How do orbits and forces affect planetary motion and satellite trajectories?

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The discussion focuses on understanding how orbits and forces influence planetary motion and satellite trajectories. Key questions include comparing centripetal forces and energies at different points in an elliptical orbit, estimating the Moon's gravitational force on a person, analyzing the speeds of planets in circular versus elliptical orbits, and determining the necessary speed for a satellite in geosynchronous orbit. Participants emphasize the need for evidence of attempted solutions to these problems. Overall, the conversation seeks clarification and guidance on these fundamental concepts in orbital mechanics.
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Please Help! (Orbits and Forces in Space)

Quetions are below on 3rd post.. Thanks for helping!
Help on any or all of the 4 questions at the above link would be greatly appreciated. Thanks soo much! :blushing:
 
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In order to help you we need to see evidence of an attempt to try these problems. Show what you've done so far.
Also, I don't see just 4 questions on that site. I only see the objectives. Are these what you mean?
 
Oh oops sorry, ill just post the questions:
1) Image for this problem: http://cwx.prenhall.com/bookbind/pubbooks/giancoli3/chapter6/medialib/chap6gifs/chap6_wu_1.gif
A planet's orbit around the sun is an ellipse. Consider points A and B on the ellipse. How does the centripetal force exerted on the planet at point A compare to the centripetal force exerted on the planet at point B? How about the potential energies at A and B? Kinetic energies? How about angular momenta? --> My guess is that the centripital force is greater at point A. I am not sure on the energies. I think there is greater angular momenta at B.
2) Estimate the force that the Moon exerts on you when it is directly overhead.--> My guess is that this number is very small and it is the same process as why we have high and low tides in the ocean.
3) Image for this problem: http://cwx.prenhall.com/bookbind/pubbooks/giancoli3/chapter6/medialib/chap6gifs/chap6_wu_3.gif
Two different planets are orbiting the same sun along two different orbits. The red orbit is circular, the blue orbit is elliptical. Compare the speeds of the planet in the the blue orbit at points A, B, and E. Compare the speeds of the planet in the red orbit at points C, D and E. The planet in the blue orbit is to be shifted to the red orbit as passes point E. Does it have to speed up or slow down?---> My guess is that the points on the inner orbit have a higher speed
4) The space commnunication company is planning to take a spy satellite to a spot 35,800 km above the Earth's surface and release into a geosynchronous orbit. ( In a geosynchronous orbit the satellite will orbit at the same rate as the points on the surface of the Earth below it so as to appear to hover over the same spot.
Is this possible?
If yes, how fast must the satellite be moving when it is released?---> My guess is that this is possible and that the satellite needs to move at a speed high enough to keep it in orbit.
What do you guys think?
 
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Thread 'Variable mass system : water sprayed into a moving container'
Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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