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Use this page to generate SPICE kernels for the bodies of interest, and then use SPICE routines to calculate whatever you like to your heart's content.

Aarrr. I don't be knowin why ye be reinventing th' wheel.

Alrighty ya scurvy bilge rat, here it be:

$$x=a\left(\cos\tau-e\right)$$ $$y=a\sqrt{1-e^2}\sin\tau$$ $$z=0$$

That be givin it t' ye in th' plane. Then ya be rotatin th' plane with that land lubber Euler's transform in $\Omega$, $i$, $\omega$ (longitude of ascending node, inclination, and argument of periapsis), by multiplyin his matrix by yer vector up there:

$$\left( \begin{array}{ccc} \cos\omega \cos\Omega-\cos i \sin\omega \sin\Omega & -\cos\Omega \sin\omega -\cos i \cos\omega \sin\Omega & \sin i \sin\Omega \\ \cos i \cos\Omega \sin\omega+\cos\omega\sin\Omega & \cos i \cos\omega\cos \Omega-\sin\omega\sin\Omega & -\cos\Omega \sin i \\ \sin i \sin\omega & \cos\omega \sin i & \cos i \\ \end{array} \right)$$

Ye also be needin th' time it be ($\mu$ being th' $GM$ of the Sun):

$$t=\sqrt{a^3\over\mu}\left(\tau-e\sin\tau\right)$$

Yer $\tau=0$ and $t=0$ being yer time of periapsis. Ye be seein that ev'ry $2\pi$ in $\tau$, it be one a yer spins about th' Sun.

If yer scurvy rock be gettin close to a planet, then ye be wastin yer time, as th' orbit be changin on ye.

Use this page to generate SPICE kernels for the bodies of interest, and then use SPICE routines to calculate whatever you like to your heart's content.

Aarrr. I don't be knowin why ye be reinventing th' wheel.

Alrighty ya scurvy bilge rat, here it be:

$$x=a\left(\cos\tau-e\right)$$ $$y=a\sqrt{1-e^2}\sin\tau$$ $$z=0$$

That be givin it t' ye in th' plane. Then ya be rotatin th' plane with that land lubber Euler's transform in $\Omega$, $i$, $\omega$ (longitude of ascending node, inclination, and argument of periapsis), by multiplyin his matrix by yer vector up there:

$$\left( \begin{array}{ccc} \cos\omega \cos\Omega-\cos i \sin\omega \sin\Omega & -\cos\Omega \sin\omega -\cos i \cos\omega \sin\Omega & \sin i \sin\Omega \\ \cos i \cos\Omega \sin\omega+\cos\omega\sin\Omega & \cos i \cos\omega\cos \Omega-\sin\omega\sin\Omega & -\cos\Omega \sin i \\ \sin i \sin\omega & \cos\omega \sin i & \cos i \\ \end{array} \right)$$

Ye also be needin th' time it be ($\mu$ being th' $GM$ of the Sun):

$$t=\sqrt{a^3\over\mu}\left(\tau-e\sin\tau\right)$$

Yer $\tau=0$ and $t=0$ being yer time a periapsis. Ye be seein that ev'ry $2\pi$ in $\tau$, it be one a yer spins about th' Sun.

If yer scurvy rock be gettin close to a planet, then ye be wastin yer time, as th' orbit be changin on ye.

Use this page to generate SPICE kernels for the bodies of interest, and then use SPICE routines to calculate whatever you like to your heart's content.

Aarrr. I don't be knowin why ye be reinventing th' wheel.

Alrighty ya scurvy bilge rat, here it be:

$$x=a\left(\cos\tau-e\right)$$ $$y=a\sqrt{1-e^2}\sin\tau$$ $$z=0$$

That be givin it t' ye in th' plane. Then ya be rotatin th' plane with that land lubber Euler's transform in $\Omega$, $i$, $\omega$ (longitude of ascending node, inclination, and argument of periapsis), by multiplyin his matrix by yer vector up there:

$$\left( \begin{array}{ccc} \cos\omega \cos\Omega-\cos i \sin\omega \sin\Omega & -\cos\Omega \sin\omega -\cos i \cos\omega \sin\Omega & \sin i \sin\Omega \\ \cos i \cos\Omega \sin\omega+\cos\omega\sin\Omega & \cos i \cos\omega\cos \Omega-\sin\omega\sin\Omega & -\cos\Omega \sin i \\ \sin i \sin\omega & \cos\omega \sin i & \cos i \\ \end{array} \right)$$

Ye also be needin th' time it be ($\mu$ being th' $GM$ of the Sun):

$$t=\sqrt{a^3\over\mu}\left(\tau-e\sin\tau\right)$$

Yer $\tau=0$ and $t=0$ being yer time of periapsis. Ye be seein that ev'ry $2\pi$ in $\tau$, it be one a yer spins about th' Sun.

