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Dec 15, 2020 · In July 2018, an international team of astronomers concluded a study of a triple-star system 4,200 light-years from Earth. A light-year being the distance light travels in one year (about six trillion miles), this means that the astronomers here on Earth were observing light-revealing phenomena that actually occurred in about 2,200 B.C.
Sep 12, 2019 · This is what happens to light traveling through space: When it comes too close to a massive object, it encounters warped space-time and curves not because it’s being pulled by gravity, but ...
Jul 30, 2020 · The light’s gravity, due to its energy-momentum tensor, is the only gravity determining the dynamics of that cosmology. Our own universe, which we believe is homogeneous and isotropic on the largest scales and thus can be modeled using the Friedmann metric, had an early radiation-dominated phase.
- Important Concepts
- Non-Inertial Frames and Fictitious Forces
- The Force of Gravity: Newton vs. Einstein
- The Apple Falling
- Spacetime Geometry
- Curved Spacetime and Tidal Gravity
- The Surface of The Earth
- Summary and Key Points
Spacetime: the combination of 3 dimensions of space and 1 dimension of time into a unified 4D “manifold”.Coordinate systems: mappings between events in spacetime and 4 numbers called coordinates. Usually, the coordinates involve a 1-time coordinate and 3 spatial coordinates.Proper acceleration: the acceleration measured by an ideal accelerometer. This is the acceleration that you physically “feel”.Coordinate acceleration: the 2nd derivative of position in some given coordinate system.Physics is traditionally taught using inertial frames, however, there is no restriction that prevents the use of non-inertial frames (e.g. a rotating reference frame). In a non-inertial frame inertial objects undergo coordinate acceleration, and in order to use Newton’s 2nd law in such frames additional “fictitious forces” (e.g. the centrifugal and...
In Newtonian mechanics, gravity is considered to be a real force, even though it shares the first two properties of fictitious forces listed. This makes Newtonian gravity a bit of a strange force. You cannot determine if a given reference frame is inertial or not simply by using accelerometers, you have to additionally know the distribution of mass...
As mentioned above, an apple freely falling to the ground is considered to be inertial in GR. If we make a coordinate system where the apple is at rest, it is an inertial coordinate system. In this reference frame, the apple does not accelerate, instead, the ground accelerates upwards at g and slams into the apple. This corresponds to the fact that...
Now consider a “spacetime diagram” of the apple, where time is plotted on one axis and the apple’s vertical position is plotted on the other axis. In such a diagram the apple can be represented by a line (called a “worldline”) which shows its position at each point in time. If we take the frame where the apple is at rest then the apple travels alon...
While this is all well and good for a single apple falling in a uniform gravitational field, what happens when we consider tidal gravity (gravity that varies over space) such as two apples falling on opposite sides of the world? Let’s suppose that there is a hole completely through the Earth and no atmosphere so that we can neglect the ground and t...
In the previous section we neglected the ground, but now let’s consider the ground. If the ground is accelerating upwards and the direction corresponding to “up” changes around the globe, then it seems that the surface of the Earth should be expanding, with the distance from one point to another continually increasing. This reasoning is incorrect i...
In GR the force of gravity is considered to be a fictitious force, and inertial reference frames are free-fall frames where falling apples have straight worldlines and the ground continuously accel...In order to model tidal gravity (where gravity varies from location to location), we must use curved spacetime.This allows for two apples to each have straight (geodesic) worldlines but still, accelerate relative to each other.It also allows for the ground to continuously accelerate upwards without the Earth expanding.Apr 26, 2019 · If the elevator is stationary on the ground, the gravitation of the Earth still causes every object inside to accelerate downwards at 9.8 m/s 2: the same result as if the elevator were ...
- Ethan Siegel
In general relativity, gravity affects anything with energy. While light doesn't have rest-mass, it still has energy --- and is thus affected by gravity. If you think of gravity as a distortion in space-time (a la general relativity), it doesn't matter what the secondary object is. As long as it exists, gravity affects it.
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Jan 14, 2019 · Gravity space-time cone of earth: Gravity space-time funnel of a black hole: (source: interestingengineering.com) [Note]: Singularity: A singularity is basically, in calculus/algebra terms, just when you divide by zero. A 2D singularity might just look like this: $\mathrm{f(x) = 1/x}$ (the singularity is there in the middle at $\mathrm{x=0}$).
