Comet's Velocity Homework: Answer What Speed at Perihelion?

[Jtappan]

Homework Statement

The orbit of Halley's Comet around the Sun is a long thin ellipse. At its aphelion (point farthest from the Sun), the comet is 5.7 * 10^12 m from the Sun and moves with a speed of 11.0 km/s. What is the comet's speed at its perihelion (closest approach to the Sun) where its distance from the Sun is 8.4 * 10^10 m?
_____km/s

Homework Equations

PEi+KEi=PEf+KEf

The Attempt at a Solution

do the m and g values cancel out when doing this because they are not given? I am totally lost...

 

[Mindscrape]

Weak, they gave you the perihelion. Since they gave perihelion distance, a lot of trouble is saved. Now this begs the question of what is the difference between the aphelion and the perihelion? Is there any kind of easily attainable relation you can use? To give you a hint, you might want to consider more than energy conservation. (Hint hint: one of them types of momentum, and one is better than the other.)

Did you know that you can solve for the perihelion with the information they have given you? If you feel ambitious, give it a try.

 

[ninadgadre]

using kepler's second law,that areal velocity is constant for anybody in gravitational revolution in elliptical orbit,and applying it for positions at perigee and apogee,taking infifitesimally small orbital motion,we get the areas for the respective triangles at these positions...dividing the obtained relation with infitesimally small time duration 'dt',we get a ratio of velocities at these two positions with relation to the distances...the relation obtained is... v1.d1 = v2.d2

thus,simply using this inverse ratio,we can find the answer...

the velocity at the nearmost point of comet from sun is '746428.571428...m/s'

in short,i applied kepler's law at small intervals of distances and differentiated it wrt time to obtain velocity...