Understanding the concept of the effects on an orbit

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Replacing the sun with a rock of the same mass would not change Earth's orbit, as orbits are determined by gravitational forces rather than energy. The key force that keeps Earth in orbit is gravity, which acts between the Earth and the sun (or the rock). While kinetic and gravitational energy are involved in the dynamics of the orbit, they do not directly dictate the shape or stability of the orbit itself. The discussion emphasizes that it is the gravitational force that maintains the orbital path, not the energy levels. Understanding this distinction is crucial for grasping orbital mechanics.
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I am having trouble understanding the concept of the effects on an orbit. The question asks if we replaced the sun with a rock of the same mass, would Earth's orbit change? I think it doesn't because orbits don't change because of its orbital energy. but I'm not sure because i wonder if the kinetic and gravitational energy would change and thus affect the orbit?
 
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What effect keeps the Earth in orbit?
 
i thought orbital energy keeps it in orbit
 
Wrong. A force keeps it in orbit. Not an energy. Which force?
 
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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