orbital velocity and Kepler's Law (1 Viewer)

[laurabeaven]

I was just wondering if anybody would be able to help me understand this syllabus point:
- Define the term orbital velocity and the quantitative and qualitative relationship between orbital velocity, the gravitational constant, mass of the central body, mass of the satellite and the radius of the orbit using Kepler's Law of Periods.

Out of 10 im about 11 stucks. I really dont understand what im meant to know. i can define orbital velocity. but im really bad at maths and when my teacher tried to explain it to me she wrote down all these weird derivations (i dont even know what they are, some weird equations).

Anywho, if you could explain to me just exactly what i am meant to know that would be marvellous. We dont need to know how to derive the equation do we? i hope not because i do general maths for a reason.

Thanks!!

 

[_Mave_]

As far as I can make out this is usually used in short answer questions, either you have to define orbital velocity ect or you have to answer a question using the formulae's in the formuale sheet (unless, unlike me, you can actually remember the formulaes from the textbook, I can't so instead I just join formulaes on the formulae sheet together until I get what I need) You will most likely need to derive some sort of answer or sometimes an equation by re-arranging (or remembering) formulaes to work out either the period, radius, gravatational constant (G) velocity etc. My way does require maths skills however, sorry but thats the only way I can do them, re-arranging formulaes gets easier with practice however.

What you have to do all depends on what question you get asked. For example one past question was "Derive a mathematical expression for the speed of a satellite in a stable circular orbit around the Earth in terms of Earth's mass (M), Newton's Universal Constant (G) and the satellites distance from the centre of the Earth (r)"

From formuale sheet: F= mv^2/r and F=Gm1m2/dm

Therefore: mv^2/r = Gm1m2/d

(Cross multiplying) dmv^2 = Gm1m2

(dividing by dm) v^2 = Gm1m2/dm

(getting rid of ^2) v = (square root) Gm1m2/dm

(to m's cross out) v = (square root) Gm/d

I think that is the sort of thing that the syllabus point refers to (someone please correct me if I am wrong), hope it helps and makes some sense.

 

[exa_boi87]

I might be mistaken, but as far as i know, orbital velocity in terms of keplers law of periods (with mass, radius etc.. as defined by the dot point) is:

r^3/T^2 = GM/4(pie)^2 ... on the formula sheet

edit: my mistake, rereading the question it doesnt specifically ask for the incorporation of period, however that formula *is* defined as Keplers Law of Periods

 

[serge]

I might be mistaken, but as far as i know, orbital velocity in terms of keplers law of periods (with mass, radius etc.. as defined by the dot point) is:

r^3/T^2 = GM/4(pie)^2 ... on the formula sheet

edit: my mistake, rereading the question it doesnt specifically ask for the incorporation of period, however that formula *is* defined as Keplers Law of Periods

you're right

curse you kepler's law!

[I derived it one day before the 4unit maths exam
and couldnt remember what to do, remember kids w=2Pi/T]

 

[_Mave_]

Your right about keplers law, I picked a bad example because once I had started the example I realised I didn't really need it, however the process should be the same just with a different formulae and question for keplers law