Chapter 3: Analyzing Scales and Motions of the Universe
How long does it take a planet to complete one orbit if it is twice the distance from the central star as the planet described in the Question above.
2.75 years
Look at the table and pictures on page 24 of the Lecture Tutorials. Which of the three orbits shown most closely matches the shape of Earth's orbit around the Sun? Explain your reasoning.
A because Earth's orbit is very close to an eccentricity of 0
Which of the listed objects would experience the largest change in orbital speed and which would experience the smallest change in orbital speed?
C would experience the largest, A the smallest
What is a light year?
The distance that light travels in one year
At which position would the planet have been traveling the fastest? The slowest? Explain your reasoning.
The fastest at G because it is closest to the Sun. The slowest at A because it is farthest from the Sun.
Given that Earth is much larger and more massive than the Moon, how does the strength of the gravitational force that the Moon exerts on Earth compare to the gravitational force that Earth exerts on the Moon? Explain your reasoning.
The gravitational force is the same because the Moon accelerates faster than the Earth
What are Kepler's three laws?
The orbit of a planet about the Sun is an ellipse with the Sun at one focus. A line joining a planet and the Sun sweeps out equal areas in equal intervals of time The square of the sidereal period of a planet is directly proportional to the cube of the semimajor axis of the orbit.
Look at the picture on page 22 of the Lecture Tutorials. How would the time it takes the planet to travel from Position A to Position B compare to the time it takes to travel between Position E and Position G? Explain your reasoning.
The same amount of time. It would just travel faster between points E and G.
Explain why the the phases of Venus are such compelling evidence that the Sun, not the Earth, is at the center of our planetary system.
When Venus is on the opposite side of the Sun from Earth, it appears full and has a small angular size. When Venus is at the greatest angle to either side of the Sun, it appears half illuminated. When Venus is on the same side of the Sun as Earth, it has the largest angular size.
If Venus is visible high in the evening sky after sunset, is it leading Earth in its orbit or behind earth?
When Venus is visible in the western sky, it is at its greatest eastern elongation and the faster-moving Venus has not yet caught up with Earth, as Earth is momentarily in front of Venus as they orbit the Sun.
Why does Venus have its largest angular diameter when it is new and its smallest angular diameter when it is full?
When it is new, Venus is closer to the Earth. When it is full, Venus is on the opposite side of the sun
If Esus and Sulis were to switch positions, would your answer change? If so, how? If not, why not?
Yes. Sulis would be faster because it would have the smaller semimajor axis.
At what point in a planet's elliptical orbit does it move the fastest? At what point does it move the slowest?
fastest at perihelion, which is when it is closest to the Sun slowest when it is farthest from the Sun at a point called the aphelion
During which dates does this mystery planet appear to move with backward, retrograde motion, as compared to the background stars? In what direction (east-to-west or west-to-east) does the planet appear to be moving relative to the background stars during this time?
from June 15 to July 15; east-to-west
Which phase will Venus be in when it is at maximum distance from Earth?
full or gibbous
At Position D, is the speed of the planet increasing or decreasing as time goes on? Explain your reasoning.
increasing because it is getting closer to the Sun
If a planet were moving with retrograde motion, how would the planet appear to move across the sky in a single night? Where would it rise? Where would it set?
it would still rise and set; retrograde motion happens over the course of many days
What is the significance of Occam's Razor as a tool for analyzing theories?
states that the idea that the most simple and most straightforward explanation of observations in nature is most likely to be correct
Do you think the orbital period for Esus would increase, decrease, or stay the same if its mass were increased? Explain your reasoning.
stay the same. Mass does not affect orbital period.
How fast is Earth spinning on its axis in the Greeks' geocentric model?
the Greeks used a nonspinning stationary Earth where the stars, planets, and the Sun all moved around Earth
How is an astronomical unit (AU) defined?
the average distance between the Earth and the Sun
What causes the planets to actually stop and change their direction of motion in the Ptolemaic model?
the planets are continuously orbiting in circles such that they appear to move backward for a brief time. However, the planets never actually stop and change their direction.
Your wright on Earth is simply the gravitational force between you and Earth. Would your weight be more, less, or the same on Mars? Explain your reasoning.
Less because Mars is less massive
Look at the table on page 99 of the Lecture Tutorial. On what date was the mystery planet located farthest to the west? What was the azimuth value of the planet on this date?
May 1; 240
At what configuration (for example, superior conjunction, greatest eastern elongation, and so on) would it be best to observe Mercury or Venus with an Earth-based telescope? At what configuration would it be best to observe Mars, Jupiter, or Saturn? Why?
