(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Pluto moves in a fairly elliptical orbit around the sun. Pluto's speed at its closest approach of 4.43x10^{9}km is 6.12km/s.

What is Pluto's speed at the most distant point in its orbit, where it is 7.30x10^{9}km from the sun?

2. Relevant equations

Conservation of energy:

[tex]K_{2} + U_{2} = K_{1} + U_{1}[/tex]

3. The attempt at a solution

[tex]M_{p}[/tex] = Mass of Pluto (actually cancels out when re-arranging the eq to get [tex]v_{2}[/tex])

[tex]M_{s}[/tex] = Mass of Sun

[tex]\frac{1}{2}M_{p}v_{2}^{2} - \frac{GM_{s}M_{p}}{r_{2}} = \frac{1}{2}M_{p}v_{1}^{2} - \frac{GM_{s}M_{p}}{r_{1}}[/tex]

After fiddling with the equation above, I get:

[tex]v_{2} = v_{1} + \sqrt{\frac{2GM_{s}}{r_{2}-r_{1}}}[/tex]

The correct answer is 3.71 km/s, but my answer comes out differently. I'm using the following numbers in the equation above:

[tex]v_{2} = 6.12\cdot10^{3}m/s + \sqrt{\frac{2(6.67\cdot10^{-11})(1.99\cdot10^{30})}{7.30\cdot10^{12} - 4.43\cdot10^{12}}} = 15.7km/s[/tex]

Perhaps a 2nd set of eyes could find where I went wrong on this.

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# Homework Help: What is Pluto's speed at the most distant point in its orbit?

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