How can the satellite have an centrifugal force?

[revesz]

Imagine a universe with nothing in it exept for the earth. Now if you were to put a satalite up in space with a geosyncronized orbit, the gravity of Earth would not pull the object down. but how can that happen if the Earth is not spinning? At least not spinning relative to anything(because there is nothing), so there is no gravity at the altitude that the satalite is at. and if you were to place the satalite any further out it would just fly off into space. How can this happen?

How can the satalite have an centrifical force(or momentum), if there is nothing to be moving relative to?
and why wouldn't this happen in reality, or would it?

 

[enigma]

Originally posted by revesz
so there is no gravity at the altitude that the satalite is at.

Whatever gave you that idea?

The gravity due to a body at any and every point in space is given by:

F=G\frac{Mm}{r^2}

Where
G is the gravitational constant
M is the mass of the attracting body
m is the mass of the satellite
r is the distance between them

 

[revesz]

If that is not true, then what prevents geosyncronized satalites from crashing to earth? If all motion is relative you may observe both the Earth and the satalite as stationary, so there would be no centrifical force holding the satalite up, and so it would be pulled down be gravity.

 

[enigma]

According to Newton's First Law, an object will go in a straight path unless acted upon by a force.

That is what would happen to a satellite if there were no gravity: it would continue in a straight line forever, and it would not be in an orbit.

The satellite is geo-synchrinous because it goes around the Earth once every 24 hours - the same period as the Earth's rotation.

Now if you assume that the Earth isn't going through it's daily rotation, then a geo-synchronous orbit would be impossible. A satellite which is now in geo-synch would be orbitting once every 24 hours, and a satellite which appears to be geo-synchronous (not moving tangentially) would crash into the Earth in a matter of hours.

Does that make sense?

 

[revesz]

Yes it does make sense, but I'm just really confused about momentum. If its all relative then what if you view the satalite and Earth while spinning really fast, the geosyncronized satalite will be orbiting around the Earth and so it would have enough momentum to hold its possition or even fly off into space. I know this is not true because it doesn'y make sense, but how do you decide wether something has momentum or not?

another question: can an object such as the Earth be spinning around only one axis, or can it have 2 or 3? for example take the earth, it is rotating around a line between the north and south poles, can you have rotation around opposite sides of the equator at the same time, or does this just move the axis?

 

[enigma]

If the Earth is spinning really fast, then the geo-synch satellite isn't going to be a geo-synch satellite.

The only thing special about geo-synch is its distance from the Earth.

Satellites in low Earth orbit (LEO) go around once every 45 minutes or so. The farther out you go, the slower the satellite goes, and the longer the orbit lasts. GPS satellites are in an orbit about 25000km up, and they go around once every 12 hours. Geo-synch sats are in an orbit 36,000km up, and they go around every 24 hours. The moon is in an orbit over 100,000km up, and it goes around once every 28 days.

If you take a Geosynch satellite, and speed up the rotation of the Earth to 45 minutes (somehow), then the satellite will still be orbitting once every 24 hours at an altitude of 36,000km. Nothing will change except it's title. In this case, the LEO satellites are the ones which are geo-synchronous, because they go around once for every rotation of the Earth.

 

[russ_watters]

Originally posted by revesz
Yes it does make sense, but I'm just really confused about momentum. If its all relative then what if you view the satalite and Earth while spinning really fast, the geosyncronized satalite will be orbiting around the Earth and so it would have enough momentum to hold its possition or even fly off into space. I know this is not true because it doesn'y make sense, but how do you decide wether something has momentum or not?

I think the problem here is this rotating frame of reference you've constructed. You cannot call it stationary - you can tell you are rotating by the effects of the rotation, the various forces felt and observed in action. As a result, you CAN measure the rotational rate of the Earth and the speed of a satellite in orbit.

another question: can an object such as the Earth be spinning around only one axis, or can it have 2 or 3? for example take the earth, it is rotating around a line between the north and south poles, can you have rotation around opposite sides of the equator at the same time, or does this just move the axis?

Certainly. Google a "multi-axis trainer." You get to play on it in Space Camp (if you can hold your lunch).

And sorry to nitpick enigma, but an orbit at LEO distance takes roughly 90 minutes and the moon is roughly 340,000 km away. You're right on the GEO distance though.

 

[HallsofIvy]

"Spinning" involves acceleration, not just straight line motion at a constant speed, and so is NOT relative. If the Earth were the only object in the universe, people on it could still detect and measure its rotation.

 

[enigma]

Originally posted by russ_watters

And sorry to nitpick enigma, but an orbit at LEO distance takes roughly 90 minutes and the moon is roughly 340,000 km away.

Uh, yeah, right. Good catch

That's what I get for posting at 2AM after looking at GPS satellite data all day long (which are visible for 45 minutes)

Guessed on the moon distance.

 

[russ_watters]

Originally posted by enigma
...after looking at GPS satellite data all day long (which are visible for 45 minutes)

Is that what you do for a living? Who do you work for if I may ask? I applied for a job at Lockheed doing systems integration for GPS III. They build the satellites about 10 miles from where I live.

"Spinning" involves acceleration, not just straight line motion at a constant speed, and so is NOT relative. If the Earth were the only object in the universe, people on it could still detect and measure its rotation.

Incidentally, I recently participated in a conversation on www.badastronomy.com about this phenomenon. Nothing we could say could convince this one guy of what you just said. Not even a dozen links to info about pendulums could convince him that the Earth rotates on its axis in 23h56m not 24h00m.

 

[enigma]

Originally posted by russ_watters
Is that what you do for a living? Who do you work for if I may ask? I applied for a job at Lockheed doing systems integration for GPS III.

No. I'm still a senior at the moment. I'm doing a project for a space navigation class which reads in satellite ephemeris data and pseudoranges to an observation site, converting the ephemeris data into Earth fixed coordinates and trilaterating with 4 satellites to obtain the site location and clock bias.

The professor does that kind of stuff for a living at NRL. Based on his class there is no way I want to do that for the rest of my life... I'm blind enough now as it is. Can you imagine looking at this kind of stuff for 8 hours a day?

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