Comet Elliptical Orbits Question

[Chaso]

Homework Statement

Comets move around the sun in very elliptical orbits. At its closet approach, in 1986, Comet Halley was 8.79 x 10^7 km from the sun and moving with a speed of 54.6 km/s.

What was the comet's speed when it crossed Neptune's orbit in 2006?

Homework Equations

Mv1r1=Mv2r2

The Attempt at a Solution

What I did was use the equation above, and solve for v2. But it says I'm wrong. Any Suggestions?

 

[Simon Bridge]

What did you use for r2?
What did you get for v2?

 

[Chaso]

For r2, I use the radius from Neptune to the sun.

 

[Simon Bridge]

Oh I see ... excuse me, didn;t read it properly.
That formula should be:

$\vec{r}_1\times m\vec{v}_1=\vec{r}_2\times m\vec{v}_2$

At Neptune's orbit, the velocity won't be tangential to the radius.

 

[gneill]

Homework Statement

Comets move around the sun in very elliptical orbits. At its closet approach, in 1986, Comet Halley was 8.79 x 10^7 km from the sun and moving with a speed of 54.6 km/s.

What was the comet's speed when it crossed Neptune's orbit in 2006?

Homework Equations

Mv1r1=Mv2r2

The Attempt at a Solution

What I did was use the equation above, and solve for v2. But it says I'm wrong. Any Suggestions?

The formula you've chosen would apply when the velocities are both perpendicular to the radii, say at perihelion and at aphelion. Here this holds true for only one of the given points (the closest approach).

Instead, consider a conservation of energy approach.

 

[Chaso]

The formula you've chosen would apply when the velocities are both perpendicular to the radii, say at perihelion and at aphelion. Here this holds true for only one of the given points (the closest approach).

Instead, consider a conservation of energy approach.

So use K2 + U2 = K1 + U1

expansion to:
(1/2)(Mc)(v2^2) + -(G)(Me)(Mc)/(R) = (1/2)(Mc)(v1^2) + -(G)(Me)(Mc)/(R2)

R = Distance of neptune from sun
R2 = 8.79 x 10^7

Is this what I do?

 

[Simon Bridge]

Mc is the mass of the comet and Me is the mass of the body the comet is orbiting?

Note: another way thinking about it is "potential energy gained equals kinetic energy lost".