How Fast Are We Moving - Right Now?
Do you think you are motionless as you sit at your computer reading this page?
Wrong!
Long ago, people thought the Earth was the stationary centre of the Universe and everything else moved around it.
It was people like the following that really figured out where Earth fits in the Universe and how it moves:
| Nicolaus Copernicus | (1473-1543) | - proposed a Sun-centered universe to replace the old Earth-centred universe put forth by ancient astronomers like Ptolemy |
| Johannes Kepler | (1571-1630) | - proved planets follow elliptical orbits around the Sun and wrote the three Laws of Planetary Motion |
| Galileo Galilei | (1564-1642) | - studied the motions of objects, and using the first astronomical telescope, observed that not everything revolved around the Earth |
| Sir Isaac Newton | (1642-1727) | - developed and published the Universal Laws of Gravitation in his Principia - proving why orbits are ellipses |
| Harlow Shapley | (1885-1972) | - determined the size and shape of the Milky Way Galaxy |
| Edwin Hubble | (1889-1953) | - discovered the Galactic Universe - our galaxy is but one of a huge number of galaxies receding from each other |
| Albert Einstein | (1879-1955) | - discovered the Relativity of Space-Time, and applied it to Mercury's fast orbit |
Now we know the Earth rotates on its axis, and it revolves around the Sun which revolves around the Milky Way Galaxy.
OK, so if the Earth moves, then how fast are we moving?
To answer the question we need to understand that the Earth is moving in a number of different directions all at the same time.
(For the "purists" in the audience I am going to talk about speed, not velocity vectors, to keep things simple.)
Let's look at each type of movement separately:
1. The Earth Rotates on its axis once a day
2. The Earth-Moon system orbits a common point
3. The Earth Revolves around the Sun once a year
4. The Sun and Planets revolve around the Solar System Barycentre
5. The Earth's Orbit precesses every 25,770 years
6. The Sun Revolves around the Galaxy once every 250,000,000 years
7. The Galaxy is moving through the Universe
8. So what's the total?
0. Summary
10. So why is this important?
1. The Earth Rotates on its axis once a day
- The Earth has a circumference (distance around at the Equator) of approximately 40,075 km (24,901 mi)
- The Earth rotates on its axis relative to the Sun in one "mean solar day", but as explained
here, it rotates exactly
360° in one "Mean Sidereal Day" which is 86,164.0909 seconds, or 23 hrs 56 min 4.0909 seconds
- If you were standing on the North or South Pole you would rotate very slowly - taking an entire day to just turn around
- If you were standing on the Equator, you would be going all the way around the distance of Earth's circumference in one day - a lot faster!
- As explained here, 1° of Longitude (i.e. an indication of how far you move) depends on your Latitude
and ranges from 0 (nothing) at the poles increasing towards the Equator
- So, how far you travel during one Earth rotation depends on the cosine of the Latitude of your location.
- The actual formula is: distance in km = 360 * (111.41288 * cos(latitude) - 0.09350 * cos(3 * latitude) + 0.00012 * cos(5 * latitude))
- To make things simple, we'll calculate the speed at the Equator
- speed = distance/time = circumference/time = 40,075 km / 23 hrs 56 min 4.0909 seconds = 1,674 km/hr (1,040 mi/hr)
- Yes - this is faster than the speed of sound! which is called Mach 1 and is 1,192 km/hr (740 mi/hr). (It's a good thing our atmosphere rotates with us!)
- (This is also the reason that historical astronomers thought the Earth had to be stationary - they thought the winds would blow us all off the planet.)
- At the latitude of Calgary, Alberta (51° N) we are traveling at 25,271 km / 23 hrs 56 min 4.0909 seconds = 1,056 km/hr (656 mi/hr) which is below the speed of sound
- Note - The Earth rotates from West to East, so as you read this you are traveling at approximately Mach 1 towards your eastern horizon
- It would take a military jet traveling at Mach 1.4 flying East to West at the equator to counteract the Earth's rotation and keep the Sun directly overhead.
- On the other hand, you could walk in a small clockwise circle around the North pole, taking 24 hours, and keep pace with the Sun as well (in the summertime of course).
- By the way, the Earth's rotation is slowing down - about 1 second every 40,000 years.
- Also Note - relative to the distant stars, you spend half the day traveling towards them, and the other half the day traveling away from them.
- So when the day is over, you actually haven't moved much at all due to the Earth's rotation!
