Another way to look at this, if you throw a screwdriver towards the Earth - yes it's traveling toward the Earth when you throw it.
But now look at what happens half an orbit later (about 45 minutes later),
The extra velocity is in the same direction as before but because of the orbit, that direction now points away from the Earth.
So it doesn't keep going towards the Earth. Roughly half the time it's traveling towards the Earth relative to the ISS and roughly half the time it's traveling away from the Earth depending where it is in its orbit,
The result is to change the orbit.
If the orbit of the ISS is perfectly circular, the new orbit will be more elliptical - with a perigee - time when it's closest to the Earth a quarter of an orbit later, and an apogee, three quarters of an orbit later.
The screwdriver you threw would cross the orbit of the ISS roughly half an orbit after you throw it, and cross it a second time, a full orbit later.
It probably won't return exactly to your hand half an orbit later even in the most ideal situation, because by throwing it towards the Earth, that means it orbits closer to the Earth and so goes around it faster, for the first half of its orbit. Then in the second half of the orbit it is further away from the Earth than the ISS, and goes around the Earth more slowly than the ISS.
So, you'd see it travel away from you, go around in a big arc, and one orbit later it would arrive back in your hand from behind your head.
However you'd need to throw it with great precision to preserve its major axis (longest axis of the ellipse) otherwise the period will change and it will get back to the same spot, true, but will get there before, or after the ISS so they miss each other.
If you throw it directly towards the Earth in a circular orbit - then that raises it's apogee (point when it is furthest from the Earth) - but it decreases its perigee by exactly the same amount. So the major axis is unchanged.
If you throw it slightly forward or backwards however, then it will instead go into an orbit with a slightly different period from the ISS, and wouldn't return exactly and gradually go out of phase with the ISS.
If you throw it directly backwards from a circular orbit,then this would reduce its apogee, and the perigee is unchanged, so reduces the major axis and so it goes into a faster orbit.
Throw it directly forwards and this will raise its apogee, perigee is unchanged and it goes into a higher and slower orbit.
Then, if you throw it sideways at an angle to the ISS orbit then it will go into an orbit with a slightly different inclination as well, reducing the chance of it ever reaching the ISS, because there are only two places in its orbit where it can hit the ISS - and they will almost never be in the right places at the right times both at the same time if they have slightly different orbital periods.
So, if you want the best chance to miss the ISS then throw it a bit sideways and backwards along its orbit as fast as you can.
It will be days probably before it gets back to the same position in its orbit as the ISS, and by then probably already in a lower orbit through drag effects especially if the ISS has done some boosts in between.
The ISS does major boosts once or twice a month
Plot of height of the ISS from Heavens Above - for the up to date plot see the website Height of the ISS
This is all of course assuming an ideal situation. In practice there are other complications that would need to be looked into.
First - the drag of the upper atmosphere is bound to be different which may affect the orbit - just because of different shape and density.
Minor effects would include solar wind pressure and light pressure from the sun, would be different as well of course.
Also the Earth's gravitational field is not perfectly spherical but has many anomalies in it, e.g. over continents and mountain ranges and ocean depths. So a ball that follows a slightly different trajectory from the ISS would be affected by those anomalies differently.
I'm not sure how much of a difference that makes so just mentioning them, if it was important to catch that ball half an orbit later - they would be things to check out to be sure..
They do actually throw things out of the ISS from time to time as scientfiic experiments. They choose the direction to throw it to make sure it won't come back and hit the ISS - which is a risk if you put it into a similar orbit to the ISS, same inclination as well, probably not after one orbit but several orbits later on.
Here is a steel ball thrown out of the ISS to help test how well ground stations can track orbital debris
Also the rather dramatic "suitsat" using a discarded Russian spacesuit
Cosmonaut Valery Tokarev preparing the old Russian Orlan spacesuit ready to throw it overboard the ISS as Suitsat".
Suitsat spinning away from the ISS. You can watch it on NBC. They threw it backwards along its orbit, so that it would gradually get further and further behind the ISS - by the time it got back to the location of the ISS then drag would have pulled it down to a lower orbit because the lighter spacesuit would have more drag than the ISS.
Another complication, the ISS changes its orbit slightly from time to time, sometimes to avoid orbital debris, also boosting in order to avoid falling back to the Earth because of the slight drag of the few atoms of our atmosphere at its altitude.
Then the gravitational field of the Earth is not perfectly uniform, you are in an inclined orbit also, and the Earth is oblate rather than spherical, to first approximation, with various mass anomalies. All this will mean it goes into a slightly different orbit no matter how precisely you throw it, and the drag will be different as well.
So would be hard to arrange it to come back exactly to your hand, but in theory it could happen.
On the other hand if you did want to hit the Earth, you'd need to throw it, counter intuitively, backwards along your orbit.
Throw it at 17,100 mph (7.644 km / sec), about twenty two times the speed of sound on Earth, backwards along your orbit and you'll counteract the orbital velocity of the ISS, and it will then just fall directly towards the Earth under acceleration due to gravity and hit it a few minutes later.
