I wrote a program to simulate the Tiangong-1 reentry.

To better understand how its orbit is changing, I created the attached graphs using 62 TLEs. For each TLE, I calculate the satellite's position, speed and eccentricity by mean of the SGP4 propagator. I collect those values for 5 orbits starting from the TLE epoch with a step of 0.5 s.

 

The "ecc min" and "spd min" behavior seem strange to me in the left half.

Is there any chance that the engines (main or RCS) was accidentally fired (I mean a malfunction)?

I change my question.

The POS/VEL graph (the one on the right) shows that the mean orbital speed is increasing as the mean altitude is decreasing, while I thought that the speed decreases because of the atmospheric drag and as a result the satellite falls to Earth.

Please, could someone explain?

Speed is indirectly proportional to circumference. IIRC, orbital drag causes a decay in altitude not speed. When the space station does a burn to push it deeper into space, it loses a little speed.

I'm not sure if Alan Pickup still does the re-entry stuff for NORAD, but he designed a program called SatEvo, which calculates the re-entry of orbital objects.

Speed is indirectly proportional to circumference. IIRC, orbital drag causes a decay in altitude not speed. When the space station does a burn to push it deeper into space, it loses a little speed.

 

I agree on your first and last phrases, but in my understanding, the drag is a force that decelerate the satellite, hence the satellite should slow down.

 

I'm not sure if Alan Pickup still does the re-entry stuff for NORAD, but he designed a program called SatEvo, which calculates the re-entry of orbital objects.

It seems no longer available.

https://en.wikipedia.org/wiki/Orbital_decay

 

Atmospheric drag at orbital altitude is caused by frequent collisions of gas molecules with the satellite. It is the major cause of orbital decay for satellites in low earth orbit It results in the reduction in the altitude of a satellite's orbit.

 

Tidal drag in an orbit can also decay by tidal effects when the orbiting body is large enough to raise a significant tidal bulge on the body it is orbiting and is either in a retrograde or is below the synchronous. The resulting tidal interaction saps momentum from the orbiting body and transfers it to the primary's rotation, lowering the orbit's altitude until frictional effects come into play.

 

Gravitational radiation is another mechanism of orbital decay. It is negligible for orbits of planets and planetary satellites, but is noticeable for systems of compact objects, as seen in observations of neutron star orbits.

There is no doubt that the atmospheric drag is the major cause of the loss of altitude.

My point is that the atmospheric drag is a force acting opposite to the motion of the satellite; it seems a paradox to me that the drag accelerates the satellite.

There is no doubt that that's true, but how that can be explained?

Edited June 29, 20178 yr by Cristiano

When an aircraft is moving faster than the minimum required speed, altitude is controlled by pitch and speed is controlled by the throttle. Slow flight (near minimums) is the opposite. On final approach, to control speed you'll apply pitch. To control altitude you'll apply throttle.

 

Re-entering objects are near minimums. Maintaining orbital parameters requires applying more velocity because it needs to travel a greater distance to maintain the same time period.

 

As the statement on tidal drag suggests, drag is not instant. It's a cumulative result.

While I'm very thankful for your explanations and for your patience, I still don't see a clear cause-and-effect rule.

Probably I should find something that links the kinetic energy with the potential energy for the orbital motion…

Edited June 29, 20178 yr by Cristiano

There is no doubt that the atmospheric drag is the major cause of the loss of altitude.

My point is that the atmospheric drag is a force acting opposite to the motion of the satellite; it seems a paradox to me that the drag accelerates the satellite.

There is no doubt that that's true, but how that can be explained?

I think you are thinking of the satellite as travelling in a straight line. It's not, it's actually continually FALLING towards the Earth, in a constantly changing direction.

So the speed that it gains, through a drop in altitude, (like a falling stone), is redirected to a rise in it's rotational velocity.

 

Something similar happens when a spinning skater pulls his arms in towards his body.

Probably the best answer I can get comes from an orbital mechanics book, where it is said that for an (unperturbed) elliptical orbit, the conservation of energy may be written:

 

V² / 2 = mu / r - mu / (2 * a)

To get a mental picture of it, I would picture a ball bearing on a hard surface.

If the surface is slightly downhill, the ball accelerates horizontally. So it loses potential energy due to it's vertical drop, and gains kinetic energy in a direction that it's rolling, at nearly 90 degrees to the drop.

 

The vehicle is basically rolling downhill as it drops in it's orbit. Instead of it's weight being balanced by a hard surface, it's balanced by the effective centrifugal force of it's orbit. But the effect is the same. It speeds up in a direction at approx 90 degrees to it's drop.