Satellite Speed Challenge

Dear Jorrie

Yes, that is true. Velocity of the satellite decreases with drag force.

Lower the orbit, lower is the required velocity to remain in orbit and greater is the friction. However, satellite still remains at geostationary orbit for long and only keeps drifting towards earth for a final fall. There are stearing rockets that keep the fuel gas for few years in orbit by bringing back satellite in place. Satellite not only has circular or elliptic or parabolic rotatory motion, it also has spin motion such that it is not driven out of the orbit easily by winds of all types including solar winds and radiation push ups and air drag. There must be some effect of moon also on the satellite if satellites are far from earth. I am not a perfact space research man and can't give you exact data on all forces influencing the satellite motion but sure all these I need to look into if I have to plan and compute one satellite launch myself.

Shyam, you said: "Lower the orbit, lower is the required velocity to remain in orbit and greater is the friction."

I'm also no expert, but this sounds the wrong way around to me! Are lower orbits not faster?

Low Earth Orbit (LEO) satellites are surely not geostationary? They whiz around Earth in about 90 minutes! Geostationary satellites, on the other hand, surely encounter no atmosphere at 35 000 km up?

That is funny with all geo-stationary satellites.

In geo-stationay satellite system - farther you go faster you need to move to keep to the same place with respect to earth. Near you are slower you move to keep at the same relative place to the earth.

Earth spin is to be matched with the freater satellite velocity to move together. Hence, there is an optimum orbit for it. If you are below that, then you move slow, and if you are above that then you move faster to keep looking at the same point on the earth. This, getting into orbit is never perfact so life of the satellite is affected by orbit launch.

You end up wasting fuel to keep the satellite in position else it drifts away and becomes useless.

What else is the possible way?

Shyam, when you write: "In geo-stationary satellite system - farther you go faster you need to move to keep to the same place with respect to earth. Near you are slower you move to keep at the same relative place to the earth", I am afraid that you are missing it completely!

Satellites cannot be geo-stationary and in low-earth-orbit at the same time. Geo-stationary orbits only exist at about 35 786 km height, where the natural orbital speed is 3.075 km/s - nowhere else!

So to get the challenge back on track, it is about normal low-earth-orbits, say at between 200 and 500 km altitude, where there is a measurable amount of drag from air molecules. The question is, do the air molecules slow the spacecraft down?

Sorry, Jorrie. I completely misunderstood your question.

The atmospheric drag will alter the orbit of the satellite. The net effect would be to lower the orbit towards Earth. In so doing, the velocity of the spacecraft or satellite would increase, not decrease. However, the orbit would not be stable and a reentry would follow at some point.

Interestingly enough, the effects of the sun and the solar radiation pressure will tend to puff up the atmosphere a little on the day side of Earth and aggravate the situation of drag.

Sorry, that is not true.

Kepler's second law states that the orbit of objects about a central mass sweep out equal areas over equal time. That means that objects closer to the Earth have a higher orbital velocity versus objects further away.

Remember Skylab? Round and round it goes, where it falls, no-one nows!

You are right. There is lots of debrid above that is human made. We are dirty not only on earth but where ever we go. Time to invent some kind of space JHADU that can be used for cleaning space including those skylabs.

Well, I think that drag is a factor, but not really a large one. There are two primary reasons orbits are impacted at low altitudes and result in a perturbed Keplerian orbit.

First, orbital speeds for satellites change due to the ellipsoid composition of the Earth. The Earth is not a true sphere, nor is it a true ellipsoid! Additionally, the gravity density of the Earth's geoid is not consistent (producing a non-central gravitational field) and varies in both latitude and longitude. Even though the satellite orbits about the Earth's center of gravitational mass, the satellite experiences abnormalities as it circles the globe. Polar orbits are even more subject to this effect.

Second, orbits are impacted by the crossing of the equatorial bulge of the Earth in two ways. First there is the non-radial component force on the satellite that produces a torque that results in the rotation of the orbital plane of the satellite relative to the Earth. This effect is zero fro a true polar orbit, but is at its maximum for an equitorial orbit about the Earth as the Earth rotates. Second, the equatorial bulge produces a harmonic perturbation each time the satellite approaches the crossing of the equatorial plane, which speeds up the orbit at that point and slows back down as it moves away from the equatorial plane.

Additional elements that affect the ephemeris orbital data are tidal forces from the moon (the larger affect) and the sun (as well as other planets to a smaller degree) and the solar radiation pressure (A.K.A solar wind (which is nil when the satellite is in the Earth's shadow)). The magnitude of the solar radiation pressure depends on the cross sectional area and mass of the satellite.

Although the affect of all of these forces are individually small, the impact is the sum of these factors and over time will change the orbit significantly. For example, the moon alone can displace a GPS satellite as much as 25 meters from its predicted orbit over the course of 24 hours!

There are too things.

