out an equal area in an equal amount of time. To do this, the planet must be moving fastest where it is closest to the Sun (perihelion) and slowest at its farthest point from the Sun (aphelion)

10. Explain how the Sun moves each day relative to the fixed stars. How many degrees does it move and how long does it take to return to its original location?

From our perspective on Earth the Sun appears to move through a background of 12 constellations. In reality, the Earth is moving relative to the Sun. The path of the Sun on the sky is called the ecliptic and the Sun moves 1 degree per day along that path. It takes 1 Earth year for the Sun to complete its journey along the ecliptic.

17. Compare and contrast the scientific contributions of Copernicus and Galileo.

Galileo and Copernicus both believed in the heliocentric theory for the Solar System. Copernicus developed his evidence solely on naked eye observations and used them to explain retrograde motion, where the explanation was simpler than using epicycles. Galileo went beyond Copernicus because he developed the telescope and showed that Jupiter hosted its own moons. This discovery solidified the heliocentric theory as an accurate description of nature.

1. Describe how scientists know that a hypothesis in astronomy is a reasonable description of nature.

In general, scientists use experiments to test whether a hypothesis is a reasonable description of nature, where astronomers use observations instead because most objects are not within reach to test through normal experimentation. The hypothesis must be testable and often leads to a prediction that can be observed.

9. Explain, according to both geocentric and heliocentric cosmologies, why we see retrograde motion of the planets.

In the geocentric theory retrograde motion was explained using epicycles, which are composed of a small circle on a larger circle. The heliocentric theory is self-consistent where the retrograde motion is only what we see due to a changing relative perspective.

2. What was Newton's major contribution(s) to science? Which principles did he borrow from his predecessors?

Isaac Newton developed the fields of mechanics, optics, thermodynamics, and some chemistry. He also invented a whole branch of mathematics called Calculus, although another mathematician, Leibniz, was working on it at the same time. In mechanics, Newton introduced his three laws of motion and universal gravitation. His first law of motion (Law of Inertia) is a restatement of Galileo's work.

1. Which scientist developed 3 Laws for Planetary motion? What are the Laws?

Johannes Kepler developed three laws for planetary motion using the observations from Tycho Brahe. The three laws of planetary motion are: 1) a planetary orbit is an ellipse with the Sun at one of the foci, 2) the planet sweeps out an equal area within equal amounts of time, and 3) the planetary period squared is proportional to the planetary semimajor axis cubed.

6. What was the great insight Newton had regarding Earth's gravity that allowed him to develop the universal law of gravitation?

Newton had two insights concerning gravity, where the first one showed that gravity extended beyond objects on Earth. The second insight was a repudiation of Aristotle's ideas of natural motion (i.e., the natural state of objects is to be on the ground at rest). Galileo had doubts about Aristotle as well, but Newton showed that an apple falls because the Earth tugs on it and not because of any "natural state".

10. In the future, several students living on board a space station decide to have a race among different types of electromagnetic radiation. Which type of EM radiation travels through space the fastest?

No one type of EM radiation travels faster than another in space. In a vacuum, all EM radiation travels at the same speed which is m/s.

11. Is the ecliptic the same thing as the celestial equator? Explain.

No., the ecliptic is the Sun's path in the sky and is tilted from the celestial equation by ~23.5 degrees (equivalent to Earth's tilt). The celestial equator is a project of Earth's equator onto the Celestial Sphere.

14. Which star is closest to the North Celestial Pole? Has this always been the case?

Polaris is the closest star to the North Celestial Pole. Due to the precession of Earth's tilt, this has not always been the case. A few thousand years ago, the North star was Thuban, where this is shown by how the Egyptians built their pyramids.

5. Describe how the laws of nature are determined by scientists.

Scientists determine (or understand) the laws of nature through the scientific method. In this method: an observation is made which prompts a hypothesis to explain it; the hypothesis is tested through experimentation or additional observations to see if it holds true; afterwards the hypothesis is re-evaluated and discarded if it cannot withstand the scrutiny of the test; and a hypothesis is provisionally true if it holds up to the test, but more tests are performed by others for additional verification.

12. Explain how emission lines and absorption lines are formed. In what sorts of cosmic objects would you expect to see each?

Spectral lines are formed when light passes from a source, through an intermediate material, and is detected by an observer. If the material is along the line-of-sight of the observer, absorption lines are formed, which are gaps within the continuous spectrum of the source (assumed as a blackbody). If the source, material, and observer are not aligned, then emission lines are formed from the absorption and random re-emission of photons. We expect to see absorption lines within stellar and planetary atmospheres and emission lines from nebulae.

