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The Roche Limit

# The Roche Limit - The Roche Limit A satellite cannot...

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The Roche Limit A satellite cannot approach its primary too closely (the Roche limit) or stray too far (the instability limit) without break-up or loss to the system respectively. The Roche Limit is the point within which a satellite would be torn apart by tidal forces if the only force hloding it together is its self-gravity. Taking a primary mass M, radius R, a distance d from its satellite mass m radius r (where M>>m) we have: If the satellite is large enough (r greater than about 500km) its self-gravity dominates other cohesive forces. It will be torn apart if it approaches the primary closer than: which is known as the Roche Limit, after the mathematician who first derived it. For our Moon d = 2.44(5.5/5.3) 1/3 or about 2.9R E - around 18,500 km. Roche's calculation was complicated by the fact he took into account the tidal distortions in the satellite just before break-up. We can get a similar (though not the "full") term if we just consider a rigid spherical satellite. Then the centripetal acceleration of the orbit is w 2

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The Roche Limit - The Roche Limit A satellite cannot...

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