There are guns able to fire as fast as that, e.g. this one
But don't know if there are any outside of laboratories. Hypervelocity Impact Testing
You don't need to fire it quite as fast as that though. We don't need to hit the Earth directly. It is enough to get the bullet into an orbit that dips into the Earth's atmosphere low enough for re-entry like the Apollo astronauts or like shooting stars.
To do that - well the ISS at its highest is at 435 Km altitude. If we can get our bullet down to 70 km altitude it should re-enter.
So putting that into this orbit change calculator
Orbit injection calculator
then a velocity of 100 meters per second or 0.1 km / second will do.
Many rifles can achieve this.
So - it seems that if you had a rifle on the ISS - and actualy the Russians do carry one with them for use in case they land in a remote place and need to scare off wild animals on return. It can also shoot distress flares. This is it.
Every Soyuz has one - and the Soyuz remains docked to the ISS in case of an emergency return - so the gun is always available - though only intended for use on Earth.
Well - seems from this calculation - that if they fired bullets at the Earth they could achieve re-entry and create miniature shooting stars :).
Easy peasy indeed.
Again it is best to fire backwards along the orbit of the ISS to remove as much velocity as possible to get the perigee as close to the Earth as you can make it for maximum atmospheric drag. But with only 100 meters per second delta v needed, you wouldn't need to be especially careful to achieve bullet re-entry.
The fastest baseball pitchers can pitch at over 100 mph or over 44 meters per second.
Fastest Pitcher in Baseball by Baseball Almanac
This is enough for the baseball to go into an orbit that dips down to 175 km if you threw it from the ISS at its lowest orbit of 330 km. Not low enough for reentry. So I think safe enough to say that nobody will ever throw a ball from the ISS and manage to get it to re-enter the Earth's atmosphere.
A golfer could do it however. Hit a golf ball from the ISS and you could give it enough delta v to re-enter the Earth's atmosphere, especially when the ISS is in its lower 330 km altitude orbit.
I've now written this up for my science blog as Why A Ball Thrown To Earth From Orbit "Boomerangs". Can Astronauts Hit Earth With A Ball, Arrow Or Bullet?
You can also read it as one of my answers in my new kindle book: Simple Questions - Surprising answers - In Astronomy. You can read it online with the kindle cloud reader, or on a kindle device, or use the kindle app on any other device (quick and easy to install).
Everything in the book is also available to read for free online, but it's all gathered together as a book.
But now look at what happens half an orbit later (about 45 minutes later),
The extra velocity is in the same direction as before but because of the orbit, that direction now points away from the Earth.
So it doesn't keep going towards the Earth. Roughly half the time it's traveling towards the Earth relative to the ISS and roughly half the time it's traveling away from the Earth depending where it is in its orbit,
The result is to change the orbit.
If the orbit of the ISS is perfectly circular, the new orbit will be more elliptical - with a perigee - time when it's closest to the Earth a quarter of an orbit later, and an apogee, three quarters of an orbit later.
The screwdriver you threw would cross the orbit of the ISS roughly half an orbit after you throw it, and cross it a second time, a full orbit later.
WHY IT'S HARD TO GET IT TO RETURN TO YOUR HAND EXACTLY
It probably won't return exactly to your hand half an orbit later even in the most ideal situation, because by throwing it towards the Earth, that means it orbits closer to the Earth and so goes around it faster, for the first half of its orbit. Then in the second half of the orbit it is further away from the Earth than the ISS, and goes around the Earth more slowly than the ISS.
So, you'd see it travel away from you, go around in a big arc, and one orbit later it would arrive back in your hand from behind your head.
However you'd need to throw it with great precision to preserve its major axis (longest axis of the ellipse) otherwise the period will change and it will get back to the same spot, true, but will get there before, or after the ISS so they miss each other.
If you throw it directly towards the Earth in a circular orbit - then that raises it's apogee (point when it is furthest from the Earth) - but it decreases its perigee by exactly the same amount. So the major axis is unchanged.
If you throw it slightly forward or backwards however, then it will instead go into an orbit with a slightly different period from the ISS, and wouldn't return exactly and gradually go out of phase with the ISS.
If you throw it directly backwards from a circular orbit,then this would reduce its apogee, and the perigee is unchanged, so reduces the major axis and so it goes into a faster orbit.
Throw it directly forwards and this will raise its apogee, perigee is unchanged and it goes into a higher and slower orbit.
Then, if you throw it sideways at an angle to the ISS orbit then it will go into an orbit with a slightly different inclination as well, reducing the chance of it ever reaching the ISS, because there are only two places in its orbit where it can hit the ISS - and they will almost never be in the right places at the right times both at the same time if they have slightly different orbital periods.
So, if you want the best chance to miss the ISS then throw it a bit sideways and backwards along its orbit as fast as you can.
