Question regarding Gravity
I simply do not understand what's happening on the mark scheme, an explanation would be much appreciated.
Reply 1
Basically i think first you need to use the info to find the time period of jupiter using keplers 3rd law - t^2=kr^3 which comes out as 142 months. So the next time the 2 planets are aligned Jupiter will have barely moved compared to Earth which will have completed a bit more than one orbit. So then it says to equate anglar displacement of each planet as this will be the same using theta=2pit/T, but since Earth wil reach this angular displacement theta a year prior you must use t=t-12months for Earth. Then soling for t you find t=13.1 months. Hope this made some sort of sense, definitely a tricky question took me a minute to get my head around it.
Reply 2
Okay this took me a minute to think about.
I've attached a proper explanation but the jist of it is, since Earth is travelling faster than Jupiter, before they align again it'll have gone all the way around (2pi radians, maybe look at a solar system gif and it'll make more sense) to get back to its original spot, and then some more to get to the same angular displacement as Jupiter. So if we set up our equations for angular distance, we need to account for the Earth already having gone all the way around. If anything doesn't make sense pls let me know.
I forgot to write it down but n is the number of full rotations.
The mark scheme subtracted the time period (time for a full rotation) from the time, instead of subtracting the angle of a full rotation (2pi radians) from the angular distance like I did, their way seems much less intuitive to me but whatever, hope it makes sense now.
If you're fuzzy on the difference between angular distance and angular displacement: https://physics.stackexchange.com/questions/112827/angular-distance-vs-angular-displacement
I've attached a proper explanation but the jist of it is, since Earth is travelling faster than Jupiter, before they align again it'll have gone all the way around (2pi radians, maybe look at a solar system gif and it'll make more sense) to get back to its original spot, and then some more to get to the same angular displacement as Jupiter. So if we set up our equations for angular distance, we need to account for the Earth already having gone all the way around. If anything doesn't make sense pls let me know.
I forgot to write it down but n is the number of full rotations.
The mark scheme subtracted the time period (time for a full rotation) from the time, instead of subtracting the angle of a full rotation (2pi radians) from the angular distance like I did, their way seems much less intuitive to me but whatever, hope it makes sense now.
If you're fuzzy on the difference between angular distance and angular displacement: https://physics.stackexchange.com/questions/112827/angular-distance-vs-angular-displacement
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