two objects in orbit..please HELP!!!?

Question

Two objects X and Y are observed traveling in space under the influence of the gravitational attraction of the Sun. The closest distance of X to the sun (perihelion) is measured to be r_X,P   = 5·10^10m at which point it travels with a speed of  v_X,P   = 7·10^4 m/s, while for Y the closest distance to the sun is 
r_Y,P   = 8·10^10m traveling at v_Y,P   = 6·10^4 m/s.

a.)   Determine which object has a bound orbit around the sun and which one doesn't.
                -What I did was get the Sun's escape velocity ( 3.8*10^11 m/s) and since it is more than the velocity of X & Y, I said that they are both bonded orbits, please correct me.

b.)  For the object in a bound orbit:  
          Determine the eccentricity e of the bound orbit.  This will require (i) the geometry of an 
ellipse, (ii) conservation of angular momentum, and (iii) conservation of energy.  Then also find the 
lengths of the semi-major and the semi-minor axes,  a and b . 

c.) Determine its period in years. 


d.)  Determine the smallest speed of the object in the orbit.


Please explain the steps

   Thank You

Anonymous · Accepted Answer

It's 3 in the morning and I decide to give up!

Christopher · Answer

I only found part a) recall:

if E(r)<0, bound orbit, if E(r)>0, non-bound orbit

E(r)=K(r)+U(r)=1/2mv^2-GMm/r

I have this same thing due tomorrow, so i'm still trying to figure out parts B-D, which i'm not having much luck with.

but I hope this helps.

Anonymous · Answer

For part (a), only x is bounded because the total energy is negative, while Y's energy is positive so it escapes. I still need some help on part (b) because I'm stuck on that and it's due tomorrow.

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two objects in orbit..please HELP!!!?

3 Answers