# Would a considerably big asteroid be disintegrated by the Earth's Roche limit?

If there was a big asteroid with a diameter of say 50km+ in a collision course with the Earth (not orbiting), would it disintegrate into smaller chunks due to the Earth's Roche limit, or the time it will spend in the Roche radius won't be enough for the tidal forces to have an effect?

My simple calculations and assumptions of an asteroid with density as the moon will have ~9500km Roche radius with the Earth, so an asteroid with velocity of 20km/s will have about 8 minutes as soon as it enters the Roche radius until it collides with the surface of the Earth. My question here : is this time enough to disintegrate the asteroid?

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This. Tidal acceleration goes by $\frac{\mathrm{d}}{\mathrm{d}R}(R^{-2})\Delta r \propto R^{-3} \Delta r$ so the loose bits of the asteroid experience micro-gee for a few minutes. Think of that astronaut's tool bag drifting off a couple of years ago. –  dmckee Feb 12 at 3:04
@AbanobEbrahim Compute it using, say, $10^{-4}$--$10^{-3}\,\mathrm{m/s^2}$ to get a feeling for the time scale. Define "significant change" however you want, but I'd use a number on order of 1/10 the diameter at a minimum. –  dmckee Feb 12 at 20:18