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For the earth sun system, the force of gravitation is an internal force ( forces* a newtons third law pair) and this INTERNAL force is causing the earth to accelerate. . it is providing the necessary centripetal force.

Reasoning behind the question: centripetal forces dont do any work and hence dont cause a change in mechanical energy, dont cause a change in kinetic energy therefore and dont cause a change in velocity.

QUESTION question 1) but the earth is undergoing a change in velocity?

so, is the the gravitational force on the earth an external force? but ive considered our system containing the sun too. shouldn't that be an internal force then?

2) in the earth sun system if for simplicity we call the earth's movement uniform circular motion, is momentum conserved in this system? how?

i suppose ive mixed up too many things

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    $\begingroup$ Internal forces do not accelerate the center of mass of the complete system. They do accelerate the parts of the system they act on. $\endgroup$ – alephzero Nov 7 '18 at 10:41
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    $\begingroup$ Related question by OP physics.stackexchange.com/q/439417 $\endgroup$ – Aaron Stevens Nov 7 '18 at 11:28
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Answer to Q1:

Centripetal force does change velocity of the object, but not the magnitude of the velocity. Only the velocity direction changes.

Answer to Q2:

If your system includes both Earth and Sun, then momentum of the whole system is conserved as there is no net force acting on the whole system.

If your system is focusing only the Earth or Sun, then their individual momentum is not conserved since there is a net force acting on each of them.

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  • $\begingroup$ in this earth sun system, the internal force gravity is causing a change in direction of the earth. it is a centripetal force causing a centripetal acceleration.. right? $\endgroup$ – Fatimah Rashid Nov 7 '18 at 11:19
  • $\begingroup$ @FatimahRashid Yes, and your question is ? $\endgroup$ – K_inverse Nov 7 '18 at 11:20
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The internal forces cannot change the total momentum but they can change the KE of the system (not just of its components). So there is no contradiction if the velocities of the components change. If the internal forces are conservatives, then the total mechanical energy (kinetic + potential) is conserved. If there are non-conservative internal forces even this mechanical energy may change. Other forms of energy need to be taken into account.

A force perpendicular to the trajectory (like centripetal force) does no work. This means the speed is constant but not so the velocity. The velocity changes direction so it changes. This change is described by centripetal acceleration.

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