Investigating Comet 67P's Elliptical Orbit

[paintingstars]

Homework Statement

Currently, I am trying to prove the "conservation of energy" concept within a comet's elliptical orbit by finding the mechanical energy of the aphelion and perihelion point to see if they're equal. However, they don't equal each other when I calculate both points.

(aphelion, perihelion and semi-major axis given in AU)
Comet Mass: 2.8x1012 kg

Homework Equations

I understand that the mechanical energy equation is:

and that to find the velocity variable, the equation must be rearranged by substituting ME with MEbound

to obtain this:

The Attempt at a Solution

Thank you in advance for the help! I'm actually not a physics student, so all these astrophysics concepts are new to me. I'm doing it for a math report investigating comet 67P's elliptical orbits. While I'm posting this thread, I'm also having trouble coming up with a way to find the amount of time it will take comet 67P to reach its perihelion point given its current distance from the sun in the orbit. I'm aware of Kepler's 2nd Law, so I know I can't find the average speed of the comet since it varies along its orbit. Is there a way for me to find the remaining amount of time the comet has before reaching its perihelion? Its current position is at 312.78 Million Km. I'd prefer if the equation or solution was simple (much simpler than Kepler's equation), as this is just a high school math report that's too advanced.

Thank you again!

 

[tms]

I don't know whether this is your problem, but you need to use a consistent set of units. Specifically, you need to convert the AU to meters. As it is, your answers certainly are not in joules.

 

[SteamKing]

And you don't need to use an absurd number of decimal places in your calculations. You know the mass of the comet to only two significant figures (2.8*10¹² kg).

 

[SteamKing]

For reference, the speed of light is 299 792 458 m / s. Comets (and everything else) travel at less than this velocity. It's like a fundamental law of the Universe.