Astronomy Lecture 4
What happens if the object has a velocity greater than escape velocity ?
It will follow a hyperbola and escape the earth
What was Galileo's thought experiment?
According to Aristotle, if a one pound cannonball falls a given distance in a given time, then if the ball is cut in half, each half pound ball should fall less far in the same interval. But, reasoned Galileo, what happens if the two balls are attached by a thread or stick. Aristotle's ideas about falling bodies start to look absurd
What is weight?
Amount of force needed to keep an object from falling in a particular gravitational field
What is Newton's first law?
Aristotle concluded that a constant force was needed to keep an object moving. This was disproved by Galileo. A body remains at rest or moves with constant speed in a straight line unless acted on by an outside force. Newton realized some force must pull the moon toward earth's center. If there were no force altering the moon's motion, it would continue moving in a straight line and leave earth forever. It can circle only if earth attracts it. Newton's insight was to recognize that the force that holds the moon in its orbit=gravity.
How is the orbit of Venus?
As of January 2016, Venus is ahead of earth in its orbit and is moving toward the far side of the sun (know the picture) It's easy to see in the morning sky before sunrise. Its phase is waxing toward full. It's the brightest object after our moon in the morning sky.
How did Newton's laws predict tiny violations of Kepler's laws due to gravitational attractions between planets?
By comparing the observed violations with predictions, astronomers measured the masses of Mercury and Venus, which do not have satellites. The gravitational attractions of the other known planets did not explain how Uranus is observed to violate Kepler's laws. Adams and Leverrier showed that these violations could be due to an 8th planet. Neptune, was discovered in 1846 at the predicted position. Unexplained violations of Kepler's laws by Neptune and Mercury led to predictions of two more planets. Pluto was discovered in 1930, but its mass is too small to affect Neptune's orbit. The slow precession of Mercury's orbit was finally explained by Einstein's theory of General Relativity. The long-term effects of gravitational attractions between planets are hard to predict. But planetary orbits can be changed dramatically. Any planets that formed (e. g.) between Jupiter and Saturn have been thrown out of our Solar System. Present planetary orbits look stable. But many planets have been ejected from other solar system. There may be more free roaming planets in interstellar space than there are stars.
Why is gravity a universal force?
Everything pulls on everything
When was the first astronomical use of the telescope?
Galileo learned about the invention of the telescope in 1609 in Holland. He built several telescopes and made himself famous by showing Venetians how to use it for military and commercial purposes. Galileo was the first to use the telescope for systematic study of astronomy-the study of the place of earth at the time.
What is this string that keeps a planet in orbit around the Sun?
Gravity
What are the 4 kinds of forces?
Gravity-Holds together the earth, solar system, and galaxy. Holds you to the earth. Electromagnetic force-holds you together and holds together most objects in your daily lives. Strong nuclear force-Holds the atomic nucleus together. Weak nuclear force-Is involved in some radioactive decays. Gravity=weakest force. Gravity and electromagnetic forces are long range; the others are important only on tiny scales (smaller than an atom)
What did Galileo discover about Jupiter?
He discovered 4 new planets circling Jupiter, known as Galilean moons. Strong evidence for Copernican model. Critics of Copernican had said earth could not move b/c the moon would be left behind, but Galileo showed that Jupiter was able to keep its moons. This suggested that earth could keep its moon. 4 moons of Jupiter, a Copernican Solar System in miniature. They showed that other planets and not just earth have moons. Aristotle believed that all heavenly motion=centered on earth. Galileo's observations showed that Jupiter's moons revolve around Jupiter, suggesting that there could be other centers of motion besides earth. Everything does not revolve around earth. Jupiter moves, but it does not leave its moons behind. He also noticed that the innermost moon moved fastest, and that the moons further away from Jupiter traveled slower
What did Newton realize about gravity?
He realized that the gravity that holds the Moon to the earth is the same gravity that holds onto you and me and makes apples fall. Therefore, Newton was the first person to realize that the same laws of physics control the heavens and earth. The laws of motion and law of gravitation were the first mathematical physical laws that were understood to apply to everything. They explained a much wider range of phenomena than the ones they were derived to explain. They allowed accurate calculations of how things behave. And they allowed us to derive further physical laws. Newton's laws opened the floodgates of discovery.
What were Newton's ideas about gravity?
He showed that planets in circular orbits would obey Kepler's third law if they were attracted to the sun with a force proportional to the inverse square of their distance. Taking this idea further: he postulated that any 2 bodies attract each other with a force proportional to the product of their masses divided by the square of the distance between them or F=G*Mm/r^2, where M and m are the masses of the 2 bodies, r = the distance between them, and G is a constant of nature. Newton showed this assumption plus his 3 laws of motion predict that the planets move according to Kepler's laws. But universal gravity doesn't just explain the motion of the planets. It also connects the motion of celestial bodies such as the Moon with terrestrial bodies such as an apple falling from a tree
What important problems did Galileo figure out?
Heavy and light objects fall at the same rate
What is Newton's third law?
If 2 bodies interact, the force exerted on the first body by the second is equal and opposite to the force exerted on the second body by the first. This points out that forces occur in pairs, so if one body attracts another, the second body must also attract the first. Thus, gravitation must be mutual and universal meaning all masses attract all other masses in the universe. The force between the 2 bodies depends on the masses of the bodies and the distance between them.
What happens to a satellite above earth's atmosphere?
If it feels no friction it will fall around indefinitely. It will eventually fall back to earth if it orbits too low and experiences friction with the upper atmosphere.
What did Newton realize in his third law?
