If an object orbiting Earth gets too far away, it will leave orbit because of tidal influences of other objects (mainly the Sun and the Moon). If the object gets too close, it can break up if Earth’s tidal forces are stronger than its own gravity; or if it’s small and mechanically strong, it can instead get close enough to be dragged out of orbit by friction with the fringes of Earth’s atmosphere.
The maximum orbital distance around a body like Earth which itself moves in a larger system, is determined by the distance at which small tidal perturbations from the initial orbit grow with time. Thi
If an object orbiting Earth gets too far away, it will leave orbit because of tidal influences of other objects (mainly the Sun and the Moon). If the object gets too close, it can break up if Earth’s tidal forces are stronger than its own gravity; or if it’s small and mechanically strong, it can instead get close enough to be dragged out of orbit by friction with the fringes of Earth’s atmosphere.
The maximum orbital distance around a body like Earth which itself moves in a larger system, is determined by the distance at which small tidal perturbations from the initial orbit grow with time. This occurs basically at the distance of the L1 Lagrange point between the Earth and Sun, where the primary body (Sun’s) gravity balances with the secondary (Earth’s) gravity and Sun-orbital motion. More precisely it is the Hill sphere radius
[math]r_H \approx a(1-e)\Big(\dfrac{m}{3M}\Big)^{1/3} \approx a\sqrt[3]{\dfrac{m}{3M}}.\tag*{}[/math]
https://en.wikipedia.org/wiki/Hill_sphere#/media/File:Lagrange_points2.svg ; distances are not to real scale.
For Earth, with eccentricity [math]e \approx 1/60.0[/math], solar orbit radius [math]a \approx 149.6\text{ million km}[/math], Earth/Sun mass ratio [math]m/M \approx 1/333\,000[/math], the Hill radius is about [math]1.47\text{ million km}[/math], nearly four times further out than the Moon. As Bill Otto explains, in practice there are enough perturbations that the practical limit is about the Moon’s orbital distance of [math]384\,000\text{ km}[/math], in fact at the Earth-Moon stable Lagrange points 60 degrees ahead and behind the Moon in its Earth orbit. (These are not the same as the Lagrange points for the Earth-Sun system diagrammed above.)
The minimum orbital radius depends on the type of satellite. If it is large enough to need gravity rather than its own material strength to hold it together, then Earth’s tidal influence will break it apart if it gets as close as the Roche limit. For Earth and say a rocky or icy satellite (somewhat less dense), the Roche limit is about [math]1.5[/math] Earth radii, that is about [math]9600\text{ km}[/math] from Earth’s center or about [math]3500\text{ km}[/math] above the surface.
https://en.wikipedia.org/wiki/Hill_sphere#/media/File:Comparison_of_Hill_sphere_and_Roche_limit.svg ; distances are not to real scale
For a smaller body like an artificial satellite, held together by its own mechanical strength, the lowest orbit is determined by atmospheric drag; as Bill Otto nicely details here and in other answers,
the practical limit for completing more than a few orbits is at least 200 km above Earth’s surface, and [math]400[/math] to [math]500\text{ km}[/math] if regular boosts aren’t available.
The minimum distance is about 170 km. The object cannot even orbit once at that altitude because the atmospheric drag would cause it to re-enter. The lowest longer term practical altitude is 300 to 400 km, but that still requires frequent boosting to maintain orbit. The higher the ballistic coefficient, the longer it can stay in orbit, but without boosting, a couple of years is about the limit at 400 km. Something with a lot of drag, like a hammer, can only last about 3 months.
At the higher end, the Lagrange points are probably a practical limit. SOHO observed some atmosphere around the Earth
The minimum distance is about 170 km. The object cannot even orbit once at that altitude because the atmospheric drag would cause it to re-enter. The lowest longer term practical altitude is 300 to 400 km, but that still requires frequent boosting to maintain orbit. The higher the ballistic coefficient, the longer it can stay in orbit, but without boosting, a couple of years is about the limit at 400 km. Something with a lot of drag, like a hammer, can only last about 3 months.
At the higher end, the Lagrange points are probably a practical limit. SOHO observed some atmosphere around the Earth as high as 900,000 km which is about the limit of the Earth's gravitational influence. Beyond that, a satellite could easily slip into orbit around the Sun, leaving the vicinity of the Earth.
