Unit 5 Flashcards
Newton’s realization about gravity.
- gravity extends beyond the Earth and is universal
- the moon is falling around Earth
- all objects are attracted to all other objects in the universe in a way that involves only mass and distance.
constant that tells how much the circumference of a circle will grow when diameter is increased
C = D*pi
gravitational constant
G tells how much Force of gravity (F) will increase when you increase the masses of the objects involved.
Gravity decreases…
as the objects get farther apart
what is responsible for our tides?
combined effect of the sun and the moon on Earth.
- Water is very “moveable” and responds to the gravitational fields more easily than continents or oceanic crusts do.
- Thus the water bulges out, and the Earth spins beneath the bulge.
Why does the moon not hit Earth, according to Newton?
The moon is falling towards Earth, but it has great enough tangential velocity to avoid hitting Earth.
What would happen if tangential velocity of a planet was reduced to zero?
Their motion would be straight towards the sun and would crash into it.
Newton’s Law of Universal Gravitation
Every object attracts every other object with a force.
Law of Universal Gravitation Equation
Force ~ (mass(1) * mass(2))/distance^2
OR
F ~ (m(1)m(2))/d^2
Equation of Universal Gravitation
F = G * (m(1)m(2)/d^2)
G =
6.67 * 10^-11 N*m^2/kg^2
Law of Universal Gravitation Equation for G
G = F/(m(1)m(2)/d^2) = 6.67 * 10^-11 N*m^2/kg^2
Inverse-square law
When a quantity varies as the inverse square of its distance from its source.
Gravity decreases according to…
the inverse-square law. The force of gravity weakens as the square of distance.
Gravitational field
The force field that exists in the space around every massive body.
Earth can be thought of as being surrounded…
by a gravitational field that interacts with objects and causes them to experience gravitational forces.
What is the gravitational field of Earth at its center?
Zero. Things weigh nothing.
What is force against earth?
The sensation that is interpreted as weight.
Weightlessness
Absence of a support force.
Ocean tides are caused by…
differences in the gravitational pull of the moon on opposite sides of Earth.
Spring Tide
High or low tide that occurs when the sun, Earth, and moon are all lined up
Neap tide
Occurs when the moon is halfway between a new moon and a full moon, in either direction.
When a massive star collapses into a black hole, there is no…
change in the gravitational field at any point beyond the original radius of the star.
Perturbation
The deviation of an orbiting object from its path around a center of force caused by the action of an additional center of force.
Why are there no large objects in the solar system today with very low tangential velocities?
They crashed into the sun long ago.
When a satellite companion to a star that collapses to become a black hole, how will the orbit of the companion satellite be affected by the star’s transformation into a black hole?
The orbit will not be affected. The star’s mass has not changed and the distance from center of mass to center of mass has not changed, so the gravitational field remains the same.
Why are planets and moons round?
Gravity caused them to attract themselves together before they became solid. Any “corners” were pulled in so that planets and moons are giant spheres.
geostationary/geosynchronous orbits
- exact same spot at all times
- used to give very precise information about a specific location
A geometric fact about the curvature of the Earth is that its surface drops a vertical distance of __?__ meters for every ___?___ meters tangent to its surface.
5 meters; 8000 meters
What would happen if your satellite was launched with a tangential speed of 9 km/s or 10 km/s?
-would get farther away from the Earth before being pulled back down, resulting in an elliptical orbit.
Elliptical motion is governed by the same rules of…
conservation of mechanical energy as linear motion or projectile motion
As a satellite gets farther from Earth, its PE…
increases, but its KE drops.
When it is close to Earth, its KE…
is high, but its PE has dropped.
Satellite
Projectile moving fast enough to fall continually around the Earth
A satellite in circular orbit around Earth is always moving…
perpendicular to gravity and parallel to Earth’s surface at constant speed
All Earth’s satellites follow…
elliptical orbits, both manmade and natural
Ellipse
Closed path taken by a point that moves in such a way that the sum of its distances from two fixed points is constant.
Foci
Two fixed points of an ellipse
Satellite speed…
varies in an elliptical orbit. Fastest closest to mass, slowest furthest to mass
The sum of the KE and PE of a satellite is…
constant at all points along an orbit
Apogee
Point in satellite’s orbit farthest from center of Earth. PE greatest; KE least.
Perigee
Point in a satellite’s orbit closest to center of Earth. PE least, KE greatest
Kepler’s first law of planetary motion
The path of each planet around the sun is an ellipse with the sun at one focus.
Kepler’s second law of planetary motion
Each planet moves so that an imaginary line drawn from the sun to any planet sweeps out equal areas of space in equal intervals of time.
Kepler’s third law of planetary motion
The square of the orbital period of a planet is directly proportional to the cube of the average distance of the planet from the sun. (T^2/r^3)
Escape speed of earth
horizontally launched from Earth at 8km/s
Escape speed
Minimum speed necessary for an object to escape permanently from a gravitational field that holds it
What happens if a payload is given more than 62MJ/kg of energy at the surface of earth, neglecting air resistance?
