Chapter 7
If the radius of an object's orbit is reduced by a factor of 5.00, then in order for angular momentum to be conserved, the velocity must increase by a factor of
5.00
Jupiter has a mass equal to 318 times Earth's mass, an orbital radius of 5.2 AU, and an orbital velocity of 13.1 km/s. Earth's orbital velocity is 29.8 km/s. What is the ratio of Jupiter's orbital angular momentum to that of Earth's?
726.92
Now we run into a problem: if the protostellar cloud spins faster as it collapses, it will also heat up. As gases heat up and their individual particles move faster, the gas expands, potentially stopping the collapse of the cloud before it can form a star system. One way to get past this is that the moment of inertia also depends on the way the mass in an object is distributed with respect to its axis of rotation. The following diagram shows how this varies for an object of different shapes rotating in different ways. Small moment of inertia → Large moment of inertia Based on the above diagram, and the fact that objects with increasing moment of inertia will spin more slowly to conserve angular momentum, click on the most likely way a cloud of gas will collapse in the picture below. Choose one:
A - picture
A new star is forming inside this glowing cloud of gas. The dark band in the middle is made of a disk of thick dust, which obscures the light within it and hides the forming star from view. Newly forming stars are surrounded by gas and dust. Based on this observation, what is the most likely scenario for the formation of the Solar System?
A cloud of gas and dust collapsed into a flattened disk, within which the Sun and planets formed
The composition of the protoplanetary disk varies with distance from the protostar due to temperature. Starting with those closest to the protostar, place these materials in order based on where they can be found predominantly in their solid states.
Closest - Iron, silicates, carbon - Water - Methane, ammonia, CO
Put the following stages of planet formation in order of occurrence.
Earliest Stage - An interstellar cloud collapses into a disk of gas, dust - Gas pushes smaller dust grains into larger grains - Larger dust grains grow into clumps - Clumps of dust collide and stick, forming planetesimals - Km-sized planetesimals attract other objects by gravity - Planets of various sizes form Latest Stage
Study the size difference of the gas giants as shown in the above image (distance from the Sun increases from left to right), and choose the best explanation below for your observations.
Gas giants decrease in size with increased distance from the Sun because the Solar Nebula was less dense farther out
The diagram shown illustrates the location of the Solar System's eight planets and three large dwarf planets. Sort each object according to its basic composition (q2)
Gaseous: Jupiter, Saturn, Uranus, Neptune Rocky: Mercury, Venus, Earth, Mars, Ceres Rock/Ice Mixture: Pluto, Eris
Planets must form somehow within the flattened protoplanetary disk. A clue to this process comes from meteorites, which are pieces of debris that have fallen from space to Earth. Most are made of materials that have remained unchanged since the time that the Solar System was first forming, which make them excellent indicators of what conditions were like during that time.Study this picture of a meteorite that has been sliced open to show its interior, and use your observations to determine the most likely formation scenario for a planet. Scroll down and select the best answer below. Choose one:
Individual particles in the nebula stick together to form larger pieces, which later collide with and stick to other pieces to gradually form larger objects, which eventually grow to the size of a planet.
If the radius of a spherical object is halved, what must happen to the period so that the spin angular momentum is conserved?
It must be divided by 4
If the radius of an object's orbit is halved, and angular momentum is conserved, what must happen to the object's speed?
It must be doubled
The following graph shows multiple transit events recorded while observing a star. The colored arrows indicate transits caused by three different planets. Rank the orbital periods of these planets, from shortest to longest.
Shortest Period - Red Planet - Blue Planet - Purple Planet Longest Period
Rank the following types of bodies commonly found in star systems in order of their masses, from smallest to largest.
Smallest Mass - Terrestrial Planet - Jovian Planet - Brown dwarf - Red dwarf star - Sun-like star Largest Mass
The nebular theory states that star systems form by the gravitational collapse of a cloud of gas and dust that, to match observations, must flatten into a disk within which planets can form. Why would this flattening occur? Consider the law of conservation of angular momentum, which states that a quantity related to the size of an object (its moment of inertia) times the speed of rotation (angular speed) has to remain the same at all times as long as no outside forces act on that object. Based on this law, if a collapsing cloud is isolated in space with no external forces, what must happen to it as its size decreases?
The cloud will spin faster
Imagine that you are observing a car that is out of control and spinning on the ice on the highway. The car suddenly stops spinning and starts spinning in the other direction as it slides down the highway. In order for this to happen, what must have taken place?
There must have been external forces acting on the car—for example, the spinning car struck another car
The diagram shown indicates the location of exoplanets orbiting their star. The light green ring represents the habitable zone for that star. Determine whether each of the planets in this system is located in a region that is too hot, too cold, or just right for liquid water to potentially exist on the surface.
Too hot for liquid water: Planet b, c, d, e Too cold for liquid water: n/a Just right for liquid water: Planet f
If scientists want to and out about the composition of the early Solar System, the best objects to study are
asteroids and comets
Clumps grow into planetesimals by
colliding with other clumps
The nebular hypothesis describes what happens when a cloud collapses into a star system. Where does the majority of the angular momentum of the original cloud go?
into the orbital angular momentum of planets
A planet in the "habitable zone"
is at a distance where liquid water can exist on the surface
The amount of angular momentum in a spherical object does not depend on
its temperature
The radial velocity method preferentially detects:
large planets close to the central star
The spectroscopic radial velocity method preferentially detects
large planets close to the central star
The transit method preferentially detects
large planets close to the central star
The planets in the inner part of the Solar System are made primarily of refractory materials; the planets in the outer Solar System are made primarily of volatiles. That difference occurs because
no volatiles were in the inner part of the accretion disk
Because angular momentum is conserved, an ice-skater who throws her arms out will
rotate more slowly
Since angular momentum is conserved, an ice-skater who throws her arms out will
rotate more slowly
Imagine that a star-forming cloud collapses but retains all of its mass in a single blob. In order to conserve angular momentum, the cloud must
spin faster
The direction of revolution in the plane of the Solar System was determined by
the direction of rotation of the original cloud
The concept of disk instability was developed to solve the problem that
the early solar nebula probably dispersed too soon to form Jupiter
Unlike the giant planets, the terrestrial planets formed when
the inner Solar System was hotter than the outer Solar System
The terrestrial planets and the giant planets have different compositions because
the terrestrial planets formed closer to the Sun
Suppose you hear of the discovery of an Earth-mass planet around a star. This planet was most likely discovered through the __________ method
transit