The maximum distance for an object to remain in orbit around the Earth is 1.5 million kilometers. The space within this boundary is called the Hill Sphere.
* Hill's Sphere
The Hill Sphere is a region in space where a body has a gravitational domain. You can calculate Hill's Sphere for anybody using the formula for calculating Hill's Sphere.
In opposition to the Hill Sphere, we have the Roche Limit
The maximum distance for an object to remain in orbit around the Earth is 1.5 million kilometers. The space within this boundary is called the Hill Sphere.
* Hill's Sphere
The Hill Sphere is a region in space where a body has a gravitational domain. You can calculate Hill's Sphere for anybody using the formula for calculating Hill's Sphere.
In opposition to the Hill Sphere, we have the Roche Limit which is the minimum distance that one object can orbit another. If an object exceeds the Roche limit, the gravity that holds the body together becomes weaker than the tidal for...

An object can remain in orbit around the Earth at various distances, depending on its speed and the gravitational pull of the Earth. Here are some key points regarding orbital distances:
- Low Earth Orbit (LEO): This region extends from about 160 kilometers (100 miles) to 2,000 kilometers (1,200 miles) above Earth's surface. Satellites in LEO, such as the International Space Station (ISS), typically orbit at altitudes around 400 kilometers (about 250 miles).
- Medium Earth Orbit (MEO): This region ranges from about 2,000 kilometers (1,200 miles) to approximately 35,786 kilometers (22,236 miles). GPS
An object can remain in orbit around the Earth at various distances, depending on its speed and the gravitational pull of the Earth. Here are some key points regarding orbital distances:
- Low Earth Orbit (LEO): This region extends from about 160 kilometers (100 miles) to 2,000 kilometers (1,200 miles) above Earth's surface. Satellites in LEO, such as the International Space Station (ISS), typically orbit at altitudes around 400 kilometers (about 250 miles).
- Medium Earth Orbit (MEO): This region ranges from about 2,000 kilometers (1,200 miles) to approximately 35,786 kilometers (22,236 miles). GPS satellites, for example, are in MEO at about 20,200 kilometers (12,550 miles).
- Geostationary Orbit (GEO): At approximately 35,786 kilometers (22,236 miles) above the Earth, satellites in GEO orbit at a speed that matches the Earth's rotation, allowing them to stay over the same point on the Earth's surface.
- High Earth Orbit (HEO): This includes orbits above GEO, often used for specialized satellite missions, such as communications or scientific observation.
In summary, an object can remain in orbit at distances ranging from a few hundred kilometers to tens of thousands of kilometers above the Earth, depending on its specific orbital parameters and the mission requirements.
Theoretically, the distance does not play any role when one body orbits other body. However, there are two factors limiting the distance for Earth orbits. 1. The atmosphere. Orbiting object has to be high enough to avoid the Earth atmosphere, otherwise its velocity is decreased by drag and it gradually descends and eventually decays in the atmosphere. That’s why the “low Earth orbits” are above some 100 km. 2. Gravitational influence of other bodies. The Earth is not alone in space; there are other bodies with their own gravitational forces, e.g. the Moon and the Sun, to name the most signific
Theoretically, the distance does not play any role when one body orbits other body. However, there are two factors limiting the distance for Earth orbits. 1. The atmosphere. Orbiting object has to be high enough to avoid the Earth atmosphere, otherwise its velocity is decreased by drag and it gradually descends and eventually decays in the atmosphere. That’s why the “low Earth orbits” are above some 100 km. 2. Gravitational influence of other bodies. The Earth is not alone in space; there are other bodies with their own gravitational forces, e.g. the Moon and the Sun, to name the most significant ones. Gravitational force decreases with distance. So when the object is sufficiently far from the Earth, the gravitational force of the Moon or the Sun can prevail and the object is no longer on the Earth orbit. Considering (nearly) circular orbit with orbital plane close to the Moon’s, the theoretical upper limit could be close to 8/9 of the Earth-Moon distance, but such orbits would be highly unstable due to perturbations (gravitational influence) caused by the Moon. The highest stable Earth orbit distance for a satellite probably is the Lagrange point L2 of the Earth-Moon system, i.e. approximately 60 000 km “behind” the Moon (from our point of view), with orbital period equal to the Moon orbital period. It has been used for a radio satellite covering the far side of the Moon. EDIT: A satellite could orbit the Earth anywhere in the so called Hill sphere (where gravitational influence of the Earth is dominant, which is roughly up to 1.5 million kilometers from the Earth), but I think such orbits could sustain for relatively short periods.
