Calculating Jupiter's Orbital Period Around the Sun: A Physics Problem

AI Thread Summary
To calculate Jupiter's orbital period around the Sun, the discussion emphasizes using Kepler's Third Law, which states that the square of the orbital period is proportional to the cube of the semi-major axis of the orbit. The provided formula, T(period) = 2πr^(3/2)/√(GMearth), is intended for this calculation but requires proper manipulation. Participants express confusion about setting up the problem and suggest considering relative periods of Earth and Jupiter. The conversation highlights the importance of understanding circular motion and acceleration in solving orbital mechanics problems. The discussion concludes with a suggestion to clarify the setup and approach for accurate calculations.
mobius
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The Earth orbits the Sun once a year at a distance of 1.50x1011 m. Jupiter orbits the Sun at distance of 7.78 x 1011 m. These distances are between the centre of the planet and the sun. How long ( in Earth days ) does it take for Jupiter to make one orbit around the Sun?

T(period = 8.64E4 sec) = 2πr^(3/2)/√(GMearth)

i have tried adding and subtracting the two radiis together and then plugging it into the equation...however it is incorrect...i am either not understanding the problem or is it just human error...?
 
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Hi mobius,

We welcome homework problems here, in the Homework Help forum. We also ask that you attempt the problems first, and show us your work up to the point where you get stuck.

- Warren
 
Originally posted by mobius
i cannot manipulate the formula in order to solve this, maybe it's because i do not understand the problem fully...i just need an explanation on setting this up...much appreciated

Start by identifying all the forces acting on the body (the pilot), then tell us what you know about acceleration, circular motion, and Newton's laws!
 
Hint: You use keplers third law where (time period)^2= (radius of orbit)^3
 
if I'm not understanding wrong, we have to find the 'relative' time period of the planet w.r.t earth. Here relative means : let car A & B start from pt. P in diff. Circles with diff. Speeds. Now relative time period will be that when both will reach pt. Again simultans. To do this problem u can take the help of concept of beats from waves.
Therefore use this:
1/T=1/T1 - 1/T2
Where T1 , T2 are the periods of Earth and Jupiter resp.
Tell me if it's right
 
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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