Putting a satellite into orbit

[wizzart]

Geez it's been ages since I last was here. Anyway, I was thinking a little on the subject below and remembered this place. It's probably ridiculously trivial, but still I wonder:

A satellite stays in orbit around the Earth because it's falling at the same pace as the Earth's surface curves, simply put. But that's a sattelite in stationary orbit. What happens if I release a sattelite in an orbit that's to high for it's speed? My guess: it falls back to Earth and because it's angular momentum needs to be preserved it gradually picks up more tangential speed until it lands into a stationary orbit, which would be somewhere between the orbit where it should've been and where it was released...

Correct or rubbish?

 

[DaveC426913]

What happens if I release a sattelite in an orbit that's to high for it's speed?

You've put it in an elliptical orbit. Its apogee (maximum altitude) is where you released it, its perigee (minimum altitude) will be where it is closest to the Earth (but moving fastest). Provided the perigee is still above Earth's atmospheric drag, it will remain in that stable, elliptical orbit.

BTW, ALL orbits are elliptical, though some have an eccentricity of nearly zero (meaning it is nearly circular).

gradually picks up more tangential speed until it lands into a stationary orbit, which would be somewhere between the orbit where it should've been and where it was released...

Rubbish. See above.

...stationary orbit...

There is no such thing as a "stationary orbit".

 

[wizzart]

hm...sounds plausible too

There is no such thing as a "stationary orbit".

Well, quasi-stationary then...slowly spiralling down to earth.

 

[Farsight]

The thing to note, wizzart, is that if you're in an orbiting spaceship and you want to get into a higher orbit, you put your foot on the gas and go faster.

You don't point the nose up and fire the rockets, because that doesn't give you the forward velocity that stretches your arc of fall into a bigger circle. It would just give you an eccentric orbit, like Dave says.

 

[BobG]

hm...sounds plausible too


Well, quasi-stationary then...slowly spiralling down to earth.

I think your term, stationary, is wrong, making readers wonder what you mean. Do you mean stable orbit? Circular orbit?

Any object with any tangential velocity at all travels in an elliptical orbit. Some of those orbits just happen to intersect the Earth (a Roger Clemens fastball, for example).

If the satellite's trajectory misses the Earth and is high enough that it isn't affected by the Earth's atmosphere, the satellite's mechanical energy stays constant through the entire orbit. The balance between potential and kinetic energy just changes.

As DaveC explained, by time the satellite reaches perigee, it has enough kinetic energy that starts gaining altitude again and returns to the same point it started. The orbit is just as stable as a circular orbit. The orbit remains elliptical and never becomes circular.

The only way the satellite spirals down to Earth is if the satellite is low enough to be affected by the Earth's atmosphere. Generally, only satellites with an altitude lower than 1000 km are affected and circular orbits are affected more than elliptical orbits. In this case, atmospheric drag is decreasing the total mechanical energy rather than just changing the balance between potential and kinetic.

Edit: For an elliptical orbit where perigee is low enough to be affected by atmospheric drag, your assumption would be correct. If you slow a satellite at perigee due to atmospheric drag, it's not the perigee altitude that changes; it's the apogee altitude. As soon as the satellite was slowed, a new orbit was created and the satellite's current location has to be part of that new orbital ellipse. So atmospheric drag would slowly decrease the apogee height until you had a circular orbit, at which point the satellite would 'spiral' into the Earth's atmosphere.

 

[WhyIsItSo]

hm...sounds plausible too


Well, quasi-stationary then...slowly spiralling down to earth.

Did you mean Geo-Stationary?

 

[DaveC426913]

Well, quasi-stationary then...slowly spiralling down to earth.

There is no such thing as a quasi-stationary orbit. The words stationary and orbit used in conjunction with each other are very nearly an oxymoron. (The only combination that makes sense is geo-stationary orbit which is something completely different and has nothing to do with this thread.)



An orbit that is "slowly spiralling down to earth" is an orbit that is decaying. The only thing (within reason) that could be causing this is drag, sapping forward motion from the satellite.

I think the term you are looking for is stable orbit. Unless acted upon by an outside force (such as another gravitational body, or friction) (or, an inside force such as rockets), a satellite will remain in a stable elliptical orbit. Period. This is critical to your understanding of orbits.


Now, if you play with the adjustments carefully, you can get the satellite's orbit to have virtually zero eccentricity, meaning its orbit is circular, and meaning that it will move around while maintaining a constant altitude above the Earth.

 

[DaveC426913]

Look at the attached illo.

 

[wizzart]

Dang, it's right here in my 1st year Relativity book...need to critically review some of the old stuff I guess.

As for stationarity: stationary to me means nothing changes. For the orbiting object everything changes constantly, without drag the orbit itself (circle or ellipse) doesn't change shape, hence my use of the word stationary. If you prefer stable, I can see why.

 

[DaveC426913]

Dang, it's right here in my 1st year Relativity book

You're in post-2ndary??

 

[wizzart]

Dude, I'll make it a lil worse...I'm one subject away from my bachelors degree :P Did research on noise in Quantum Dots and all that.

The mechanics course was 5 years ago, and back then I didn't really get the whole orbit stuff (and the big point in the course was relativity, so I got away with it)...read through it again now and makes perfect sense. It's just one of those questions that pops into your head and you go "I'm pretty sure I should know this...but I don't".