Mercury and Venus can best be seen when they are near greatest eastern elongation because it can be visible after sunset. Mars, Jupiter, and Saturn are best seen when they are at opposition, when the planet is in the part of the sky opposite the Sun and is highest in the sky at midnight. This is when the planet appears brightest.
If the spaceprobe had lost all ability to control its motion and was sitting at rest at the midpoint between Earth and Mars, would the spacecraft stay at the midpoint or would it start to move? In what direction? Would it speed up or slow down? How would the net total force on the spaceprobe change during this motion? When and where would the spaceprobe experience the greatest acceleration?
Move toward Earth speed up more force from Earth closest to Earth
Look at the graph on page 26 of your lecture tutorials. How far from the central star does a planet orbit if it has an orbital period of one year?
1 AU
How fast is the space shuttle traveling 3 s after launch if it is accelerating at a rate of about 20 m/(s^2)?
Acceleration is how much the velocity of an object is changing every second. If the space shuttle starts at a velocity of zero on the launch pad and increases its velocity 20 m/s every second, then after 3 s, the space shuttle is moving at roughly 60 m/s (135 mph).
If Pluto's orbit has a semimajor axis of 39.5 AU, how long does it take Pluto to orbit the Sun once?
According to Kepler's Third Law, P^2= a^3. So, if P^2= (39.5)^3, then P = 39.5^(3/2) = 248 years
The space shuttle typically orbited Earth at an altitude of 300 KM whereas the International Space Station orbits Earth at a higher altitude of 370 km. Although the space shuttle took less time to orbit Earth, which one actually moved at a faster rate?
According to Kepler's third law, planets closer to the Sun move faster than planets farther from the Sun. For objects orbiting Earth, the object closer to Earth's surface is also moving the fastest, which, in this case, is the space shuttle.
If the 815 kg unmanned Voyager 2 interplanetary space probe was traveling at 38,000 mph without any rocket engines firing in 2009, how fast will it be moving in 2015, still without engines?
According to Newton's first law, if no outside forces were acting on an object, then it will remain in that state of motion. In other words, a spacecraft in outer space will continue at the same speed as it moves far from our Sun's gravitational influence.
How much does the gravitational force of attraction change between two asteroids if the two asteroids drift 3 times closer?
According to Newton's universal law of gravitation, the gravitational attraction between two objects depends on the square of the distance between them. In this case, if the asteroids drift 3 times closer together, then the gravitational force of attraction increases 3^2 times, or, in other words, becomes 9 times greater.
What are Newton's three laws?
An object remains at rest, or moves in a straight line at a constant speed, unless acted upon by a net outside force. In order to give an object an acceleration, a net outside force must act on the object. Whenever one object exerts a force on a second object, the second object exerts an equal and opposite force on the first object.
On what date was the mystery planet located farthest to the east? What was the azimuth value of the planet on this date?
August 15; 120
If Aristarchus had estimated the Sun to be 100 times farther from Earth than the Moon, how large would he have estimated the Sun to be?
Because the diameters of the Sun and Moon must be in the same proportion as their distances, if Aristarchus assumed the Sun to be 100 times farther away when they appeared to be the same diameter in the sky, he would have porposed that the Sun is 100 times larger than the Moon.
Imagine both Esus and Sulis were in orbit around the same central star at the same distance and that their orbital positions would never intersect. Which of the two planets will move around the central star in the least amount of time? Explain your reasoning.
Both would move around the star in the same amount of time because their semimajor axis would be the same.
During which of the two time intervals is the distance traveled by the planet greater?
E to G
Imagine a planetary system that has an average star, like the Sun, at the center and two planets. A huge planet named Esus orbits close to the star, while a small planet named Sulis is in orbit far away from star. Which of the two planets will move around the central star in the least amount of time? Explain your reason.
Esus because it has a smaller semimajor axis of orbit
During which dates does the mystery planet appear to move with normal, prograde, motion as compared to the background stars? In what direction (east-to-west or west-to-east) does the planet appear to be moving relative to the background stars during this time?
From May 1 to June 15 and July 15 to August 15; west-to-east
How would the strength of the force between the Moon and Earth change if the mass of the Moon were somehow made two times greater than its actual mass?
It would increase
Why had Jupiter's moons not been observed prior to Galileo's time?
Galileo used a telescope
If Eratosthenes had found that the Sun's noontime summer solstice altitude at Alexandria was much closer to directly overhead, would he then assume that Earth was larger, smaller, or about the same size?
If the noontime position of the Sum on the summer solstice was much closer to being directly overhead, he would assume that the Earth was larger because Earth's surface between the two cities would be much less curved, implying a much larger, circular Earth.
