Friday, July 29, 2011

Geostationary orbit: Are satellites faster than the space shuttle?

Two colleagues and I went out for lunch today and one of them asked what the word 'geosynchronous' meant. It's a term to describe the orbit of a satellite that appears to be stationary over the Earth, we answered, and then we all three pushed our imaginary glasses up the bridge of our noses.

We were half right with our explanation. Geosynchronous is a term used to describe the orbit of a satellite that moves at the same speed that the Earth rotates about its axis. However, because this orbit can be titled over the Earth like an angel with a lopsided halo, the satellite can appear to move north and south in the sky throughout the day, though it always stays over the same line of longitude.

A geostationary orbit, the one we often think of when we hear the word "geosynchronous," is when a satellite is in a geosynchronous orbit over the equator. In this kind of orbit, the satellite appears to be stationary over the Earth.

In the same way that a square is always a rectangle but a rectangle isn't always a square, a satellite in a geostationary orbit is always in a geosynchronous orbit, but not the other way around.

Communications satellites are often in geosynchronous orbits so that the antennas of ground stations can remain constantly pointed at the same spot in the sky. Weather satellites are also common geostationary orbiters so that they can constantly monitor the same spot on the Earth.

Back to our lunch discussion: How fast, we wondered over our kebabs, would a geostationary satellite have to be moving to stay stationary in the sky? The space shuttle orbiter, we know, orbits at around 8,000 meters per second (18,000 miles per hour) but it does a complete orbit in about 90 minutes. Would a geostationary satellite be going faster or slower?

To find out, I did a little math. To find the speed of an object, we divide the distance it crosses by the time it takes to cross that distance. (Speed equals distance divided by time.) The speed of the Earth's rotation is 465 meters per second, which we get from dividing it's circumference, 40,075 km, by 86,4000 seconds (the number of seconds in a day).

To find the circumference of the geostationary satellites' orbit, we add the radius of the Earth, 6,378 km, to the height of the satellite's orbit, 35,786 km, (which we obtained from Wikipedia) to get 42,164 km. We then multiply that number by 2*pi (the equation for the circumference of a circle is the circle's radius times 2*pi) to get 264,924 km.

Because the satellite has the same orbital period as the Earth's rotation, we divide the orbital circumference by 86,400 seconds and we get 3,066 meters per second (or 6,858 miles per hour) -- quite a bit slower than the space shuttle. Still, that's way faster than the average bear.

19 comments:

  1. For my conceptual astronomy class, I often express Kepler's Third Law (P^2=a^3) not as a formula in terms of distances and times, but as a description in terms of speeds: a planet closer to the Sun orbits faster than a planet farther from the Sun. Mathematically, if you assume circular orbits or T^2=r^3, you can rearrange this to be in terms of speed (use circumf/T=v) and you get that v^2∝1/r. (I don't give my students that derived formula, but in case you wanted a proof you can check my algebra.)

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  2. I'm confused. That last paragraph says did you see cradle satellite is going 6800 mph? Is it more like 33,000 mph

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    1. I was confused too. And are they talking about angular velocity or how fast it's moving through space or? And We have to take into account the Earth's gravity to keep it in orbit

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    2. Speed depends on height. And angular velocity is not measured in m/s or mph. It's rad/s

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  3. I'm confuse what is it talking about 600 i'm confuse what is it talking about 6858 mph. Geo secret all satellite is more like 32,000 mph

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  4. Is the satellite traveling with or against earth's rotation

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    1. Geosync sats always orbit in the direction of Earth's rotation as that's the only way they can maintain a relatively fixed position over a particular point. Satellites can otherwise orbit in pretty much any direction, but they would by definition not be Geosync sats if they did.

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  5. With the rotation. That's why it stays still in the sky.

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    1. Earth's rotation only comes into play at launch as it can add speed to the launch vehicle headed easterly. A launch to the west would need to overcome the speed of earth's rotation before gaining enough speed to stay in orbit. After that, in orbit the earth's rotation has no effect except on the earth view from orbit. Satellites going east to west are rare. North to south or visa versa orbits are not uncommon but the majority are variants of west to east, mostly at angles such as south-south-west to north-north-east.

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    2. All true, but in the context of the article and comments being about Geosync sats, they must orbit with the Earth's rotation. There is no way to simultaneously orbit against the Earth's rotation and also be Geosync. You can do either, but not both. Cheers.

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  6. what happens if a geo-satellite lost contact from ground station (so the ground station loses an ability to, say, turn on thruster)? does it get velocity and orbits the earth faster than earth rotation?
    may i see the valid references/sources please?

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  7. I disagree with all of you. If the Earth spins at 1038 mph or there abouts, (and we have no scientific experiments that detect this spin, in fact, Airy's Failure Michelson Morely, Michelson Gale and Sagnac prove it isn't spinning) but I digress.. then any object in a geostationary orbit Must Necessarily (no matter the distance from Earth), always spin at 1038 mph also. This speeding up and slowing down due to distance is a logical trap and a lie to bolster the heliocentric model. We do Not experience these conditions when measuring them in a lab the speed of an object always remains the same.

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    1. Think about the size of the orbit it needs to cover. I have my doubts about the heliocentric model myself but a merry go round goes much faster at the edges than it does at the center. It has to cover more distance in the same time. Simple math really.

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  8. What is the Spees of an object moving with same speed as earth moves if we kept the object in centre of earth in equator

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    1. Zero! If the object your are referring to is at the absolute centre of the earths rotation it has no speed. But this is only if the said object has no size or diameter itself, I.E the perfect centre of rotation. If the object your talking of has any size at all it will have a definate surface speed at whatever the radius you believe your object to be.

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  9. All speeds must be related to another object. Typically, orbital "speeds" are expressed in relation to the center of the object (planet, star) being orbited. Some commenters seem to be relating the orbits to the surface of the Earth, not its center. Obviously, a geo-stationary (& any other geosynchronous) orbit would, by definition, have zero speed in relationship to the surface point over which it orbits.
    In relation to the Earth's center, these orbits must be 164.6 thousand miles up. That makes the circle they cover equal to two Pi times 164.6 miles, which is 164.6 thousand miles. In twenty-four hours, that speed is about 6.86K miles/hour, or 1.9 miles/second.

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  10. satellites do no exist Earth is Flat

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  11. satellites maybe fake, but earth is a sphere for sure.

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  12. Earth does not exist, only satellites

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