Every now and again you hear someone say the way to get rid of nuclear waste is to send it into the Sun. First the idea of putting seriously radioactive material on rockets that tend to explode every now and again is daft, but there's another problem - making it to the Sun.
Figuring out orbital motion, Newton used a simple thought experiment. Imagine a special mountaintop cannon that can shoot balls as fast as you like. You fire off a ball parallel to the horizon and watch as gravity pulls it down. Now fire one faster .. it goes further before falling back to Earth. Keep increasing the speed and it goes farther and farther until you make it all the way around about 88 minutes later. The cannonball is now in orbit.. its velocity is high enough that it continually misses the Earth as it falls.. technically it's always in free fall.
Astronauts in orbit never escape gravity - they're just in free fall.. the same you sometimes get in a roller coaster or an elevator when the cable suddenly breaks.
Now consider the Earth as it orbits the Sun. Our orbit is reasonably close to circular with an average speed of about 30 kilometers per second. If you want to send something into the Sun you have to burn off that speed - all of it. the rocket would have to go 30 kilometers per second in the other direction. It would then have an orbital velocity of zero and would fall directly into the Sun. Anything less and it would end up in some kind of orbit.
Thirty kilometers per second is a tall order and impossible with chemically fueled rocket technology. By comparison adding about 11 kilometers per second to Earth's orbital speed lets you escape the influence of Earth's gravity and head out into the outer solar system. At about 16 kilometers per second you can entirely escape the solar system's influence and travel to the stars.
It is much easier to build a rocket to go to the stars than to the Sun.
There's a trick if you don't mind taking the scenic route. Circular orbital velocity is ~ (GM/R).5, where G is the gravitational constant, M the mass you're orbiting around, and R the orbital radius. Bodies orbiting close to the Sun move fast - Mercury is moving about 48 kilometers per second, while those farther out are slower - Neptune is just 5.4 kilometers per second. If you send a rocket deeper into the solar system the amount of speed you need to burn off is lower. Travel to the inner solar system becomes more practical and you could even send something into the Sun with current technology.
The Parker Solar Probe is making a series of close approaches to the Sun - it uses this trick along with using Venus as a gravitational brake to move well within Mercury's orbit. A most amazing mission ultimately coming within about 5.3 million kilometers of our star's surface and probably touching it's corona.
Finally a bit of gee whiz. Standing on either of the Martian moons Phobos or Deimos, you could easily throw a baseball into orbit. Most of you could probably throw a ball fast enough to reach escape velocity. One of you could serve a volleyball fast enough.
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