In addition to mass, the distance between two objects affects the gravitational attraction between them. He recognized that the force of gravity decreases as the square of the distance between the objects increases. EX: If the distance from the Moon to earth doubled, the gravitational force between them would decrease by a factor of 4. This is known as inverse square relation.
What did Galileo discover about many sun spots?
Indicating that the sun, like the moon, is not perfect or "unchanging". By noting the movement of the spots, he concluded that the sun was a sphere that rotated on its axis.
How is the orbit of Mercury?
It is almost always hard to see b/c it never gets more than 28 degrees from the sun
What did Galileo discover about the moon?
Moon=not perfect. Mts, valleys, craters on the moon. The moon isn't a water composed of heavenly aether but a rocky, dusty, sovereign world. Aristotle believed moon=perfect, but Galileo showed that it was not only imperfect but was a world with features similar to earth.
How did Newton connect motion in the heavens to motion on earth?
Newton's thinking about universal gravitation went like this: If the Moon is 60 times as far from the center of the earth as is the apple (4000 miles for the apple, 240,000 miles for the Moon) and gravity gets weaker as the square of the distance, then the apple must feel a gravitational force that is 60^2 or 3600 times stronger than that experienced by the Moon. The moon therefore should fall along the curve of its orbit 1/3600th as far each second as does the apple. And so it does (time AB=time CD)
What do closed orbits do?
Return the orbiting object to its starting point. The moon and artificial satellites orbit earth in closed orbits. A circle is also an ellipse, so all closed orbits are elliptical.
What happens in an open orbit?
The cannonball travels at escape velocity, the velocity needed to leave a body. An open orbit does not return the cannonball to earth. It will escape. This will have a parabola.
What illustrates all 3 of Newton's laws?
The circular motion of a weight whirled around on the end of a string (look at picture)
When the captain of a spaceship says, put us into a circular orbit, what must be calculated?
The circular velocity which depends only on the mass of the planet and distance from the center of the planet.
What did Newton conclude when comparing a falling apple to a falling moon?
The force of gravity that makes apples fall is the same force of gravity that holds the Moon in its orbit around the earth
What is Newton's second law?
The outside force acting on a body is equal to the body's mass times its acceleration.
In the Ptolemaic system, what must the centers of the epicycles of Venus and Mercury must always lie on?
The same Sun-earth line
What does G measure?
The strength of gravity. Nobody knows how to derive G from any theory. G=6.67x10^-11 m^3/kg s^2
What is the problem with Kepler's laws?
They accurately describe planetary motion, but they do not describe the motion of the objects on earth. Newtonian physics explains Kepler's laws in terms of more basic principles that apply equally to terrestrial and celestial motion.
What did Galileo discover about many stars?
They are too faint to be seen with the naked eye, suggesting that the sky has depth.
What happens when you put 2 protons 1 mm apart?
They attract each other gravitationally, they repel each other electrically, and electrical repulsion is 10^40 times stronger than gravitational attraction. You would have to move the protons more than a light year apart to make the repulsion there equal to the attraction at 1mm. You are attracted gravitationally by the person sitting next to you. But you are attracted 5 billion times more strongly by the earth.
What happens to 2 bodies of different masses?
They balance at the center of mass, which is located closer to the more massive object. As the 2 objects orbit each other, they revolve around their common center of mass. As the moon orbits the center of mass on one side, the earth swings around the center of mass on the opposite side.
What happens to astronauts in orbit?
They tend to feel weightless, but they are not beyond earth's gravity. Like the moon, the astronauts are accelerated toward earth by earth's gravity, but they travel fast enough along their orbits that they continually miss the earth. They are literally falling around earth. Inside or outside a spacecraft, astronauts feel weightless b/c they and their spacecraft are falling at the same rate. Rather than saying they are weightless, you should more accurately say they are in free fall.
What happens if the object is in a perfectly circular orbit?
Velocity=constant, but if orbit=elongated, Kepler's 2nd law applies. The object has its lowest velocity at apogee when it is farthest from earth and its highest velocity at perigee when it is closest. Perigee must be above earth's atmosphere, or friction will rob the satellite of energy and it will eventually fall back to earth.
What did Galileo discover about Venus?
Venus has phases like the phases on the Moon. In the Ptolemaic model, Venus moves around in an epicycle centered on a line between earth and the sun. This means it would always be seen as a crescent. But Galileo saw Venus go through a complete cycle of phases, which proved that it did indeed revolve around the sun. Venus looks much bigger when it's a crescent than when it's full. Concluded that Venus orbited around the sun
How do objects orbit earth? (cannonball example)
With more velocity, the cannonball travels so fast it never strikes the ground. Earth's gravity pulls it toward earth's center, but Earth's surface curves away from it at the same rate it falls in orbit. The velocity needed to stay in orbit=circular velocity (17,400 mph). According to Newton's first law, the moon should follow a straight line and leave earth forever. B/c it follows a curve, Newtom knew that some force must continuously accelerate it toward earth-gravity. Every second the moon moves eastward 1020 m and falls about 1/16 inch toward earth. The combination of these motions produces the moon's curved orbit. The moon is falling.
To be precise, what should you not say about objects orbiting earth?
You shouldn't say an object orbits earth. Rather that 2 objects orbit each other. Gravitation=mutual and if earth pulls on the moon, the moon pulls on earth. The 2 bodies revolve around their common center of mass, the balance point of the system.
How can we weigh planets in mass?
a^3/P^2
If Venus traveled around an epicycle that is always between the earth and the sun,
then it should always be a thin crescent. But this is not what we see. (look at picture)