Use this page to generate SPICE kernels for the bodies of interest, and then use SPICE routines to calculate whatever you like to your heart's content.

Aarrr. I don't be knowin why ye be reinventing th' wheel.

Alrighty ya scurvy bilge rat, here it be:

$$x=a\left(\cos\tau-e\right)$$ $$y=a\sqrt{1-e^2}\sin\tau$$ $$z=0$$

That be givin it t' ye in th' plane. Then ya be rotatin th' plane with that land lubber Euler's transform in $\Omega$, $i$, $\omega$ (longitude of ascending node, inclination, and argument of periapsis), by multiplyin his matrix by yer vector up there:

$$\left( \begin{array}{ccc} \cos\omega \cos\Omega-\cos i \sin\omega \sin\Omega & -\cos\Omega \sin\omega -\cos i \cos\omega \sin\Omega & \sin i \sin\Omega \\ \cos i \cos\Omega \sin\omega+\cos\omega\sin\Omega & \cos i \cos\omega\cos \Omega-\sin\omega\sin\Omega & -\cos\Omega \sin i \\ \sin i \sin\omega & \cos\omega \sin i & \cos i \\ \end{array} \right)$$

Ye also be needin th' time it be ($\mu$ being th' $GM$ of the Sun):

$$t=\sqrt{a^3\over\mu}\left(\tau-e\sin\tau\right)$$

Yer $\tau=0$ and $t=0$ being yer time of periapsis. Ye be seein that ev'ry $2\pi$ in $\tau$, it be one a yer spins about th' Sun.

If yer scurvy rock be gettin close to a planet, then ye be wastin yer time, as th' orbit be changin on ye.

Use this page to generate SPICE kernels for the bodies of interest, and then use SPICE routines to calculate whatever you like to your heart's content.

Aarrr. I don't be knowin why ye be reinventing th' wheel.

Alrighty ya scurvy bilge rat, here it be:

$$x=a\left(\cos\tau-e\right)$$ $$y=a\sqrt{1-e^2}\sin\tau$$ $$z=0$$

That be givin it t' ye in th' plane. Then ya be rotatin th' plane with that land lubber Euler's transform in $\Omega$, $i$, $\omega$ (longitude of ascending node, inclination, and argument of periapsis), by multiplyin this matrix by yer vector up there:

$$\left( \begin{array}{ccc} \cos\omega \cos\Omega-\cos i \sin\omega \sin\Omega & -\cos\Omega \sin\omega -\cos i \cos\omega \sin\Omega & \sin i \sin\Omega \\ \cos i \cos\Omega \sin\omega+\cos\omega\sin\Omega & \cos i \cos\omega\cos \Omega-\sin\omega\sin\Omega & -\cos\Omega \sin i \\ \sin i \sin\omega & \cos\omega \sin i & \cos i \\ \end{array} \right)$$

Ye also be needin th' time it be ($\mu$ being th' $GM$ of the Sun):

$$t=\sqrt{a^3\over\mu}\left(\tau-e\sin\tau\right)$$

Yer $\tau=0$ and $t=0$ being yer time of periapsis. Ye be seein that ev'ry $2\pi$ in $\tau$, it be one a yer spins about th' Sun.

Use this page to generate SPICE kernels for the bodies of interest, and then use SPICE routines to calculate whatever you like to your heart's content.

Aarrr. I don't be knowin why ye be reinventing th' wheel.

Alrighty ya scurvy bilge rat, here it be:

$$x=a\left(\cos\tau-e\right)$$ $$y=a\sqrt{1-e^2}\sin\tau$$ $$z=0$$

That be givin it t' ye in th' plane. Then ya be rotatin th' plane with that land lubber Euler's transform in $\Omega$, $i$, $\omega$ (longitude of ascending node, inclination, and argument of periapsis), by multiplyin his matrix by yer vector up there:

$$\left( \begin{array}{ccc} \cos\omega \cos\Omega-\cos i \sin\omega \sin\Omega & -\cos\Omega \sin\omega -\cos i \cos\omega \sin\Omega & \sin i \sin\Omega \\ \cos i \cos\Omega \sin\omega+\cos\omega\sin\Omega & \cos i \cos\omega\cos \Omega-\sin\omega\sin\Omega & -\cos\Omega \sin i \\ \sin i \sin\omega & \cos\omega \sin i & \cos i \\ \end{array} \right)$$

Ye also be needin th' time it be ($\mu$ being th' $GM$ of the Sun):

$$t=\sqrt{a^3\over\mu}\left(\tau-e\sin\tau\right)$$

Yer $\tau=0$ and $t=0$ being yer time of periapsis. Ye be seein that ev'ry $2\pi$ in $\tau$, it be one a yer spins about th' Sun.