Using Orbital Energy to Calculate Velocity

[JoeyBob]

Homework Statement

See attached picture

Relevant Equations

change Ek + change Ep =0, Ek=1/2mv^2, Ep=-GMm/r

So what I did first was calculate the initial and final potential energies with Epi=-9.433*10^11 m and Epf = -1.503*10^12 m.

Then I found change in potential energy, -5.597*10^11 m.

Using this I determined the change in kinetic energy, 5.597*10^11. I then added this change to the initial kinetic energy I calculated (103.68 m) to get a final Ek of 5.597*10^11 m.

Then I calculated the final velocity, Ekm=v^2*0.5, finding that v=1058017, which is obviously way higher than the right answer.

Where am I going wrong here? Is there some non conservative work or something?

 

[haruspex]

Homework Statement:: See attached picture
Relevant Equations:: change Ek + change Ep =0, Ek=1/2mv^2, Ep=-GMm/r

So what I did first was calculate the initial and final potential energies with Epi=-9.433*10^11 m and Epf = -1.503*10^12 m.

Then I found change in potential energy, -5.597*10^11 m.

Using this I determined the change in kinetic energy, 5.597*10^11. I then added this change to the initial kinetic energy I calculated (103.68 m) to get a final Ek of 5.597*10^11 m.

Then I calculated the final velocity, Ekm=v^2*0.5, finding that v=1058017, which is obviously way higher than the right answer.

Where am I going wrong here? Is there some non conservative work or something?

Please post all your working, just as algebra, no plugged in values. This will make it much easier to see where the mistake is, unless it is purely arithmetic, which is unlikely.

 

[mjc123]

Your units are all over the place. Plugging in r in km and v in km/s means you get ΔEp = -5.597*10¹¹m mJ and Eki = 103.68m MJ. (I haven't checked the calculations, but the numbers look in the right ballpark.) It is much better to convert everything to SI units (and back at the end if necessary), and INCLUDE THE UNITS AT EACH STAGE OF THE CALCULATION. Can never stress too much the importance of units.

 

[kuruman]

Homework Statement:: See attached picture
Relevant Equations:: change Ek + change Ep =0, Ek=1/2mv^2, Ep=-GMm/r

Where am I going wrong here? Is there some non conservative work or something?

Your change in potential energy is 10³ times too high. What does this suggest to you?

On edit: I am questioning the validity of this problem. The perigee speed $v_p$, obtained from the given parameters using energy conservation, is inconsistent with conservation of angular momentum. Angular momentum conservation (per unit mass) requires that $v_1 r_1\sin\theta=v_p r_p$. Solving for $\sin\theta$ returns a value greater than 1 which is impossible if my calculation is correct.