- This is summarized in the diagram below:
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2. The Earth-Moon system orbits a common point
- The Moon doesn't orbit a stationary Earth
- Both the Moon and the Earth orbit the "barycenter" of the Earth-Moon system (sometimes called the "common centre of gravity" although that term really applies only to a single rigid body)
- The mass of the Earth (ME) is 5.9742 * 1024 kg, and the mass of the Moon is 7.349 * 1022 kg
- This means the ratio of the masses is 81.3
- This barycenter point is therefore located 1 unit from the Earth's centre and 81.3 units from the Moon's centre
or 1 / 82.3 times the distance from the centre of the Earth to the centre of the Moon which averages 384,500 km
- 1 / 82.3 * 384,500 km = 4672 km from the centre of the Earth (4672 / 6378 = about 3/4 of the way to the surface, i.e. it's within the Earth itself)
- The barycenter also moves as the Moon's elliptical orbit constantly changes the actual distance between them, but the mass ratio remains constant
- This means the Earth pivots around this point once every Lunar Month
- The maximum speed this could impart to any point on the Earth would therefore be 2 * π * R / one Lunar Month
- which works out to 29355 km / (29.53 days * 24 hr/day) = 41 km / hr - a number small enough to ignore
- Note: it is the Earth-Moon barycenter that actually orbits the Sun, not just the Earth itself, but this can be ignored in these rough calculations
- This is summarized in the diagrams below:
ANIMATION - click the image below to open a new page with a 220 KB animation of the Earth-Moon barycenter.
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3. The Earth Revolves around the Sun once a year
OK, in Section 1 we realized we were traveling near the speed of sound but actually getting nowhere over one day. So, how about in a year?
- The Earth's orbit around the Sun is an ellipse with an eccentricity (flattening) of 0.0167
- The Earth travels at different speeds during the year - slowest at Aphelion (furthest point from the Sun) and fastest at Perihelion (closest point to the Sun)
- Since the orbit is nearly a circle, and to avoid involving calculus, I'll treat the Earth's orbit as a circle with an average diameter
- The average radius of the Earth's orbit is 149,597,871 km (92,955,807.46 mi)
- Therefore the "circumference" of Earth's orbit (the path) is approximately 2 π R or nearly 940,000,000 km (580,000,000 mi) around
- It takes one year to go all the way around
- The "year" is not exactly 365¼ days (sometimes called the Julian Year).
- Even with our calendar rules for leap years and century leap years, it is not 365.2425 days (the average Gregorian Year)
- With respect to the distant stars, the "Average Sidereal Year" is 365.2421896698 days or about 99.999915 % of the average Gregorian year.
- So the Earth travels about 940,000,000 km in 365.2421896698 days
- speed = distance/time = circumference/time = 939,951,145 km / (365.2421896698 days * 24 hr/day) = 107,229 km/hr (66,629 mi/hr)
- This is 64 times faster than our rotational speed, or about Mach 90!
- In one day the Earth travels only 1/365¼ of the way around its orbit or approximately 2,600,000 km (1,600,000 mi)
- Since the Earth is 12,756 km (7,926.21 mi) in diameter, the Earth moves approximately 202 times its own size in one day!
- It's a good thing the Moon and all our satellites are gravitationally bound to the Earth or we'd leave them in the interstellar dust!
- Also Note - relative to the distant stars, we spend half the year traveling towards them, and the other half the year traveling away from them.
- So when the year is over, we actually haven't moved much at all due to the Earth's orbit around the Sun!
- This is summarized in the diagram below:
- Can we add the rotational and orbital speeds together?
- Not exactly - the Earth is tilted 23.4393° with respect to the plane of the Earth's orbit so we are rotating at
an angle with respect to the way we go around the Sun.
- ANIMATION - Click the image below to open a new window with a 184 KB animation of the way the Earth rotates. (Close the new window when you are finished with it.)
- Mathematically, the rotation imparts only part of its value in the direction we are orbiting
which works out to cosine(23.4393°) * 1,674 km/hr, or about 1,536 km/hr (again, at the Equator)
- If we are traveling in our orbit towards a certain star, and we are also being carried towards that star due to the
Earth's rotation (say at night) then we can add the rotation effect. However, half a day later the Earth's rotation is away from the star so
we would have to subtract it.
- E.g. 107,229 km/hr + 1,536 km/hr = 108,765 km/hr, and 12 hours later, 107,229 km/hr - 1,536 km/hr = 105,693 km/hr.