It will be days probably before it gets back to the same position in its orbit as the ISS, and by then probably already in a lower orbit through drag effects especially if the ISS has done some boosts in between.
The ISS does major boosts once or twice a month
This is all of course assuming an ideal situation. In practice there are other complications that would need to be looked into.
First - the drag of the upper atmosphere is bound to be different which may affect the orbit - just because of different shape and density.
Minor effects would include solar wind pressure and light pressure from the sun, would be different as well of course.
Also the Earth's gravitational field is not perfectly spherical but has many anomalies in it, e.g. over continents and mountain ranges and ocean depths. So a ball that follows a slightly different trajectory from the ISS would be affected by those anomalies differently.
I'm not sure how much of a difference that makes so just mentioning them, if it was important to catch that ball half an orbit later - they would be things to check out to be sure..
SOME OF THE THINGS THE ASTRONAUTS THROW OUT OF THE ISS AS EXPERIMENTS
They do actually throw things out of the ISS from time to time as scientfiic experiments. They choose the direction to throw it to make sure it won't come back and hit the ISS - which is a risk if you put it into a similar orbit to the ISS, same inclination as well, probably not after one orbit but several orbits later on.
Here is a steel ball thrown out of the ISS to help test how well ground stations can track orbital debris
Also the rather dramatic "suitsat" using a discarded Russian spacesuit
Another complication, the ISS changes its orbit slightly from time to time, sometimes to avoid orbital debris, also boosting in order to avoid falling back to the Earth because of the slight drag of the few atoms of our atmosphere at its altitude.
Then the gravitational field of the Earth is not perfectly uniform, you are in an inclined orbit also, and the Earth is oblate rather than spherical, to first approximation, with various mass anomalies. All this will mean it goes into a slightly different orbit no matter how precisely you throw it, and the drag will be different as well.
So would be hard to arrange it to come back exactly to your hand, but in theory it could happen.
WHAT IF YOU WANT TO HIT THE EARTH
On the other hand if you did want to hit the Earth, you'd need to throw it, counter intuitively, backwards along your orbit.
Throw it at 17,100 mph (7.644 km / sec), about twenty two times the speed of sound on Earth, backwards along your orbit and you'll counteract the orbital velocity of the ISS, and it will then just fall directly towards the Earth under acceleration due to gravity and hit it a few minutes later.
There are guns able to fire as fast as that, e.g. this one
You don't need to fire it quite as fast as that though. We don't need to hit the Earth directly. It is enough to get the bullet into an orbit that dips into the Earth's atmosphere low enough for re-entry like the Apollo astronauts or like shooting stars.
To do that - well the ISS at its highest is at 435 Km altitude. If we can get our bullet down to 70 km altitude it should re-enter.
So putting that into this orbit change calculator
Orbit injection calculator
then a velocity of 100 meters per second or 0.1 km / second will do.
Many rifles can achieve this.
So - it seems that if you had a rifle on the ISS - and actualy the Russians do carry one with them for use in case they land in a remote place and need to scare off wild animals on return. It can also shoot distress flares. This is it.
The Russian Gun At The International Space Station - James Oberg's Pioneering Space
Every Soyuz has one - and the Soyuz remains docked to the ISS in case of an emergency return - so the gun is always available - though only intended for use on Earth.
Well - seems from this calculation - that if they fired bullets at the Earth they could achieve re-entry and create miniature shooting stars :).
Easy peasy indeed.
Again it is best to fire backwards along the orbit of the ISS to remove as much velocity as possible to get the perigee as close to the Earth as you can make it for maximum atmospheric drag. But with only 100 meters per second delta v needed, you wouldn't need to be especially careful to achieve bullet re-entry.
The fastest baseball pitchers can pitch at over 100 mph or over 44 meters per second.
Fastest Pitcher in Baseball by Baseball Almanac
This is enough for the baseball to go into an orbit that dips down to 175 km if you threw it from the ISS at its lowest orbit of 330 km. Not low enough for reentry. So I think safe enough to say that nobody will ever throw a ball from the ISS and manage to get it to re-enter the Earth's atmosphere.
A golfer could do it however. Hit a golf ball from the ISS and you could give it enough delta v to re-enter the Earth's atmosphere, especially when the ISS is in its lower 330 km altitude orbit.
I've now written this up for my science blog as Why A Ball Thrown To Earth From Orbit "Boomerangs". Can Astronauts Hit Earth With A Ball, Arrow Or Bullet?
NEW KINDLE BOOK
You can also read it as one of my answers in my new kindle book: Simple Questions - Surprising answers - In Astronomy. You can read it online with the kindle cloud reader, or on a kindle device, or use the kindle app on any other device (quick and easy to install).
Everything in the book is also available to read for free online, but it's all gathered together as a book.
About the Author
Robert Walker
Writer of articles on Mars and Space issues - Software Developer of Tune Smithy, Bounce Metronome etc.Studied at Wolfson College, Oxford
Lives in Isle of Mull
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