Calculating Halley's Comet's Speed at Perihelion

[Jtappan]

1. 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




2. Homework Equations

PEi+KEi=PEf+KEf

3. 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...

 

[mgb_phys]

Yes, KE = 1/2 m v^2 and PE = M m /r where M is the mass of the sun.

 

[mdk31]

Kepler's 2nd Law is equivalent to the conservation of momentum.

r[a]mv[a]sin(x) = r[p]mv[p]sin(x)

As you can see, the mass of the central body is irrelevant and the masses of the comet cancel out.

 

[Jtappan]

what is the meaning of sin(x) in both of these? it gives no angles

 

[mdk31]

what is the meaning of sin(x) in both of these? it gives no angles

The momentum (mv) is perpendicular to the comet's path. Therefore, the angle between the r position vector and the momentum vector is 90. The sine of 90 is 1.

 

[Jtappan]

ok I tried that and got 746.4285 and that is still not the right answer...I don't know what I am doing wrong...

 

[mdk31]

Do you get the same answer when you try conservation of energy?

 

[Mindscrape]

Oh, you made another topic. mdk is right, $r_a m v_a = r_p m v_p$ so you must have misinterpreted something he said or done the numbers wrong.