Does a planet with a completely circular orbit obey Kepler's second law? Why?
In order to obey Kepler's second law, the planet would have to move at a constant speed because it is equidistant from the star at all times.
Earth is more massive than Mars. When a spacecraft is at the halfway point between both planets, how does the strength of the gravitational force on the spaceprobe by Earth compare with the strength of the gravitational force on the spaceprobe by Mars? Explain your reasoning.
It is bigger because Earth is more massive
Describe how the mystery planet moved (east or west), as compared to the background stars, during the time between May 1 and August 15.
It moved east from May 1 to June 15, then west from June 15 to July 15, and east again from July 15 to August 15
If a door on the International Space Station requires 100 newtons of force to be pushed open, and, according to Newton's third law, the door pushes back on an astronaut with an equal but opposite force of 100 newtons, why is it that an astronaut can successfully open the door?
Newton's third law states that when one object exerts a force on another object, the second object exerts an equal but opposite force on the first. In other words, if the astronaut touches the door, the door touches the astronaut. The fact that the forces are equal does not mean that the "effects" are equal. If the only force on the door is the one applied by the astronaut, the door will move, following Newton's laws of motion.
Look at the picture on page 23 of the Lecture Tutorial. Does the planet appear to be traveling the same distance each month?
No
Do Kepler's laws of planetary motion apply only to planets?
No. Kepler's laws of planetary motion apply to any objects in space that orbit around another object.
In the heliocentric mode, would an imaginary observer on the Sun look out and see planets moving in retrograde motion?
No. Planets only appear to move in retrograde motion if seen as two planets moving at different speeds passing one another. An imaginary observer on the stationary Sun would only see plants moving in the same direction as they orbit the Sun.
Describe the extent to which you think Earth's orbital speed changes throughout a year? Explain your reasoning.
Not a lot because the eccentricity of the orbit is almost circular
If the sun is at one focus of an ellipse, what is at the other?
Nothing
Which planets can never be seen at inferior conjunction? Which planets can never be seen at opposition? Why?
Planets with an orbit larger than Earth's can never be seen at inferior conjunction because it is never in a position between Earth and the Sun. Mercury and Venus can never be seen at opposition because they are never on the opposite side of Earth from the Sun.
What is retrograde motion? How did Copernicus' model explain it?
Retrograde motion is when the planets seem to stop and then back up for several weeks or months. It seems like they are moving westward. According to Copernicus, planets take different lengths of time to complete an orbit, so from time to time one planet will overtake another. When Earth overtakes Mars, for example, Mars appears to move backward in retrograde motion.
Why is Jupiter's sidereal period longer than its synodic period?
Slowly moving Jupiter does not move very far along its orbit in the length of time it takes for Earth to pass by Jupiter, move around the Sun, and pass by Jupiter again, giving Jupiter a synodic period similar to Earth's orbital period around the Sun. In much the same way, slow moving Jupiter takes more than a decade to move around the Sun back to its original starting place as measured by the background stars, giving it a large sidereal period.
What keeps the International Space Station from crashing into Earth when it has no rocket engines constantly pushing it around Earth?
The International Space station has an initial forward velocity such that as it falls around Earth, it actually misses Earth because Earth's round surface is curved away.
How did the ancient Greeks explain why the Sun and the Moon slowly change their positions relative to the background stars?
The Sun and the Moon rotate around the Earth from west to east while the celestial spear rotates from east to west
How much would a 75-kg astronaut, weight about 165 pounds on Earth, weigh in newtons and in pounds if he was standing on Mars, which has a mass of 6.4 x 10^23 kg and a radius of 3.4 x 10^6 m?
Using Newton's universal law of gravitation, the force of Mars on the astronaut= G(mass of mars) x (mass of astronaut) divided by (radius)^2 = 6.67 x 10^(-11) x 6.4 x 10^23 x 75 divided by (34 x 10^6)^2 = 277 N, which we can convert to pounds because 277 N x 0.255 lb/N = 76 lb.
Which orbit is more circlelike: Venus's orbit, with e= 0.007, or Mar's orbit, with e= 0.093?
Venus
What observations did Galileo make that reinforced the heliocentric model? Why could these observations not have been made before Galileo's time?
Venus exhibits phases and Moons revolve around Jupiter
If Mars is moving retrograde, will it rise above the eastern horizon or above the western horizon?
all objects always appear to rise in the east and set in the west because both direct and retrograde motion are slower than the apparent daily motion of the sky
In what direction does a planet move relative to the stars when it is in direct motion? When it is in retrograde motion? How do these compare with the direction in which we see the Sun move relative to the stars?
eastward; westward