Gravity works on objects in space just as it does objects at the ground, but it does slowly become weaker as you move further and further away. Being in orbit is required to keep the objects from falling back to earth!
Here’s the usual thought experiment that demonstrates the physics. Grab a ball and throw it exactly horizontally. It manages some distance but immediately gravity takes hold and the ball accelerates towards the earth until it hits the ground. If you do this again but throw as hard as you can, the ball will go further over the ground but will still get pulled back to earth. As you
Gravity works on objects in space just as it does objects at the ground, but it does slowly become weaker as you move further and further away. Being in orbit is required to keep the objects from falling back to earth!
Here’s the usual thought experiment that demonstrates the physics. Grab a ball and throw it exactly horizontally. It manages some distance but immediately gravity takes hold and the ball accelerates towards the earth until it hits the ground. If you do this again but throw as hard as you can, the ball will go further over the ground but will still get pulled back to earth. As you throw faster and faster (e.g. use a gun instead of a ball), the object travels further over the ground but still eventually comes back to earth. So what happens as speed continues to increase? Eventually the ground starts to drop away from under the object due to the curvature of the earth, and gravity always pulls the object towards the center of the earth, so it continues to follow a curved path. When the object is going about 17,000 miles per hour, the ground drops away from underneath the object as fast as the object falls towards it, and it the will make a complete circle all the way around and come back to where it started! As people like to say, you’re still falling, you just keep missing the ground.
Now, the problem, of course, is that air resistance makes this infeasible to do within the earth’s atmosphere- it keeps slowing down the object when you want to maintain a constant speed. So to actually be able to orbit, we have to also climb up to an altitude where atmospheric drag is no longer a factor- which is about 100km high. Once you get that high, as long as you’ve reached the required orbital velocity you can shut off your engines and just free-fall all the way around the earth- constantly falling, but never hitting. This is why there appears to be no gravity in a spaceship- everything is in free fall, the ship and the astronauts- but they are indeed falling towards the earth due to gravity, but at exactly the same rate with respect to each other.
In order to drift off into outer space and never fall back to earth (or remain in orbit), you need to reach a higher speed (escape velocity) where your orbital altitude continues to increase faster than earth can pull it back, and then you can finally be free of earth’s gravity, which will continue to decrease as you get further away.
Is 'orbit' obtained at some specific distance from Earth?
Yes. A specific distance for the speed the object is going.
The earths gravity effects things a loooooong way away (think of the moon). So anything within its sphere of influence will be pulled towards it to some degree depending on how far away it is. If something is traveling past the earth then it’s trajectory will be influenced. Meaning it will curve towards the earth as gravity starts to pull at it, but will also continue in the general direction it was originally heading.
If the object gets too close, or is going too slow, then it wi
Is 'orbit' obtained at some specific distance from Earth?
Yes. A specific distance for the speed the object is going.
The earths gravity effects things a loooooong way away (think of the moon). So anything within its sphere of influence will be pulled towards it to some degree depending on how far away it is. If something is traveling past the earth then it’s trajectory will be influenced. Meaning it will curve towards the earth as gravity starts to pull at it, but will also continue in the general direction it was originally heading.
If the object gets too close, or is going too slow, then it will spin into the earth and crash (or land). If it is going too fast or is too far it will curve towards the earth then continue on past it.
If the distance and speed are just right the object will move forward at the same rate it “falls” (curves) towards the earth and be in orbit.
Basically it is falling into the earth but keeps missing it.
Where do I start?
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Where do I start?
I’m a huge financial nerd, and have spent an embarrassing amount of time talking to people about their money habits.
Here are the biggest mistakes people are making and how to fix them:
Not having a separate high interest savings account
Having a separate account allows you to see the results of all your hard work and keep your money separate so you're less tempted to spend it.
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Here is a list of the top savings accounts available today. Deposit $5 before moving on because this is one of the biggest mistakes and easiest ones to fix.
