What Happens When a Silk Handkerchief Falls from Space?

Describe what happens when a silk handkerchief is jettisoned from the International Space Station. Take into account only gravity and air resistance.

Most equations about gravity include the term "ignoring air resistance".

If we melt a silk handkerchief into a pellet of bio-mass, then it would act like a pellet of lead (or at least carbon) and build up speed until it passed at great speed through the thickening atmosphere and burned up on its journey back to Earth.

But I think of a silk handkerchief as wafting back and forth in what must be a turbulent air-stream

If I drop a silk handkerchief (or a paper dart) from a tree, I expect it to drift slowly down until it reaches the soil.

If I drop a silk handkerchief from The Eiffel Tower (200 metres), I expect it to drift slowly down until it reaches the soil.

If I drop a silk handkerchief from a passenger jet cruising at 11,000 metres, I expect it to cope with the initial subsonic airspeed and then drift slowly down until it reaches the soil.

If I drop a silk handkerchief from the International Space Station orbiting at 400,000 metres, I expect it to behave initially like a missing wrench, hammer, or space-glove; that is, to gradually degrade its orbit and drift away from the ISS, dropping slowly into a lower orbit as its orbital velocity is reduced by the tenuous atmosphere at orbital altitudes.

This happens when a satellite in Low-Earth Orbit loses power – Earth's gravity gradually reclaims the satellite and the satellite burns up on re-entry.

But since the silk handkerchief encounters air resistance (like a canvas sail in the wind), then the silk handkerchief's speed through the atmosphere must be reduced.

Spectra - Material

Assume a material thirty-centimetres square that begins its journey earthwards in a two-dimensional planar state. A one-inch thick steel plate would preserve its rigid state until it began to melt.

(1) 25 mm thick steel plate

(2) 10 mm thick steel plate

(3) 1 mm thick steel plate

(4) 0.1 mm thick steel plate

(5) Aluminium cooking foil – heavy duty

(6) Aluminium cooking foil – ultra-light

(7) Canvas handkerchief – sail-cloth

(8) Canvas handkerchief – light duty

(9) Cotton handkerchief

(10) Plastic food wrap

(11) Tissue paper or Paper towel

(12) Silk handkerchief

Spectra - Size

(1) 1,000 cm square

(2) 100 cm square

(3) 10 cm square

(4) 1 cm square

(5) 0.1cm square

I believe that dust particles from meteors and asteroids do drift slowly to Earth and accumulate in our soil.

Spectra – Orbit

We might use a consistent orbital altitude , but in most cases, tracking the material is already a problem, much less avoiding collisions with useful satellites. For this reason I would select the lowest possible orbit to minimize the period during which the material must be tracked and must avoid collisions with anything other than air particles.

Read, for example, The Space Debris Mitigation Guidelines . But remember that our trial is a deliberate release of man-made material, with an increase in debris and a consequent increase in the chance of a collision in orbit.

I think of a Geosynchronous Earth Orbit as one where the satellite appears to be stationary above a defined location on Earth. Earth's rotation indicates that a GEO object over the equator must be travelling at about 40,000 Km/hour relative to Earth. A GEO object over one of the poles will be travelling at exactly ZERO Km/hour relative to Earth.

An object that counteracts an orbital speed would have to travel in the opposite direction at anything up to 40,000 Km/hour and in such a state it ought to be in free-fall. Yes?

How to Track

I can imagine a tracking device ("Beep, beep, beep, …) pasted to a 30 cm square, 25 mm thick steel plate. When the signal stops we would assume that the tracking device has melted and forms a slowly-settling dust cloud.

I cannot yet think of a suitable tracking device for a silk handkerchief.

Limiting "the orbital lifetime of resulting fragments" does not assist in tracking.

Notes

(1) See also The Canadian Space Agency

(2) Consider a sheet of paper towel from the kitchen

(3) Consider a sheet of toilet paper from the lavatory

(4) Consider a roll of toilet paper or a roll of paper towel with the outside end loose enough to catch the air and perhaps unfurl/unroll

(5) Consider a bird's feather …

(6) A wet dish cloth can be spun to a near-planar shape by flicking it from a corner (flipping it into the air with rotational speed) or see how to make a pizza. Ejecting a wet dish cloth with rotation produces a frozen-solid planar piece of cloth. Once the water sublimates we are left with a spinning dry cloth.

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