MHB Finding Orbit Type with Energy Equation

[Dustinsfl]

How does one use the energy equation to determine the type of orbit?
$$
E = \frac{v^2}{2} - \frac{\mu}{r}
$$
where $\mu = G(m_1+m_2)$ and
$$
\mathbf{r} = \begin{pmatrix}
-4069.503\\
2861.786\\
4483.608
\end{pmatrix}\text{km},\quad
\mathbf{v} = \begin{pmatrix}
-5.114\\
-5.691\\
-1.000
\end{pmatrix}\text{km/sec}
$$

 

[Ackbach]

As I understand it, $E=0$ is parabolic, $E>0$ is hyperbolic, and $E<0$ is elliptic. If $v^{2}r=\mu$, then it's circular.

 

[Dustinsfl]

As I understand it, $E=0$ is parabolic, $E>0$ is hyperbolic, and $E<0$ is elliptic. If $v^{2}r=\mu$, then it's circular.

My issue was I didn't have a mu term.

 

[topsquark]

How does one use the energy equation to determine the type of orbit?
$$
E = \frac{v^2}{2} - \frac{\mu}{r}
$$
where $\mu = G(m_1+m_2)$ and
$$
\mathbf{r} = \begin{pmatrix}
-4069.503\\
2861.786\\
4483.608
\end{pmatrix}\text{km},\quad
\mathbf{v} = \begin{pmatrix}
-5.114\\
-5.691\\
-1.000
\end{pmatrix}\text{km/sec}
$$

I'm confused about two things:
1. You are missing an "m" from the kinetic energy term.

2. You defined \mu in your original post. Is this a result you are supposed to derive perhaps?

-Dan

 

[Dustinsfl]

I'm confused about two things:
1. You are missing an "m" from the kinetic energy term.

2. You defined \mu in your original post. Is this a result you are supposed to derive perhaps?

-Dan

Later on I was told what mu is for this problem so I was able to do it.