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Once you enter space, there is nothing there to resist you enough to slow you down. You can safely depressurize your craft and open window to stick your head out like a dog sticking its tongue out the window of your car.. You will feel nothing at all. It is nothingness.. Even , you still need to attain enough speed to keep you at the same orbit level of your own choice. Satellites are put at many different levels of orbits for various reasons like need for more space from each other without collidiing , for one.
the real irony is that you need lower speed at higher levels of orbits probably bec
Once you enter space, there is nothing there to resist you enough to slow you down. You can safely depressurize your craft and open window to stick your head out like a dog sticking its tongue out the window of your car.. You will feel nothing at all. It is nothingness.. Even , you still need to attain enough speed to keep you at the same orbit level of your own choice. Satellites are put at many different levels of orbits for various reasons like need for more space from each other without collidiing , for one.
the real irony is that you need lower speed at higher levels of orbits probably because the pull of gravity is weaker at higher orbits.. I cannot explain this rocket science to you , but I can also tell you that geosynchronous or geostationary satellites only need around 4,000 mph to stay in one place in orbit about 25K miles up there. I can only think that gravity is weaker the higher the orbit is that satellites can be much slower without falling down. They can still fall down if it is slower than prescribed as per to rocket science or floating away if faster .
it is rocket science you are talking about here. The satellites at the lowest orbit levels are the fastest at around 17,.000mph.. if it is slower, it will fall down and vice versa.
I still dont understand how satellites can be launched to a precise orbit level we wanted it to be and forget about it.. with possible occassional rocket boosts to keep it level there.
it is rocket science. It can be pretty explained as simply as hanging them with a string up there somehow.. Space is nothingness and vacuum filled with nothingness. No friction. you cannot flap wings around up there.. it won’t help you..
Satellites do not float away by the same mechanism that you don’t… we call the effect “gravity”.
A ball you throw upwards comes back down… because it is not going fast enough to get away.
There is a speed you could throw it so it will get away.
What do you think would happen if you threw the ball at the exact crossover speed between it flying off and returning?
That is sort of where satellites live.
We finness it by also throwing the satellite sideways … the harder you throw a ball sideways, the farther it goes before it hits the ground. Obvious right?
The Earth is round … so it is possible to throw
Satellites do not float away by the same mechanism that you don’t… we call the effect “gravity”.
A ball you throw upwards comes back down… because it is not going fast enough to get away.
There is a speed you could throw it so it will get away.
What do you think would happen if you threw the ball at the exact crossover speed between it flying off and returning?
That is sort of where satellites live.
We finness it by also throwing the satellite sideways … the harder you throw a ball sideways, the farther it goes before it hits the ground. Obvious right?
The Earth is round … so it is possible to throw it so hard that the ball goes all the way around the Earth. With no air friction, this is easier.
It could be thrown so hard that the ball goes around the earth many times before hitting the ground.
Throw it too hard and it starts spiralling away from the Earth.
Just right, and it just keeps going round and round … with no air resistance, forever.
So to orbit, you need low air resistance … but, in principle, a satellite could orbit at any distance if it is small.
I once met a man who drove a modest Toyota Corolla, wore beat-up sneakers, and looked like he’d lived the same way for decades. But what really caught my attention was when he casually mentioned he was retired at 45 with more money than he could ever spend. I couldn’t help but ask, “How did you do it?”
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Mos
I once met a man who drove a modest Toyota Corolla, wore beat-up sneakers, and looked like he’d lived the same way for decades. But what really caught my attention was when he casually mentioned he was retired at 45 with more money than he could ever spend. I couldn’t help but ask, “How did you do it?”
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original question: At what distance from the Earth can an object remain in orbit?
Sorry, my Google Search with several different keywords did not have any variation of “high Earth orbit” come up in the first few pages. It’s been too long since I’ve done any orbital mechanics for me to derive it - I’m certain I never did. There surely are high orbits around Earth beyond geosynchronous before the Moon’s influence becomes important but I cannot think of any reason to put a satellite there. Apparently, no one else has, either.
There are reasons to put things at the Earth-Moon Lagrange Points. Things
original question: At what distance from the Earth can an object remain in orbit?
