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Okay, so the speed of revolution of earth around sun is 30 km/s[1], speed of revolution of sun around milky way's center is ~200 km/s[2], speed of rotation of milky way is 828,000 km/h[3] i.e. 230000 m/s. Since speed of light is 300000000 m/s, so on an even bigger scale (bigger than clusters) are we already moving faster than the speed of light? Or am I totally wrong?

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Short Answer

  • NO.

Long Answer -

  1. The Earth "wobbles" on its polar axis. This motion is not relevant (IMO) to the calculations needed to return to earth from interstellar space as it is an "in situ" motion, but it exists.

  2. The Earth revolves {spins} on its axis. For these calculations we will use the equator with a circumference of approx. 25,000 miles. One rotation of Earth is approx. 24 hours. Again this is "in situ" motion so not relevant to space travel, but adds to our "stationary chair" model 25000/24 =1041.7 MPH

  3. The Earth is orbiting the Sun once a year. The circumference of the Earth's orbit is approx. 607.6 million miles {or 940 million kilometers}. One year is approx. 365 days 365 days X 24 = 8760 hours 607,600,000/8760 = 69,360.73 MPH

So far we have basically 3 Directions of Motion {Wobble, Spin and Orbit} and a combined speed of 1041.70 + 69,360.73 = 70,402.43 MPH for a person sitting in a chair at the Equator.

  1. The sun {and hence the solar system} is moving towards the constellation Hercules, namely to the star Lambda Herculis at 12 miles per second {or 20 kilometers per second} which is 43,200 MPH

  2. The Solar system is also moving upwards, at 90 degrees to the plane of the Milky Way, at 4.34 miles per second or 15,624 MPH. But we are actually leaving the Galaxy, out about 50 light years now and will be moving out to 250 light years before it reverses. Details of the mechanics of this are explained in the link below. We also crossed the Galactic plane 2 million years ago.

  3. The Solar system is orbiting around the Galaxy at an "estimated" speed of 124 miles per second {or 200 kilometers per second} which is 446,400 MPH. The way that figure has been calculated can be found at the link below. So our "armchair Astronaut" is now moving through 6 different directions and a combined speed of approximately 574,585 MPH

69,361 MPH Spin and Orbit 43,200 MPH Towards Lambda Herculis
15,624 MPH Perpendicular to Galactic Plane 446,400 MPH Orbiting the Galactic Center {or Galactic Spin Rate}
574,585 MPH or 256862.478 m/s Speed of Earth within Our Galaxy


light's= velocity = 3*10^8 m/s
So the ratio = 256862.478 / 3*10^8 = 0.00085620826

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Short answer: no.

Whenever you mention a speed you must state what you are measuring the speed relative to. When a traffic sign says maximum speed 50kph it means relative to the Earth's surface. In measuring speed in space there is no such obvious frame of reference. The theory of relativity does not allow objects to move through space relative to each other, at speeds greater than the speed of light.

For objects inside the galaxy, the force of galaxy dominates their motion. We are in orbit in a galaxy, but our speed, relative to every other part of the galaxy is well below the speed of light.

For greater distances, the Hubble flow dominates motion: distant galaxies are moving away from us. The more distant galaxies are moving away from us faster. Galaxies more than about 4 billion parsecs (or 13billion light years) would be moving away faster than the speed of light. This doesn't break the theory of relativity as spacetime is being stretched between them and us. Objects can't move through space at speeds greater than the speed of light, but if the spacetime between objects is expanding, then they can appear to be moving faster than light, depending on your point of view.

None of this answer should be taken as contradicting the short answer above.

No, we are not moving through space faster than the speed of light relative to any object in our frame of reference.

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You're totally wrong, but it's a good question. Leonard Susskind actually uses something like the scenario that you're referring to in order to demonstrate how to add velocities when things like special relativity (which is a little different from what you're talking about, but similar enough for this discussion) are of concern. Here are some links to the math behind adding velocities in special relativity (again, not technically what you're talking about but similar enough).

http://math.ucr.edu/home/baez/physics/Relativity/SR/velocity.html http://hyperphysics.phy-astr.gsu.edu/hbase/Relativ/einvel.html

Nothing in your reference frame (pretend you're an observer for whom the sun is moving at the very, very, very limit of the speed of light) can travel at a speed faster than the speed of light (in a vacuum). A lot of people can describe the consequences thereof very well (well enough to have actually made sure that it's a solid theory anyway), but I don't think anybody knows exactly why the speed of light acts like a cosmic speed limit.

EDIT: Here's the Susskind lecture: https://www.youtube.com/watch?v=qfTJP7Soto4

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