Speed at a certain distance from the sun

[najatau]

Hello! These problems of mine are due in the morning. I'm not sure whether or not I will be able to figure them out in time, but I do need to understand the process in order to prepare for my finals. So any help would be much appreciated! Thank you.

1. Homework Statement
A comet is in an elliptical orbit around the Sun. Its closest approach to the Sun is a distance of 4.6

10^10 m (inside the orbit of Mercury), at which point its speed is 9.1

10^4 m/s. Its farthest distance from the Sun is far beyond the orbit of Pluto. What is its speed when it is 6

10^12 m from the Sun? (This is the approximate distance of Pluto from the Sun.)
speed

Homework Equations

[/B]
KSun,f + Kcomet,f + Uf = KSun,i + Kcomet,i + Ui

The Attempt at a Solution

I set KSun to 0 for both sides since the sun isn't moving.

Then I set up this equation:

(1/2)Mv²_{comet final}+(6.7X10^-11)(1.989x10³⁰_{mass of the sun})/(distance)_{comet final}=(1/2)Mv²_{comet initial}+(6.7X10^-11)(1.989x10³⁰_{mass of the sun})/(distance)_{comet initial}

And I isolated one of the velocities:

(v_final²/2)+((6.67x^-11)((1.989x10³⁰)/6x10¹²)=((1/2)(9.1x10⁴)²)+((6.67x10^-11)(1.989x10³⁰)/4.6x10¹⁰)

v_final=sqrt(2*((1/2)(9.1x10⁴)²)+((6.67x10^-11)-((6.67x^-11)((1.989x10³⁰)(1.989x10³⁰)/4.6x10¹⁰))

And I got 75,656 m/s, which isn't the correct answer. :(

 

[ehild]

Hello! These problems of mine are due in the morning. I'm not sure whether or not I will be able to figure them out in time, but I do need to understand the process in order to prepare for my finals. So any help would be much appreciated! Thank you.

1. Homework Statement
A comet is in an elliptical orbit around the Sun. Its closest approach to the Sun is a distance of 4.6

10^10 m (inside the orbit of Mercury), at which point its speed is 9.1

10^4 m/s. Its farthest distance from the Sun is far beyond the orbit of Pluto. What is its speed when it is 6

10^12 m from the Sun? (This is the approximate distance of Pluto from the Sun.)
speed

Homework Equations

[/B]
KSun,f + Kcomet,f + Uf = KSun,i + Kcomet,i + Ui

The Attempt at a Solution

I set KSun to 0 for both sides since the sun isn't moving.

Then I set up this equation:

(1/2)Mv²_{comet final}+(6.7X10^-11)(1.989x10³⁰_{mass of the sun})/(distance)_{comet final}=(1/2)Mv²_{comet initial}+(6.7X10^-11)(1.989x10³⁰_{mass of the sun})/(distance)_{comet initial}

The equation is wrong. Check the sign of PE.

 

[tms]

The equation is wrong. Check the sign of PE.

There's more wrong with the PE than just the sign.