When a small meteor $A$ falls vertically into the atmosphere, the terminal velocity is constant; when $A$ falls into the atmosphere at an angle $\alpha$, does the terminal velocity of $A$ return to constant? why? How to force analysis?


When the meteor reaches terminal velocity the forces on it are balanced. Otherwise there will be acceleration in the direction of the resultant force.

There are only 2 forces on the meteor : the atmospheric drag and its weight. When terminal velocity is reached these must be equal and opposite. The weight is always vertically downwards therefore the drag force is vertically upwards.

So regardless of the angle at which the meteor enters the atmosphere, if it reaches terminal velocity then it will always be falling vertically downwards and its terminal velocity will be the same. It is the same because there is only one speed at which the drag force equals the weight of the meteor.

Conversely if the meteor is not falling vertically downwards then you can be sure that it has not yet reached terminal velocity.

  • $\begingroup$ When the final velocity and the force balance are reached, the meteor will continue to move at a uniform speed along its original orbit without necessarily falling vertically. $\endgroup$ – enbin Mar 12 '20 at 14:35
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    $\begingroup$ @enbinzheng Sorry I think that is an incorrect statement. The force of gravity acts downwards, the drag force acts opposite to the direction of motion. If these are the only 2 forces acting then in order for them to balance they must act in the same straight line. So the terminal motion must be downwards and the drag force upwards. Comets which do not fall vertically have not reached terminal velocity. $\endgroup$ – sammy gerbil Mar 12 '20 at 19:08

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$V$ is the direction of the meteor and $W$ is the weight of the meteor. $W$ has two components: $W_t$ is parallel to $V$ and $W_n$ is perpendicular to $V$. The meteor is acted on by the air, producing two components: $L$ is perpendicular to $V$ and $D$ is parallel to $V$. When $W_t = D$ and $L = W_n$, the meteor moves in the direction of $V$ until it burns down or falls to the ground. This is consistent with Newton's law.

Meteors are not a standard sphere, so in some cases they will have what I said. Even bounced back from the atmosphere to cosmic space.

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    $\begingroup$ Does a meteor experience lift like a glider? Yes this is consistent with Newton's Laws but is it consistent with meteors? $\endgroup$ – sammy gerbil Mar 13 '20 at 0:51
  • $\begingroup$ @sammygerbil They are similar because meteors are also objects moving in the atmosphere. $\endgroup$ – enbin Mar 13 '20 at 1:16
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    $\begingroup$ Birds and helicopters also move in the atmosphere, but meteors cannot flap their wings nor hover. Similarity in one property does not imply similarity in another. I have never heard of meteors experiencing lift; if there was any lift force it could just as easily point downwards. $\endgroup$ – sammy gerbil Mar 13 '20 at 1:44
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    $\begingroup$ Your question was about terminal velocity. The meteors you are describing do not reach terminal velocity which is around 100-200 m/s. They enter the atmosphere at enormous speeds (11-72 km/s). The ones which ricochet off the upper atmosphere are still travelling at several km/s. Those which reach ground at terminal velocity do so vertically. See amsmeteors.org/fireballs/faqf/#12 $\endgroup$ – sammy gerbil Mar 13 '20 at 2:48
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    $\begingroup$ @enbinzheng Projectiles only travel in parabolas when air resistance is negligible. Air resistance is very much not negligible for a meteor traveling much faster than terminal velocity. $\endgroup$ – Chris Mar 17 '20 at 8:17

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