Payload will escape from Earth, never to return. Equivalently, it could be a greater speed than 11.2km/s.
If the fusion rate of the sun increases, the sun will get ___ and ____.
hotter; bigger
Time is neither…
imaginary nor unchanging. It is a real, fundamental part of our universe that can be affected by something as “simple” as motion. Is not constant.
space and time is…
entirely INSIDE the universe, rather than thinking about the universe being located within space and time.
How fast does light travel?
At a constant speed of about 300,000 km/s.
According to the special theory of relativity, how do standing still and traveling at the speed of light differ?
If you were standing still, you would be traveling at the maximum rate in time - 24 hours a day. If you were traveling at the speed of light, time would stand still.
Which of the following is/are true about motion and frames of reference?
a. All motion is relative.
b. All frames of reference are arbitrary.
c. A spaceship can measure its speed relative to empty space.
d. A spaceship’s speed must be measured relative to other objects.
a, b, and d are true.
Space-time
Two parts of one whole
Special theory of relativity
- Describes how time is affected by motion in space at a constant velocity, and how mass and energy are related.
- rests on two fundamental assumptions, or postulates
From the viewpoint of special relativity, you…
travel through space-time.
Time dilation
- Stretching of time due to motion in space
- occurs ever so slightly for everyday speeds, but significantly for speeds approaching the speed of light
- Whenever we move through space, to some degree alters our rate of moving into the future.
First postulate of special relativity
- assumes our inability to detect a state of uniform motion
- states that all the laws of nature are the same in all uniformly moving frames of reference.
Second postulate of special relativity
- assumes that the speed of light is constant
- states that the speed of light in empty space will always have the same value regardless of the motion of the source or the motion of the observer.
Equation for time dilation
t = t0/sqrt(1-(v/c)^2) v = relative velocity c = speed of light t= time
When an object moves at a very high speed relative to an observer, its measured length…
in the direction of motion is contracted
Length contraction
The observable shortening of objects moving at speeds approaching the speed of light
-does not occur unless the movement is parallel to being measured.
Equation relativistic length contraction
L = L0 * sqrt(1-(v^2/c^2))
One of the most interesting results of general relativity is that we have had to…
re-define the concepts of momentum and energy.
Relativity does not say that Newtonian physics is…
…“wrong” but that it applies to a limited set of circumstances.
In Newtonian physics, momentum is defined as mass times velocity. Note that mass times velocity works when…
…speeds are slow. When objects approach the speed of light, however, momentum must be redefined in relativistic terms.
Einstein’s equation for momentum
P = (mv)/(sqrt(1-v^2/c^2))
This is relativistic momentum
Which of the following statements are true about mass and energy?
a. Rest mass is a kind of potential energy.
b. Rest mass and energy are related by the equation E = mc.
c. Mass and energy are equivalent—anything with mass also has energy.
d. The quantity c2 is a conversion factor that converts the measurement of mass to an equivalent energy.
a, c, and d are true
Special relativity says that when you are in the system in question, you…
can’t tell whether it is stationary or moving with constant motion.
general relativity says that when you are in the system in question you …
can’t tell whether the system is accelerating or under the influence of gravity.
-there is no discernable difference between gravity and acceleration.
Which of the following statements are true?
a. General relativity tells us that the bumps, depressions, and warpings of geometrical space-time are gravity.
b. It is easy to visualize four dimensions because we are four-dimensional beings.
c. The planets that orbit the sun travel along three-dimensional geodesics in the warped space-time about the sun.
d. Every object has mass and therefore makes a bump or depression in the surrounding space-time.
a and d are true
As an object approaches the speed of light, its momentum…
increases dramatically
Rest mass
The intrinsic mass of an object, a fixed property independent of speed or energy.
Rest energy
“energy of being,” given the equation E = mc^2
Correspondence principle
New theory and old must overlap and agree in the region where the results of the old theory have been fully verified.
According to the correspondence principle, if the equations of any new theory are to be valid, they must correspond to those of…
Newtonian mechanics when speeds much less than the speed of light are considered.
General theory of relativity
Einstein’s generalization of special relativity, where gravity causes space to become curved and time to slow down
Principle of equivalence
Local observations made in an accelerated frame of reference cannot be distinguished from observations made in a Newtonian gravitational field.
Space-time dimensions
- Space dimensions (length, width, height)
- time dimension (past to future)
Geodesics
Lines of shortest distance between two points in curved space.
The presence of mass produces…
a curvature or warping of time-space
A curvature of space-time reveals…
the presence of mass
Gravitational waves
The ripples that travel outward from the gravitational sources at the speed of light
Upon developing the general theory of relativity, Einstein predicted that the elliptical orbits of the planets…
precess about the sun, deflecting starlight that is passing close to the sun, and gravitation causes time to slow down.
Gravitational red shift
Effect that causes light traveling “against gravity” to have a slightly lower frequency.
