Chapter 8 Flashcards
What is geometry?
It is the mathematics that describes the relationships of space, volumes, and areas
What are the 5 axioms of geometry?
1) It is possible to draw a straight line from any given point to any other point
2) a straight line can go infinitely and still be straight
3) a circle can be described with any point as its centre and any distance as its radius
4) all right angles are equal
5) given a line and a point not on the line, only one line can be drawn through that point that will be parallel to the first line
What does Euclidean geometry describe?
Flat spaces
What is the great circle?
The line on a circle whose centre coincides with the centre of the sphere
On Earth, this is the equator
How many great circles can there be on a sphere?
2
How many times do thee great circles bisect?
Twice
What is the issue with parallel lines on a sphere?
There are no possible parallel lines on the surface of a sphere.
What can we change about Euclid’s original 5 postulates to define the geometry of a sphere?
Change the 5th postulate: that a parallel line is not possible on a sphere
How many parallel lines can be drawn to another line from a given point?
An infinite number of lines
What kind of dimensions do geometries come in?
Arbitrary shapes
Name the 3 types of geometries
1) spherical
2) flat
3) hyperbolic
What do all the types of geometry have in common?
- they are all homogenous
- ## they are all isotropic
Why do hyperbolic geometries have a special role to play in our universe?
they are possible geometries for a homogenous and isotropic universe
Why is the weakness of our local gravitational field problematic?
It makes it difficult to test General Relativity. We cannot automatically extrapolate the data for the stronger fields
What is the nature of space time near a large object?
It is curved
What was Arthur Eddington’s experiment?
He observed the stars close to the sun during a solar eclipse and compared them to their positions at night when they were not close to the Sun
What was the result of Eddington’s Experiment?
The idea of light bending was consistent with the theory of general relativity
How many arc seconds does the orbit of mercury change by every year?
5600
How many of the arctics that the orbit of mercury changes by are accounted for by Newton’s Laws?
All but 43
What explains the alteration in the varied arc seconds of Mercury’s orbit?
General relativity
What is the alteration if Mercury’s orbit called?
the Perehelion of Mercury
How has General Relativity helped with space technology?
It has allowed for accurate communication with spacecraft
EG Viking Lander could be located to within centimetres
How can White Dwarves provide evidence of General Relativity?
The field of a WD is sufficiently strong to see gravitational redshifting in the photons that leave its surface
What happens when 2 objects of great mass in orbit about one another lose energy?
They start to spiral until they collide with each other
This was predicted by GR