There is a velocity for a geo-stationary orbit and if you miss it then have to waste fuel to keep it back. Also the orbit change requires velocity correction in opposit way. If you talk about simple satellite of any orbit and correspoinding velocity in the orbit then kinetic energy causing centrifugal force is to be balanced with gravitational pull. This can be easily achieved. This is not what for which we pay 2000 million dollars.

As satellites are increasing in mass there drag force is also increasing due to size. They are also kept low to get better picture of earth and reduce communication power losses, obtain greater focussed energy on the antenna, which is already very small. Solar panels are becoming bigger and bigger for power hungry satellites.

haha Jorrie you are diabolical....a person really has to read your guestion to understand . the velocity of the satellite decreases due to the drag of the atomsphere. but the orbital spped increases because as the velocity drops the orbital speed incerases ( or in other words it takes less time to orbit) so the slower it goes the faster it orbits. fascinating thanks for the brain tease ........Digger

Hi Digger, it's a pleasure! Just to 'tease your brain' a bit more, the speed increase is about more than what you stated "...or in other words it takes less time to orbit, so the slower it goes the faster it orbits..."

Circular orbital speed scales with the inverse square root of the radial distance from Earth's center of mass, i.e. Vo = sqrt(GM/r)...

i forgot to add that is true untill the satelite really gets into the atmosphere and loses os much velocity that it is below orbital speed and assuming some of it survives re entry, comes burning to earth ...... Digger

A lower orbit has a higher velocity. For example, Mercury moves much faster than Pluto. You are trading gravitational potential energy for kinetic energy. In orbits close to the earth where atmospheric drag occurs (a couple hundred miles) the velocity does not change much because this is small compared to the orbit radius (about 4000 miles).

Reply to Guest's "A lower orbit has a higher velocity."

Fine, but must the object not first slow down to lose altitude and then speed up to maintain the lower orbit? I recall that when Cassini was launched, it was launched in the opposite direction to Earth's movement around the Sun. This scrubbed some orbital speed (relative to the Sun) off the spacecraft, allowing it to fall in towards Venus for a gravity assist swing by.

Guest2

Jorrie,

Considering your past posting on math editors. Have you looked at using MathML for posting the equations? See http://www.w3.org/Math/

No, I have not seen it, but thanks, looks interesting. I normally use Tex and then copy and paste equations into the forum postings. I will check MathML out over the weekend.

Jorrie,

Back when I worked at the satellite test center, I "flew" low earth orbit satellites. They were launched with an elliptical orbit (roughly 700 x 200 Km) and with age they would decay to a little under 150 x 200 Km and then rapidly start spiraling in - the orbit would decay measurably each orbit. All due to atmospheric drag.

Hi LPMosher, thanks for the info.

Yes, I believe that the "re-entry interface" for orbiting satellites sits in the order of 122 km altitude. I have a feeling that this is where the drag starts to dominate the orbital mechanics, i.e., the orbital speed decreases for an inspiral, but I'm not sure. Any info on that?

Let me clarify this, if there is atmnospheric drag you won´t have a CIRCULAR ORBIT

Why?, just because the energy losses due to friction. A stable orbit could be circular, eliptic, or parabolic (a hiperbolic orbit don´t have a return), only if there are no energy losses. If you have energy losses the thing will be spiraling down to earth.

Of course a satellite is not designed to cross the atmosphere (no aerodynamical shape), so it will burn. But, let´s say it could survive somehow, you want to know its motion?. Well, you have a BALLISTIC problem (remember the ICBM missiles?), forget Kepler or orbital laws.

Regards from Mexico

Guest, wrote: "Let me clarify this, if there is atmnospheric drag you won´t have a CIRCULAR ORBIT".

Good point, but: if one wants to be perfectly correct, circular orbits do not exist in nature. There are lots of perturbations on orbits. Anonymous Hero discussed this in post no 6 above.

The small atmospheric drag on most satellites is also just a tiny perturbation on an otherwise nearly circular orbit. But, yes, there is a very small in-spiraling tendency with all but the very highest satellites, e.g. geo-stationary ones.

In Physics, electron moving at infinity also shakes another electron at the other end of the infinity. Let us be realistic in rules of thumb and not argu with quantum mechanics uncertaininty level where, satellite has a chance to disappear in nowhere without a trace like disappearing in thin air. Can you rule out that a particle of infinite velocity will not hit the satelite and push it away forever. What use talking such thing even though we all know about it and trust that.

Our real concern is our life below that crashing satellite. How safe is it in any way?

Free fall to earth always increases the velocity. In fact, that is no more an orbit but an spiral motion down towards earth heeding for a crash. It generally ends up in burning small debris but large amount of material still survives. Burning does't mean going CO2 as that is only for organic material.

I think this thread has run its course now, so I've posted the 'official' solution to my Blog. Thanks to all who participated in this quite fascinating discussion. I would appreciate further comments to be directed to my Blog.

Jorrie