Sorry, my Google Search with several different keywords did not have any variation of “high Earth orbit” come up in the first few pages. It’s been too long since I’ve done any orbital mechanics for me to derive it - I’m certain I never did. There surely are high orbits around Earth beyond geosynchronous before the Moon’s influence becomes important but I cannot think of any reason to put a satellite there. Apparently, no one else has, either.
There are reasons to put things at the Earth-Moon Lagrange Points. Things there are orbiting with the Earth-Moon system, effectively at a fixed distance from Earth.
I cannot think of a reason to put something at Earth-Moon L3. But we will probably put things at Earth-Moon L1 and Earth-Moon L2 - comsats, almost hemispherical observers, even the central stations of lunar space elevators. L5 was the name chosen by an organization intent on the settlement of space. They merged with the National Space Institute to become the National Space Society. Dr. O’Neill suggested L4 and L5 as the ideal location for space manufacturing, including the building of large space habitats and solar power satellites. The solar power satellites were to be relocated to geosynchronous orbit to sell electricity to Earth. That would pay off some of the mortgage for industrializing the Moon and cis-lunar space. Oh, and so will selling the liveable land they create.
Let’s get back to Lagrange Points - consider the Earth-Sun L1 and L2.
NASA’s EPIC::DSCOVR is at Earth-Sun L1, about 900,000 miles from Earth.
and NASA’s James Webb Space Telescope will be at Earth-Sun L2, about 930,000 miles from Earth.
https://www.nasa.gov/topics/universe/features/webb-l2.htmlI am unable, now, without a lot of preparation, to calculate how far from Earth something could orbit Earth before the Sun would interfere with the orbit. The Lagrange Points are “special”. I’m certain they are much further from Earth than any other stable orbits.
Thanks for the A2A, Andrew.
Gravity is what keeps it from floating away.
Have you ever swung a rope in a circle with a rock on the end?
Now replace the rope with earth’s gravity, and the rock with the satellite.
For a satellite to remain in a circular orbit, it must have just the right speed, and that depends on the distance from earth. If the speed is off it will go into an elliptical orbit, and it might crash into the earth, but not necessarily. If it is going
Gravity is what keeps it from floating away.
Have you ever swung a rope in a circle with a rock on the end?
Now replace the rope with earth’s gravity, and the rock with the satellite.
For a satellite to remain in a circular orbit, it must have just the right speed, and that depends on the distance from earth. If the speed is off it will go into an elliptical orbit, and it might crash into the earth, but not necessarily. If it is going very, very fast, it can escape the Earth’s gravity, and sail off into space. It will most likely go into an elliptical orbit around the sun.
The answer to that depends on how much stability you’re looking for. For short term stability, the answer would be the Earth’s Hill sphere - Wikipedia, which works out to be 1.5M km. For something to be stable long term, you need to be closer to the 0.5M-0.75M km range. This leaves you anywhere from not that far above the Moon (in the grand scale of things), at 0.384 M km, to almost twice the Moon’s altitude.
In principle, if the Earth was the only object in space, there's no limit to how big an orbit can be. The Earth's gravity extends infinitely in all directions.
The thing that limits the size of orbits in practice is the effect of other bodies like the Moon and the Sun. If you try to orbit too far away, you end up being closer to one of those than to the Earth, and that disrupts your orbit and makes it unstable.
The distance has to do with the height of the atmosphere, and the speed of the orbit. the higher you go, the slower the orbit. I think the lowest practical orbit is 100 miles, to avoid drag from the atmosphere.
An object in orbit at an altitude of less than roughly 200 km is considered unstable due to atmospheric drag. For a satellite to be in a stable orbit (i.e. sustainable for more than a few months), 350 km is a more standard altitude for low Earth orbit. Satellites with Low Earth Orbit closest to the earth at 160 – 2,000km (99 – 1243 miles), and Geostationary orbit the furthest away, at 35,786 km (22,236 miles).
The limit is about 1.5 million kilometers, or 0.01 AU. This is known as the Hill sphere. Beyond that, the influence of the Sun will pull the spacecraft out of its orbit.
If an object want to orbit around the earth will obey certain conditions
- GMm ÷ R = mv^2 or we can say the kinetic energy of the object should be equal to potential energy at the distance R.
