The method you are speaking of, sometimes
called "gravity assist" is actually fairly
commonly used when planning flight paths for space
shuttles and probes. Using this method, space
craft fly close enough to a large body of mass and
use that mass's gravitational pull to accelerate,
changing it's velocity and direction, in a
NASA's Voyager 1 and Voyager 2 probes, which
study the outermost regions of our solar system,
used a gravitational slingshot method to
accelerate themselves past Saturn and Jupiter.
Theoretically, this gravitational slingshot
method should work with any object which has a
large gravitational field, so it should work
with a black hole too. However, there are
certain considerations to take into account. If
anything gets too close to a black hole, no matter
how fast it is going, it will get pulled in and
can never escape, therefore a space probe
would have to stay much further away from a black
hole than a planet. Beyond that though, there is
the issue of distance. All known black
holes are VERY VERY far from Earth. The closest
black hole is about 2800 light years away from
Earth, that is about 16,000,000,000,000,000
miles. Just to refresh your memory, a light
year is the distance that light can travel in one
year. Compared to that distance, Voyager 1 is
the furthest human made object from Earth, it is
only 12,000,000,000 miles from Earth. That means
the closest black hole to Earth is over 1 million
times farther away than any human made object has
ever traveled, even considering that it has been
traveling for over 40 years.
So, long story short, I would say that it is
theoretically possible to accomplish such a
maneuver, it is highly unlikely that humans or
any human made object will ever travel close
enough to a black hole to actually try it out.
I hope this answers your question!
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