- The rotational speed effect is only 1.4% of the orbital speed so it doesn't make a lot of difference, and it averages out to zero over a day.
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4. The Sun and Planets revolve around the Solar System Barycentre
- Does the Earth-Sun system have a barycentre (or "barycenter")?
- Yes, but since the Sun's mass is 1.9891 * 1030 kg it is 332,950 times heavier than the Earth.
- This means the Sun-Earth barycenter is 1/332951 times the average Earth Sun Distance or about 450 km
from the centre of the Sun (450 km / 696,265 km = 0.00065 of the way to its surface).
- So, although the Earth does cause the Sun to wobble around their common barycenter, it is a very tiny motion.
- On the other hand, Jupiter (the heaviest planet in the solar system) causes a much more appreciable wobble in the Sun.
- Using the Sun's mass (1.9891 * 1030 kg), Jupiter's mass (317.833 times Earth's mass = 1.8988 * 1027 kg)
and the average Sun-Jupiter distance of 5.2019 a.u. or 778,190,000 km) we get the Sun-Jupiter barycenter at 742,150 km from the Sun's centre
or about 46,000 km outside the Sun's surface!
- This means the Sun wobbles around a point just outside its surface every 11.859 years
(the length of Jupiter's orbit).
- Although slow, this wobble is detectable - and it also means the Earth is orbiting a slowly wobbling Sun!
Click here to see a diagram of the movement of
the Solar System Barycenter from 1944-1997
due to the effect on the Sun of Jupiter and all
the other planets.
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Click here to see a diagram of the movement of
the Solar System Barycenter from 2000-2051
due to the effect on the Sun of Jupiter and all
the other planets.
|
Click here to see an animation (to
scale) of the movement of the Sun
about the Solar System Barycenter
from 2000-2050 due to the effect
of Jupiter and all the other planets.
|
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5. The Earth's Orbit precesses every 25,770 years
As explained here (on my web page describing Right Ascension and Declination), the Earth's North-South
rotation axis "wobbles" like the slow rotational tilting of a spinning top over a period of 25,770 years. This is known as Precession
and affects the direction in the sky to which the North Pole points and, in fact, the orientation of the entire orbital path of the Earth.
Precession is caused by the gravitational attraction of the Sun (and the Moon) tugging on the Earth's equatorial bulge - trying to "level" it
from its 23.4393° tilt, but never winning. Due to the laws of motion (and something called "angular momentum") the axis keeps its tilt, but the tugging force causes the axis to
wobble around in a circle rather than "straightening" up.
Since this is 25,770 times slower than Earth's orbital speed, we can ignore it for the purposes of these calculations.
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6. The Sun Revolves around the Galaxy once every 250,000,000 years
OK, in Section 3 we realized we were traveling near Mach 90 but actually getting nowhere over one year. So, how about in a Galactic Rotation?
- The Sun's position in the Milky Way Galaxy is about 2/3 of the way out from the center to the edge of the galactic disk,
(and about 20 light years north of the galactic plane).
- Estimates of the Sun's distance from the centre of the Milky Way Galaxy range from about 25,000 to 28,000 light years (a light year is 9,460,536,000,000 km)
- OK, so lets assume the Sun is about 26,500 light years from the centre of the Galaxy
- It is estimated that the Galaxy rotates once every 250 million years (so the Sun has completed about 18 orbits during its 4.5 billion year lifetime)
- Again, although the Sun's orbit is probably an ellipse with an apparent "nodding" up and down motion through the galactic plane as it goes, we'll assume a circle
- speed = distance/time = circumference/time = 2 π R / 250,000,000 years
- This works out to 1,575,000,000,000,000,000 km / (250,000,000 years * 365.2421896698 days/year * 24 hr/day) = 719,000 km/hr (447,000 mi/hr)
- This is about 6.7 times faster than our orbital speed and 430 times faster than our rotational speed (at the Equator)
- It's a good thing the Solar System is gravitationally bound to the Sun or it would leave us floating in interstellar space in no time!
- Also Note - relative to the distant galaxies, we spend half a galactic rotation traveling towards them, and the other half a galactic rotation traveling away from them.
- So when the 250,000,000 year galactic rotation is over, we actually haven't moved much at all due to the Sun's orbit around the Galaxy!
