Gravitational Orbits: True Statements about Circular & Elliptical Orbits

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In discussing gravitational orbits, key points include the characteristics of circular and elliptical orbits. For circular orbits, the planet's momentum is always tangent to its trajectory, its magnitude remains constant, and the gravitational force acts at a right angle to the momentum. In elliptical orbits, while the momentum is also tangent to the trajectory and its direction changes continuously, the magnitude of momentum is not constant due to varying speeds. The gravitational force similarly acts at a right angle to the momentum in both types of orbits. Understanding these principles is essential for grasping the dynamics of planetary motion.
Fredley_Banyo
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1. Which of the following statements about a circular orbit are true? (The planet is orbiting around the star.)a. At any instant the momentum of the planet is tangent to the planet's trajectory.

b. The magnitude of the planet's momentum is constant.

c. At every instant, dvector p/dt points from the planet to the star.

d. The direction of the planet's momentum is changing at every instant.

e.The gravitational force on the planet due to the star always acts at a right angle to the planet's momentum.

2. Which of the following statements about an elliptical orbit are true? (The planet is orbiting around the star.)a. At any instant the momentum of the planet is tangent to the planet's trajectory.

b. The magnitude of the planet's momentum is constant.

c. At every instant, dvector p/dt points from the planet to the star.

d. The direction of the planet's momentum is changing at every instant.

e.The gravitational force on the planet due to the star always acts at a right angle to the planet's momentum.I missed this problem on my homework and i would like to know what the correct statements are for each so that i can understand the concepts.
 
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Welcome to PF, Fredley!
The purpose of the forum is to help you work out the answers yourself, so we are not supposed to just give you answers. If you share your thinking or work, we'll be very glad to point out any errors or omissions and aim you in the right direction.
 
Thread 'Variable mass system : water sprayed into a moving container'

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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