It's a consequence of the reversibility of orbits that anything that free-falls from a near-interstellar distance. Take the Vis-Viva equation, the formula for the velocity of objects in Keplerian orbits/trajectories:

$$v=\sqrt{\mu\left(\frac{2}{r}-\frac{1}{a}\right)}$$

Where $r$ is the radial distance, $a$ is the semi-major axis, and $\mu$ is the standard gravitational parameter.

When $a$ is very, very large compared to $r$, things start to look like this:

$$v=\sqrt{\mu\left(\frac{2}{r}\right)}$$

Which is the formula for escape velocity.

So basically, almost anything falling from the Oort cloud to the inner solar system is going to be scraping the underside of escape velocity in the inner system, at minimum.

For an example, the inner edge of the Oort cloud is believed to start at about $2\,000\, \mathrm{AU}$ from the Sun, according to NASA's Solar System Overview. As such an object in a highly-elliptical orbit that takes it out that far would have a semimajor axis of about $1\,000\,\mathrm{AU}$. Jupiter's Semimajor axis is about $5 \,\mathrm{AU}$.

The Vis-viva calculation puts an object orbiting the Sun with a semi-major axis of $1000\, \mathrm{AU}$ moving at $18\,814\, \mathrm{m/s}$ when it reaches $5\, \mathrm{AU}$. Solar Escape velocity at $5\, \mathrm{AU}$ is $18\,837\,\mathrm{m/s}$, a difference of $23 \,\mathrm{m/s}$ that would be swallowed whole if I'd used proper significant figures in the calculation.

It's a consequence of the reversibility of orbits that anything that free-falls from a near-interstellar distance arrives at nearly escape velocity, or faster. Take the Vis-Viva equation, the formula for the velocity of objects in Keplerian orbits/trajectories:

$$v=\sqrt{\mu\left(\frac{2}{r}-\frac{1}{a}\right)}$$

Where $r$ is the radial distance, $a$ is the semi-major axis, and $\mu$ is the standard gravitational parameter.

When $a$ is very, very large compared to $r$, things start to look like this:

$$v=\sqrt{\mu\left(\frac{2}{r}\right)}$$

Which is the formula for escape velocity.

So basically, almost anything falling from the Oort cloud to the inner solar system is going to be scraping the underside of escape velocity in the inner system, at minimum.

For an example, the inner edge of the Oort cloud is believed to start at about $2\,000\, \mathrm{AU}$ from the Sun, according to NASA's Solar System Overview. As such an object in a highly-elliptical orbit that takes it out that far would have a semimajor axis of about $1\,000\,\mathrm{AU}$. Jupiter's Semimajor axis is about $5 \,\mathrm{AU}$.

The Vis-viva calculation puts an object orbiting the Sun with a semi-major axis of $1000\, \mathrm{AU}$ moving at $18\,814\, \mathrm{m/s}$ when it reaches $5\, \mathrm{AU}$. Solar Escape velocity at $5\, \mathrm{AU}$ is $18\,837\,\mathrm{m/s}$, a difference of $23 \,\mathrm{m/s}$ that would be swallowed whole if I'd used proper significant figures in the calculation.

It's a consequence of the reversibility of orbits that anything that free-falls from a near-interstellar distance. Take the Vis-Viva equation, the formula for the velocity of objects in Keplerian orbits/trajectories:

$$v=\sqrt{\mu\left(\frac{2}{r}-\frac{1}{a}\right)}$$

Where $r$ is the radial distance, $a$ is the semi-major axis, and $\mu$ is the standard gravitational parameter.

When $a$ is very, very large compared to $r$, things start to look like this:

$$v=\sqrt{\mu\left(\frac{2}{r}\right)}$$

Which is the formula for escape velocity.

So basically, almost anything falling from the Oort cloud to the inner solar system is going to be scraping the underside of escape velocity in the inner system, at minimum.

It's a consequence of the reversibility of orbits that anything that free-falls from a near-interstellar distance. Take the Vis-Viva equation, the formula for the velocity of objects in Keplerian orbits/trajectories:

$$v=\sqrt{\mu\left(\frac{2}{r}-\frac{1}{a}\right)}$$

Where $r$ is the radial distance, $a$ is the semi-major axis, and $\mu$ is the standard gravitational parameter.

When $a$ is very, very large compared to $r$, things start to look like this:

$$v=\sqrt{\mu\left(\frac{2}{r}\right)}$$

Which is the formula for escape velocity.

So basically, almost anything falling from the Oort cloud to the inner solar system is going to be scraping the underside of escape velocity in the inner system, at minimum.

For an example, the inner edge of the Oort cloud is believed to start at about $2\,000\, \mathrm{AU}$ from the Sun, according to NASA's Solar System Overview. As such an object in a highly-elliptical orbit that takes it out that far would have a semimajor axis of about $1\,000\,\mathrm{AU}$. Jupiter's Semimajor axis is about $5 \,\mathrm{AU}$.

The Vis-viva calculation puts an object orbiting the Sun with a semi-major axis of $1000\, \mathrm{AU}$ moving at $18\,814\, \mathrm{m/s}$ when it reaches $5\, \mathrm{AU}$. Solar Escape velocity at $5\, \mathrm{AU}$ is $18\,837\,\mathrm{m/s}$, a difference of $23 \,\mathrm{m/s}$ that would be swallowed whole if I'd used proper significant figures in the calculation.