- This is summarized in the diagram below:
The yellow arrow indicates the location of our Sun. Credit: NASA/JPL-Caltech/R. Hurt
- Can we add the Earth's orbital speed to the Sun's Galactic speed to get a total?
- Not really - relative to the plane of the Milky Way Galaxy, the Earth and other planets orbit the Sun kind of "up and down", in other words the Solar System is tipped on its
side as the Sun goes around the Galaxy so the speeds don't really add or subtract - they are almost at right angles to one another
- The diagram below by Brian Fenerty shows this relationship: (click on the diagram to see an animation of Earth's orbital motion in this frame of reference.)
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7. The Galaxy is moving through the Universe
- The Milky Way Galaxy and the Andromeda Galaxy are approaching each other at about 400 km/s
- The Milky Way Galaxy is orbiting among the Local Group of Galaxies
- The Local Group of Galaxies are racing towards something called The Great Attractor
- And, galaxy groups are racing away from each other due to the expansion of the Universe.
- All these impart additional motions that could be considered, but I'm going to skip these since it would take too long.
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8. So what's the total?
- To determine the total effect of all these different motions, we need to measure our speed versus some "stationary" object similar to how a car's speed is measured relative to a "stationary" road.
- However, every star, galaxy, even distant pulsars and quasars have some kind of motion relative to the Earth
- For a long time scientists thought it was not possible to directly measure the direction and speed of Earth's motion
- Then scientists discovered the Cosmic Microwave Background (CMB) radiation - electromagnetic radiation that originated from the Big Bang
- At first, this radiation seemed to arrive at the Earth from all directions at the edge of the observable universe with a constant value
- Recently, better instruments (on satellites) have been able to measure not only slight differences in this radiation from place to place,
but also the "Doppler shift" which is caused by the Earth moving towards one part of it and away from the part "behind" us
- The "Doppler shift" causes some of it to appear "redder" (red-shifted behind us) and some of it to appear "bluer" (blue-shifted in front of us)
- This can be seen in the all-sky image below:
- Finally, we could measure our speed relative to something that was so far away it could give a reasonable answer
- According to the Astronomy Picture of the Day at http://antwrp.gsfc.nasa.gov/apod/ap050508.html
"The map indicates that the Local Group moves at about 600 kilometers per second relative to this primordial radiation in the direction of approximately 10h Right Ascension and -20° Declination" (a point in the constellation Hydra between Sextans and Antlia).
- 600 km per second works out to 2,160,000 km/hr (1,342,000 mi/hr)!
- Yes - over 2 million km/hr! (but this is still only about 0.2% of the speed of light)
- And you thought you were sitting still?!
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9. Summary
(all number are approximate as described in the text above)
| Component |
Metric
per hour |
U.S.
per hour |
Metric
per second |
U.S.
per second |
| Earth's Rotation |
0 to 1,674 km/hr
(depends on latitude) |
0 to 1,040 mi/hr
(depends on latitude) |
0 to 0.465 km/sec
(depends on latitude) |
0 to 0.288 mi/sec
(depends on latitude) |
| Earth's Orbit around the Sun |
107,229 km/hr |
66,629 mi/hr |
29.7858 km/sec |
18.5081 mi/sec |
| Sun's orbit around the Galaxy |
719,000 km/hr |
447,000 mi/hr |
200 km/sec |
124 mi/sec |
| CMB value (total) |
2,160,000 km/hr |
1,342,000 mi/hr |
600 km/sec |
373 mi/sec |
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10. So why is this important?
Imagine you were trying to locate planets orbiting distant stars. Since it would be almost impossible
to see such a planet through a telescope you would need another method to detect it.
The method used is to take spectroscope pictures of stars over and over again and look for a "Doppler effect" - lines in the star's spectrum that
shift back and forth due to the star wobbling around the barycenter between it and its orbiting planet(s).
Sounds simple enough, but the Earth is moving in a number of different ways and therefore so are the telescopes used to take the
pictures (whether they are on the surface of the Earth or in orbit). All these different motions would show up in the spectrum of a distant star, not
because the star is "wobbling" but because we are.
So, first you would have to take the spectrophotographs, then measure the shifting lines, then subtract the Earth's motion at the time the image was taken and
then see what is left - and do this over and over again until you are sure that what you are measuring is due to a planet orbiting a distant star.
This is the challenge faced by the teams that are detecting distant planets.
Here is a link to a pdf file from the Berkeley Science Review on finding exoplanets
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