We are taught that the centripetal force provided to the satellite by the earth's gravitational force gets equalized to the centrifugal force produced due to the inertia of direction of the orbiting satellite. If the force which keeps the satellite in a constant motion is equaled by an opposing force, how does the satellite still keep rotating creating a resemblance to free fall. Just wanted to know it quite deep.
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1$\begingroup$ No force keeps the satellite in a constant motion. The satellite moves by inertia. The satellite essentially is in a constant free fall, but doesn't hit the ground, because the earth is round, so, with the right speed and distance, it all works out as a circular orbit. $\endgroup$– safesphereCommented Sep 12, 2017 at 18:00
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4$\begingroup$ A satellite's motion does not resemble free fall. It is free fall. en.wikipedia.org/wiki/Newton%27s_cannonball $\endgroup$– Solomon SlowCommented Sep 12, 2017 at 20:25
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5$\begingroup$ Possible duplicate of Weightlessness in Satellites $\endgroup$– sammy gerbilCommented Sep 13, 2017 at 2:46
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3 Answers
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The opposing force is not an actual force.In an inertial frame only centripetal force causes the rotation of the satellite.If you say that the centrifugal force also acts,can you explain its origin?No!this means centrifugal force is just a pseudo force as seen from a non inertial frame. Weightlessness is experienced as there is no normal force acting on the person.Weight is experienced due to normal force
answered Sep 13, 2017 at 5:35
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[...] gets equalized to the centrifugal force [...]
Just remember that this is not really a force. It is a "feeling". When a car turns and you feel slung to the side, that is not a force. It is just your body wanting to continue - it is rather the car moving towards you than you being pushed towards the car. There is no force pushing on you, and saying "centrifugal force" is a very misleading term. It simply does not exist.
Now, with that settled we can continue...
If the force which keeps the satellite in a constant motion [...]
No force is needed to keep a constant motion. The satellite motion is sideways around the planet (tangentially), and no force pushes this way. Remember that a force is not necessary to maintain a speed, only to change a speed.
If the force which keeps the satellite in a constant motion is equaled by an opposing force, how does the satellite still keep rotating creating a resemblance to free fall.
And now to the main point. We have now settled, that there is only one single force: gravity! No force is pushing sideways, no force is pushing outwards (the centrifugal "force" is not a force). Gravity is all we have.
Imagine holding the satellite up in the outer atmosphere and letting go. It starts falling. It falls and a falls and falls... And crashes.
Now you have another satellite and you don't just let go, you throw it a bit sideways. It still falls. But it also flies a bit sideways. No force stops this sideways speed. It falls and falls and falls... and crashes, but a bit more sideways than before.
Now repeat this with your third satellite but throw very, very hard this time. The satellite falls and has a sideways speed as well. It falls and falls and falls... And misses Earth! You threw so hard that it fell past Earth! Now it is at the other side of Earth, and at this now location on the other side of the Earth, gravity still pulls so the satellite falls back again. But again it misses! It misses constantly and continues this weird elliptical orbit forever.
If you throw just right, then this elliptical orbit is actually circular. The satellite does indeed fall - but it misses! Constantly.
And being in free fall gives the sense of weightlessness. Constantly free falling means constant weightlessness.
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$\begingroup$ Re, "When a car turns...There is no force pushing on you." That sounds wrong. If no force acted on you, then you would continue to move along at a constant rate in a straight line while the car goes 'round the curve. The reason you don't continue in a straight line---the reason you go around the curve with the car---is that the car pushes you. If your butt slides across the seat and you hit the door, it's because the seat is not able to push you hard enough, and you don't really start to follow the car until you hit the door. The door does a much better job of pushing you. $\endgroup$ Commented Sep 13, 2017 at 15:38
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1$\begingroup$ Re, "And now to the main point..." There's a name for that explanation, it's "Newton's Cannonball." And Wikipedia has some nice animated illustrations to got along with it: en.wikipedia.org/wiki/Newton%27s_cannonball $\endgroup$ Commented Sep 13, 2017 at 15:42
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$\begingroup$ @jameslarge Thanks for the comments and good points. $\endgroup$– SteevenCommented Sep 13, 2017 at 18:01
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If you fix your frame of reference to the earths center and do not rotate it, the net force on the satellite and all that is in is in it is the gravitation al force called here the centrepetal force. This keeps the satellite rotating. If your coordinate rotates with the satellite then in that frame of course the satellite is stationary the two forces balancing.
