Hi Mohammed,

The primary factor that affects the 'orbital lifetime' of a satellite is atmospheric drag, which itself depends on atmospheric density and the form factor of the object flying into that atmosphere: this is why a higher altitude (for circular orbits) is always associated with longer lifetimes. Things become more complicated when the orbit is highly elliptical, as the net drag over a full orbit is largely controlled by the altitude of the perigee.

The denser the atmosphere, the more critical it is to have a satellite with an aerodynamic shape: See

https://spaceflightsystems.grc.nasa.gov/education/rocket/shaped.html

for more details.

Since your question is about "perturbations", I assume you are more concerned about the environmental (atmospheric) factors that affect drag than the shape of the satellite. In this case, you need to know that the vertical profile of atmospheric density depends on the distributions of pressure and temperature, and in particular on the heating and cooling rates at the altitude of interest.

One important factor that would strongly affect the density profile is solar activity, as an enhanced influx of radiation and particles would provide some additional heating to the atmosphere and therefore change its properties.

Another useful web site on this issue is

http://www.swpc.noaa.gov/impacts/satellite-drag

Lastly, remember that adding some propulsion device to your satellite would allow you to apply orbital corrections from time to time, thereby allowing for a longer lifetime, though of course this would not be possible on nanosatellites like CubeSats.

I hope this helps. Cheers, Michel.

Thank Michel , but what about effect of Gravitational perturbation?

Hi Mohammed,

This is an interesting question: in first approximation, the gravitational potential of the Earth is broadly symmetrical at large scale, but quite heterogeneous if you start investigating it in detail at smaller scales. This is because of the non-spherical shape of the planet, important variations in mass distribution (e.g., mountain peaks versus ocean dips) and density (e.g., between rocks, water and air), as well as the displacement of masses within the system (in the Earth's core, in geophysical processes responsible for plate tectonics, or in atmospheric and oceanic currents, including tides, for instance).

These will perturb the orbit, which will therefore not be circular or a simple ellipse, for instance, but I think the impact on the lifetime of the satellite will be minimal. This is like riding in a car on a bumpy road: you get lots of vibrations and perhaps shocks, but you still pursue your travel. The processes we discussed earlier are more like friction, or brakes, which, in the case of the satellite, will force it back to the surface.

Think of this as follows from a physical point of view: for a circular orbit, the gravitational force is essentially perpendicular to the velocity vector, while the force that brings the satellite back down is a drag that acts in the opposite direction of (hence 'parallel' to) the velocity vector.

Thus, for gravitational perturbations to have an effect on satellite lifetime, they would have to have a non-zero force component along the instantaneous velocity vector direction (this actually happens for elliptical orbits), AND this component should be systematically larger in deceleration (between the perigee and the apogee) than in acceleration (between the apogee and the perigee). My guess would still be that this is a secondary effect compared to the other processes, as far as the lifetime of the satellite is concerned.

Cheers, Michel.

I agree with Michel, at 600Km the atmospheric drag is by far the main driver on your orbit lifetime, but even as the strongest component it is not "very" strong. To demonstrate, you can take an estimation of the maximum atmospheric density from the ESA standard on this topic provided to the European space industry for just such calculations:

https://www.spacewx.com/Docs/ECSS-E-ST-10-04C_15Nov2008.pdf

Table G-3, the sum of all elements at 600Km altitude comes to 4.5E+13 molecules per m³. As the majority is atomic oxygen, lets take a molecular mass of 16 a.m.u. as an average. So with the molecules standing approximately still, and your satellite hitting them with about 7.6Km/s, you will "reflect" the molecules and change their relative impulse by 2*7.6Km/s*16a.m.u., and of course the satellite will loose the same amount of relative impulse: 2.5E-23 kg*m/s. Assuming a typical 1x1 cubesat mass of 10Kg, that gives you a Delta-V per collision of: 2.5E-24 m/s.

Now, with a typical surface area of 10cm x 10xm in flight direction (0.01m²), and an orbital length of about 44 000 Km, after one orbit you will have hit every molecule in a tube with a volume of 44 000 000m x 0.01m² =  440 000 m³. With the given molecular density at this orbital height, this comes down to 44 000 x 4.5E+13 = 2.0E+19 collisions per orbit. Multiply this with the "per collision" effect, and you get a Delta-V per orbit of 2.0E+19 x 2.5E-24 = 5.0E-5 m/s. With about 15 orbits per day, this adds up to 0.27 m/s per year.

Orbital speed of a circular orbit is approximately the square root of the quotient between the standard gravitational parameter and the length of the semi-major axis. So a 600Km orbit about earth is linked to an orbital velocity of sqrt(4.0E+14 m³/s²/7 000 000 m) = 7559.29 m/s. Reducing this by 0.27m/s over the duration of a full year will reduce your semi-major axis to 4.0E+14 m³/s² / (7599.02 m/s)² = 7 000 500 m. Looks wrong, but what happens is that your orbital speeds matches a higher orbit than the one you are on, therefore you will drop, which will increase your speed, until you reach a new equilibrium. Luckily, as potential energy is twice the kinetic energy, it is easy to calculate that you will reach this equilibrium at 500m below your starting altitude.

So starting at 600Km, you will only drop half a Km per year, i.e. you will stay up much longer than your S/C will stay alive.

Now, this is already strong worst-case assessment of the orbital drag, not each collision will be elastic, not every molecule will hit a perpendicular surface and thus could introduce a lower loss of impulse. Also table G-3 of the ECSS standard is for maximum conditions at the solar maximum, if you launch within the next few years, atmospheric density in the LEO can be more than an order of magnitude below this figure. So you may drop even slower than the 0.5Km per year predicted above.

That is why you will need to consider both the shortest and longest orbital lifetime of your satellite, as a too long orbital lifetime after the loss of commanding capabilities can put you in conflict with space debris laws.