Calculating Earth's Speed Around Milky Way

[pLatOscLoSET]

I know that the Earth orbits the sun at roughly 18.5 miles/sec and the sun orbits the milky way at around 137 miles/sec. How do I calculate Earth's speed as it coils around the milky way?

 

[mgb_phys]

You take the distance of the sun from the centre of the milky way (about 30,000 lyr) and the time it takes to go around, 1 galactic year = 250million years.

 

[maverick_starstrider]

? The progress the Earth makes around the milky way IS the sun's speed. The Earth is orbiting the sun so it spends just as much time heading away from the directon of rotation as towards relative to the sun so the net velocity of the Earth around the milky way is the velocity of the sun around the milky way.

 

[pLatOscLoSET]

it spends just as much time heading away from the directon of rotation as towards relative to the sun

How do we know that?

 

[maverick_starstrider]

...because the Earth orbits the sun in an elliptical orbit...

 

[pLatOscLoSET]

The Earth is orbiting the sun so it spends just as much time heading away from the directon of rotation as towards relative to the sun so the net velocity of the Earth around the milky way is the velocity of the sun around the milky way.

I thought the the world line of the Earth is helical in spacetime... if that is so then wouldn't that contradict the statement quoted above?

 

[Nabeshin]

I think what you're getting at is motion represented by an epicycle, the same as in this picture:
http://phyun5.ucr.edu/~wudka/Physics7/Notes_www/img127.gif
(Replace the Earth with Galactic Center, and Mars with Earth, and imagine the Sun is at the center of the epicycle)

What others are saying is the radius and period of the Earth's orbit are so small compared to the galactic orbit, that for all intents and purposes, the Earth's motion (with respect to the sun) can be ignored.

 

[maverick_starstrider]

yes but the velocity of the Earth through its epicyclic path is NOT its velocity AROUND the milky way. For the velocity around the milky way we don't include the components of the velocity that aren't tangentional to the elliptical orbit. So the net velocity of the Earth AROUND the milky way is what you'd get if you projected that funky orbit onto the elliptical orbit and it would fluctuate but its net value would be that of the suns rotation around the galaxy.

 

[pLatOscLoSET]

I attached an image... I guess it is not a big deal in the grand scheme of things but the Earth definitely appears to me to travel a greater distance in an equal amount of time.

 

[russ_watters]

Yeah, you're right - the Earth's orbit is closer to perpendicular than parallel to the galactic plane. You can draw a right triangle with those two speeds on the legs and calculate the hypotenuse...