Newton's Law of Universal Gravitation

AI Thread Summary
The discussion revolves around calculating the acceleration of a satellite in orbit using two formulas derived from Newton's Law of Universal Gravitation. The first formula, a=GMm/r^2, was incorrectly applied, leading to a significant discrepancy in results compared to the second formula, a=4pi^2r/T^2. Participants suggest using the correct form a=Gm1/r^2, where m1 is the mass of the planet, to obtain accurate results. The calculated acceleration for Venus using the corrected formula yielded a value of 2.784*10^-8, which aligns more closely with expected outcomes. This highlights the importance of using the appropriate equations in gravitational calculations.
rvnt
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Homework Statement


I am doing a lab-"Kepler's Laws and Newton's Law of Universal Gravitation". There is an image representing various positions, at equal intervals, of a satelitte in an elliptical orbit around the earth. A list of planets and their radi and periods are given. I have calculated acceleration using two formulas a=GMm/r^2 and a=4pi^2r/T^2
Question states: "Calculate acceleration using the two equations and compare the results. Do your results confirm Newton's law of universal gravitation?"

Homework Equations




F=Gm1m2/r^2

The Attempt at a Solution


Ex. of results: accleration obtained for Venus using 1st equation= 5.5407*10^24 and using 2nd equation=0.0113286
I was expecting them to be the same...please help
 
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rvnt said:

Homework Statement


I am doing a lab-"Kepler's Laws and Newton's Law of Universal Gravitation". There is an image representing various positions, at equal intervals, of a satelitte in an elliptical orbit around the earth. A list of planets and their radi and periods are given. I have calculated acceleration using two formulas a=GMm/r^2 and a=4pi^2r/T^2
Question states: "Calculate acceleration using the two equations and compare the results. Do your results confirm Newton's law of universal gravitation?"

Homework Equations

F=Gm1m2/r^2

The Attempt at a Solution


Ex. of results: accleration obtained for Venus using 1st equation= 5.5407*10^24 and using 2nd equation=0.0113286
I was expecting them to be the same...please help

a=GMm/r^2 is wrong

go back to the general equation

F=Gm1m2/r^2
m1=mass of Venus
m2=mass of satellite

F=m2a=Gm1m2/r^2

a=Gm1/r^2

compare to the one you originally had (a=GMm/r^2)
 
But mass of the satellite isn't given..?
 
Wait...so as you said to use a=Gm1/r^2...for venus I got a=(6.67*10^-11)(4.8690*10^24)/(1.08*10^11)^2= 2.784*10^-8
 
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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