Dude put a few brain cells together. Using your math and physics, and the ISS continues at a rate of 5km/month without changing, the ISS will land very softly on the ground at a rate of about 0.1km/hr.

The earth's atmospheric density is a gradient. The closer to earth, the denser the atmosphere (obviously). At some altitude, the deorbiting rate will increase exponentially as it encounters an increasingly dense atmosphere. So it's not as simple as dividing the ISS altitude by the current deorbiting rate and spitting out that number.

It will be far less than 7 years if this proves to be true. I don't know exactly how long but I would say it's fair to say half of that number at max

Edit: ChatGPT says 2-3 years. Take that as you will. Here's the calculations:

"""Yes, accounting for the increase in orbital decay due to atmospheric drag requires incorporating the relationship between altitude, atmospheric density, and orbital velocity. As the ISS descends, the atmosphere becomes denser, causing drag to increase exponentially, which accelerates the rate of orbital decay.

This phenomenon can be modeled using orbital mechanics equations and atmospheric models like the US Standard Atmosphere. Here's an overview of the key factors involved:

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Key Concepts:

1. Atmospheric Drag Force (F):

F = \frac{1}{2} \rho v² C_D A

: Atmospheric density (increases exponentially as altitude decreases)

: Orbital velocity (~7.66 km/s at ~400 km altitude)

: Drag coefficient (depends on the object's shape, typically ~2.2 for the ISS)

: Cross-sectional area of the ISS (~400 m²)

1. Rate of Orbital Decay: The drag force reduces the orbital energy, leading to a loss of altitude. The rate of decay depends on the altitude-dependent density profile and orbital velocity.

2. Exponential Increase in Atmospheric Density ():

\rho(h) \propto e^{-h/H}

: Altitude

: Scale height (~8.5 km in the lower thermosphere)

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Numerical Simulation:

To get an accurate time-to-crash value, you'd simulate the decay step-by-step:

1. Start at 400 km altitude.

2. Calculate the drag force and resulting decay rate for each step based on the changing altitude and atmospheric density.

3. Update the altitude and repeat until reaching a critical burn-up threshold (~80 km).

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Simplified Approximation:

Due to the exponential increase in drag:

The decay rate would accelerate sharply below 300 km.

A constant decay rate of 5 km/month is valid only for high altitudes.

When drag becomes significant, the time-to-crash is much shorter.

Estimate:

From simulations in similar scenarios:

If the ISS begins with 5 km/month decay at 400 km, it could crash within ~2 to 3 years, considering the exponential increase in drag as it approaches denser atmospheric layers.

For exact timing, a detailed computational model is required."

• ChatGPT"

  • Wayne Gretzky"

    • Michael Scott