- M>m
- Orbital radius should be below 300000km .(because moon is orbiting around the earth at a radius 383400km other wise the object moves around the moon)
At any orbit if there is no atmosphere (case of the Moon) but in practice in order to maintain a satelite on a stable Earth oribit the distance from the surface should exceed 150 kms.
Simply put, an orbit is where the gravity of the Earth is balanced by the speed of an object. Low earth orbit (say, around 220 miles) is balanced out by a speed of 17,500mph. To achieve a higher orbit, a higher speed is required.
Objects start orbiting the Earth whenever their tangential velocity is equivalent to the necessary orbital velocity at that altitude. Below that velocity, they fall.
For a circular orbit, the equation to figure out what the appropriate velocity would be, is:
Where G is the gravitational constant. M is the mass of the body being orbited(Earth). “r” is the distance from the center of the Earth to the object in orbit.
Objects start orbiting the Earth whenever their tangential velocity is equivalent to the necessary orbital velocity at that altitude. Below that velocity, they fall.
For a circular orbit, the equation to figure out what the appropriate velocity would be, is:
Where G is the gravitational constant. M is the mass of the body being orbited(Earth). “r” is the distance from the center of the Earth to the object in orbit.
No, they do not. If you send an rocket to a height of 150 miles (approximately the minimum altitude for a stable orbit, you were off by a factor of 10) and then turn off the engine, it will fall right back to the ground. In order to orbit the Earth, the rocket has to aim sideways for long enough to build up a horizontal velocity of roughly 18,000 mph. That is more than 4 times the speed of a rifle bullet, by the way. When you see a rocket ascending from the launch pad, you will notice that as soon as it clears the tower it starts pitching over until its path is mostly sideways and only a littl
No, they do not. If you send an rocket to a height of 150 miles (approximately the minimum altitude for a stable orbit, you were off by a factor of 10) and then turn off the engine, it will fall right back to the ground. In order to orbit the Earth, the rocket has to aim sideways for long enough to build up a horizontal velocity of roughly 18,000 mph. That is more than 4 times the speed of a rifle bullet, by the way. When you see a rocket ascending from the launch pad, you will notice that as soon as it clears the tower it starts pitching over until its path is mostly sideways and only a little bit upward.
In fact, if you consider that rocket when it is sitting fully fueled on the pad waiting to launch, less than 10% of the energy in the fuel it contains will be spent in reaching orbital altitude. More than 90% of the fuel is used in accelerating the rocket sideways until it achieves the necessary velocity for a sustainable orbit.
Out as far as the orbit is primarily tied to Earth. Out to where the gravity of all other bodies, other than Earth and the sun, are small compared to those two.
It's a balance between velocity and the pull of the earth's gravity.
An object can orbit the earth at 35,000 feet if you have enough power to overcome the constant drag of the atmosphere and deal with the heat from moving through the dense air.
Practically an object needs to be high enough to be out of most of the atmospheric drag. The International Space Station is 254 miles and even at that altitude there is a slight drag from the very very thin atmosphere so it has to receive a little rocket boost every so often to maintain its orbit.
The generally accepted lowest practical orbit is about 100 miles. A satellite in that orbit will experience some atmospheric dr
An object can orbit the earth at 35,000 feet if you have enough power to overcome the constant drag of the atmosphere and deal with the heat from moving through the dense air.
Practically an object needs to be high enough to be out of most of the atmospheric drag. The International Space Station is 254 miles and even at that altitude there is a slight drag from the very very thin atmosphere so it has to receive a little rocket boost every so often to maintain its orbit.
The generally accepted lowest practical orbit is about 100 miles. A satellite in that orbit will experience some atmospheric drag and will slowly slow down and reenter earth’s atmosphere and burn up.
Edit: I should make clear that it is not altitude that causes an object to orbit the Earth, it is the speed parallel to the surface of the Earth that causes something to orbit the Earth. At an altitude of 200 miles the velocity required to stay in orbit is about 17,000 MPH or 27,360 KPH.
If an object was at 200 miles altitude with no velocity it would fall straight down to the ground.
Do you want the simple answer or the complicated answer?
We’ll start simple: two objects in the same orbit around Earth will orbit at the same speed, provided they are both small enough that their mass is insignificant compared to the mass of Earth.