7. What is the average distance from the Sun (in astronomical units) of a planet with an orbital period of 45.66 years?

The average distance from the Sun (or semimajor axis) can be calculated from the orbital period using Kepler's 3rd Law, as long as the period is in units of years. To use Kepler's 3rd Law, one must first square the orbital period and cube root the result. This is the same as raising the orbital period to the 2/3 power. This planet would have an average distance of 12.77 AU and be placed between Saturn and Uranus in the Solar System.

8. Identify the closest natural (not manmade) object to the Earth.

The closest natural object is the Moon. The Moon's origin is still being debated, but the leading theory is that a Mars-like object struck the Earth and the leftover debris from the collision coalesced to form the Moon.

12. What two factors made it difficult, at first, for astronomers to choose between the Copernican heliocentric model and the Ptolemaic geocentric model?

The first impediment to the heliocentric model was the expectation for stars to shift in position (or parallax), where this wasn't measurable for the ancients. The ancients and critics of Copernicus also expected that objects would be sliding along Earth's surface due to Earth's rotation. The rotation of the Earth was a necessary assumption to explain how the constellations changed from day-to-day.

7. Place the Moon, Mars, Sun, center of the Milky Way, and Andromeda galaxy in order by distance to us.

The order by distance (relative to the Earth) is: Moon, Mars/Sun, Sun/Mars, center of the Milky Way, and Andromeda's galaxy. Depending on the relative position of Mars and Earth, Mars can be closer to the Earth than the Sun and at other times it can be farther away.

6. 6. Place the Earth, Solar System, Jupiter, Milky Way Galaxy, and the Universe in order by size.

The order by size (from smallest to largest) is: Earth, Jupiter, Solar System, Milky Way Galaxy, and the Universe. The size of the Earth or Jupiter can be measured in kilometers, where the Solar System is more easily measured in Astronomical Units (AU). The Milky Way Galaxy and the Universe are measured in light-years due to their immensity.

8. A scientist worked out the connection between electricity and magnetism. Who did this and did the scientist think of everything on his own?

The scientist who joined electricity and magnetism was James Clerk Maxwell, which are now called Maxwell's equations. Before Maxwell, many people identified properties of materials by its ability to conduct electricity or magnetically attract objects separately. Maxwell did not think of everything on his own, where he was standing on the shoulders of Giants, much like Newton.

16. What problem has precession caused for many of the schools of astrology?

The slow precession of Earth's tilt causes a drift in the Vernal Equinox, where some constellations move onto, and others leave the ecliptic for the zodiac. This is a problem for Astrology, which doesn't update its predictions relative to the precession and it should have 13 signs today.

3. A star is 40 light-years away. Describe how we interpret the light coming from the star. What would happen if the star was instantaneously removed from the universe?

The speed of light is a constant (in vacuum) and astronomers interpret the light coming from a star as how the star appeared in the past. The star is in the past due to the travel time required by light to cross the distance between the star and us. If a star that is 40 ly away was instantaneously removed from the universe, we wouldn't know it was gone until 40 years later.

3. A star forms from a gas cloud, is initially spinning slowly, and is quite large. Over time, the star collapses (or contracts). What happens to its spin rate?

The spin rate of the star increases as its radius decreases due to the conservation of angular momentum. Angular momentum is a property of spinning objects and conservation means that the initial quantity is equal to the final quantity. On Earth, figure skaters use angular momentum conservation to increase their spin (e.g., triple lux) and decrease their spin on the landing (kicking out their leg).

14. Explain why astronomers use the term "blueshifted" for objects moving toward us and "redshifted" for objects moving away from us.

The terms "blueshifted" and "redshifted" refer to how the spectral lines from an object change due to the motion of the object. The spectral line moves to a lower wavelength (towards the blue) when the object is moving toward us, but this doesn't mean that the color changes dramatically to blue.

4. An astronomy textbook, when printed out, weighs four pounds on the surface of the Earth. After finishing your course, you are so tired of the book, you arrange for NASA to shoot it into space. When it is twice as far from the center of the Earth than when you were reading it, what would it weigh?

The weight of an object is calculated as the product of the object's mass with the acceleration due to gravity, g. On Earth's surface, g is equal to 9.8 m/s2. But g decreases as an object moves away from the surface. When an object is twice as far (or two Earth radii away), the value of g decreases by ¼. In this problem the mass of the book stays the same and so the book would weigh one pound.

13. Describe how the zenith and horizon affect the celestial sphere for an observer.

The zenith is simply a point on the Celestial Sphere that marks the location of the observer. The horizon cuts the Celestial Sphere in half for the observer because the bottom half is not visible.