View Full Version : Calculating the Movement of the Earth and Solar System Through Space

tricksterpython

05-25-2014, 06:15 AM

I need someone who is good at math, and knows how fast the earth, and our solar system is moving through space. In other words I need some rather specific calculations. I'm hoping someone here can help me, because all the math stuff is making my head hurt.

Pretend there is a line through space that doesn't move, and is directly in the path our solar system. Say at the starting point, earth would just barely not touch this line as it orbits around the sun. This is side A. Now, how long would it take for the solar system to be on the other side (side B) of that line to the point where once again the earth is just barely not touching that line as it orbits around the sun?

Assuming it takes years, for how long, and at what times of the year would the earth be touching that line during each year? For how long, and at what time of the year would it be on side B?

Thank you to anyone who can help with this. It's too complex for me, but would be very helpful.

benbradley

05-25-2014, 08:04 AM

I need someone who is good at math, and knows how fast the earth, and our solar system is moving through space. In other words I need some rather specific calculations. I'm hoping someone here can help me, because all the math stuff is making my head hurt.

Pretend there is a line through space that doesn't move, and is directly in the path our solar system. Say at the starting point, earth would just barely not touch this line as it orbits around the sun. This is side A. Now, how long would it take for the solar system to be on the other side (side B) of that line to the point where once again the earth is just barely not touching that line as it orbits around the sun?

I'm not sure if I'm visualizing this right, but see below for "absolute" speeds of the Earth and Sun.

Assuming it takes years, for how long, and at what times of the year would the earth be touching that line during each year? For how long, and at what time of the year would it be on side B?

Thank you to anyone who can help with this. It's too complex for me, but would be very helpful.Perhaps this will help, the paragraph starting with "The Sun is currently traveling through the Local Interstellar Cloud ... (http://en.wikipedia.org/wiki/Local_Interstellar_Cloud)"

http://en.wikipedia.org/wiki/Sun

According to this, the Earth orbits the Sun at 29.78 km/s (18.5 miles per second), so you can add or subtract that, depending on which part of the orbit Earth is in:

http://en.wikipedia.org/wiki/Earth

but that's less than 1/10th the speed of the Earth and Sun through space (from the Sun article, 370 km/s).

Rereading your first paragraph again and thinking about it - since the total total Solar System motion is substantially faster than the Earth's orbital speed around the Sun, it won't make much difference where the Earth is in its orbit.

The Solar System is moving at 370 km/s, the Earth's diameter is 12.742 km, the Earth will pass through an arbitrary line fixed in space in 12.742/370=0.34 seconds.

If you're asking how long Earth's ORBIT would take to pass the line, that's a distance of 2 AU, or 149598261 km. 149598261/370= seconds, or 18 minutes and 12 seconds.

ETA: No, that can't be right, light goes from the Sun to Earth (1 AU) in 8 minutes, and if we move 2 AU in 18 minutes, then we're going near lightspeed, which we ain't.

Since the Solar System is moving through space about ten times Earth's orbital speed ... the Earth moves 2pi AU in one year, so the solar system moves ten times that (20pi AU) in a year, or it moves 2 AU in 2 AU / 20pi AU = 0.0318 year, or 0.38 months, or 11 days, plus or minus a few days or so for the approximations.

Now I just need to figure out what I did wrong in my earlier calculations.

Here we go, don't know how I missed this:

149598261/370= 404319 seconds, or 112 hours. Dividing by 24 gives 4 days, 16 hours. Okay, that's 11 days plus or minus 7 days. :-)

Telergic

05-25-2014, 08:24 AM

Let me rephrase this to see if I understand -- you use some ambiguous terms, for example, I assume the line you talk about is orthogonal to the path of the Sun. Another ambiguity is this: with respect to what are you measuring speed? The Sun moves at one velocity with respect to the center of the galaxy, but since the galaxy itself is moving, the Sun moves at another velocity with respect to the cosmic background radiation.

So let us suppose that at a certain date the Earth is directly in "front" of the Sun in terms of the direction of the Sun's motion. I think you're asking how long it will take before the Sun and Earth together reach the point at which the Earth will once again be on or near this spot, but directly behind the Sun.

Arithmetic time. I hope I don't screw this up....

I think you're making the false assumption the Sun will take a long time to make this journey, so the Earth will not have time to orbit to the "far side" as I believe you are suggesting.

Actually, the Sun moves at 370 km/sec with respect to cosmic background radiation, and the Earth is just 150,000,000 km from the Sun. So in just a few days the Sun will have rushed far past your line, but the Earth will still be close to where it started. It will only take the Sun 4.6 days to touch the line, and 9.2 days to mirror its starting position on the far side, and in that time, the Earth will still be close to its own starting position relative to the sun (having only moved 9.2 degrees around the orbit, pretending the orbit is a circle).

So really you can imagine the Earth moving around the Sun so slowly it is almost motionless while the Sun rushes past your line.

Now suppose you ignore the cosmic background radiation and the motion of the Milky Way, and just consider the Sun's motion with respect to the Milky Way itself. In that case, I believe the Sun's velocity is around 220 km/sec. This is still so fast that the Sun will have rushed far past your line by the time the Earth finally swings around to the opposite side from which it started (6 months later).

I hope I didn't mess up my arithmetic.

Edit: Of course there are only 360 degrees in a circle, so the Earth would move a little less than 9.2 degrees in 9.2 days.

BDSEmpire

05-25-2014, 10:51 AM

Here are all the stats about planetary motion you could possibly want:

https://www.youtube.com/watch?v=buqtdpuZxvk&feature=kp

tricksterpython

05-25-2014, 06:54 PM

Thanks guys. I guess I didn't realize just how fast the solar system moves. I should have realized, but it's like I can't even imagine something actually moving that fast.

I'm going to have to rethink some things in the sci-fi novel I'd come up with. It's a good thing I asked, rather than make a mistake that big.

King Neptune

05-25-2014, 07:31 PM

Another problem is that there is not fixed frame of reference. And everything is moving. If you draw a line in the sand, so to speak, in the universe somewhere, the the line will look like a distorted corkscrew after a while.

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