The simplified formula for calculating the speed of a circular orbit is:
[math]v_{orbit} = \sqrt{\frac{GM}{r}}[/math]
Where G is the Universal Gravitational Constant, approximately equal to [math]\rm 6.674\times10^{-11} \; m^3kg^{-1}s^{-2}[/math].
M is the mass of the parent body, in this case Earth. The mass of Earth is [math]\rm 5.972\times10^{24} \; kg[/math].
r is the radius of the orbit.
Do you want the simple answer or the complicated answer?
We’ll start simple: two objects in the same orbit around Earth will orbit at the same speed, provided they are both small enough that their mass is insignificant compared to the mass of Earth.
The simplified formula for calculating the speed of a circular orbit is:
[math]v_{orbit} = \sqrt{\frac{GM}{r}}[/math]
Where G is the Universal Gravitational Constant, approximately equal to [math]\rm 6.674\times10^{-11} \; m^3kg^{-1}s^{-2}[/math].
M is the mass of the parent body, in this case Earth. The mass of Earth is [math]\rm 5.972\times10^{24} \; kg[/math].
r is the radius of the orbit. An object orbiting 500 km above Earth’s surface has an orbital radius of [math]\rm 6.871\times10^6 \; m[/math].
You can see that the formula does not require the mass of the orbiting body. Given the values we’ve supplied, the orbital speed of an object 500 km above Earth’s surface ought to be about 7616 m/s (about 17,000 miles per hour).
We have pretended that the mass of the orbiting body doesn’t matter, because for relatively small objects like spaceships, it doesn’t. But what if the orbiting body has a mass that is a significant fraction of Earth’s mass? In that case, its mass does matter, and the orbital speed formula becomes a bit more complex.
[math]v_{orbit} = \sqrt{\frac{G(M + m)}{r}}[/math]
Where m is the mass of the orbiting body. When m is tiny compared to M, we can say that M + m is essentially equal to M. But if m is a good fraction of M, it changes the orbital speed significantly.
Bear in mind that this calculates the orbital speed with respect to the center of Earth - not the barycenter, which, for a very massive satellite, does not line up with Earth’s center.
Let’s say that our orbiting satellite has a mass equal to 1% of Earth’s mass, or [math]\rm 5.972\times10^{22} \; kg[/math]. That’s slightly less than the mass of Earth’s moon, and there’s no way it would be in a stable orbit only 500 km above Earth’s surface, but we’re not worried about that right now…this is just for comparison. Plugging the mass of the satellite into the modified orbital speed formula, we get an orbital speed of 7654 m/s relative to Earth’s center - about 38 m/s faster than the orbital speed of a much less massive object.
Now you might say that’s not a big difference, and you’d be correct. But the fact remains that if you want to get super nit-picky, more massive objects do orbit faster than less massive objects, if only by a small margin.
It depends on what you consider an orbit around the Earth. By Newton’s laws of dynamics and gravitation, a body really does not orbit another body, but both orbit around their combined center of mass. So, if a mas [math]m_1[/math] is at [math]x_1[/math] and [math]m_2[/math] is at [math]x_2[/math], then its center of mas is at
[math]\frac{m_{1}x_{1}+m_{2}x_{2}}{m_{1}+m_{2}}[/math]
and therefore the distance between the body 1 to the center of mas is given by
[math]\left|\frac{m_{1}x_{1}+m_{2}x_{2}}{m_{1}+m_{2}}-x_{1}\right|=\frac{m_{2}}{m_{1}+m_{2}}\left|x_{2}-x_{1}\right|=\frac{m_{2}}{m_{1}+m_{2}}d[/math]
where [math]d[/math] is the distance between bodies 1 and 2.
Now, suppose that the
It depends on what you consider an orbit around the Earth. By Newton’s laws of dynamics and gravitation, a body really does not orbit another body, but both orbit around their combined center of mass. So, if a mas [math]m_1[/math] is at [math]x_1[/math] and [math]m_2[/math] is at [math]x_2[/math], then its center of mas is at
[math]\frac{m_{1}x_{1}+m_{2}x_{2}}{m_{1}+m_{2}}[/math]
and therefore the distance between the body 1 to the center of mas is given by
[math]\left|\frac{m_{1}x_{1}+m_{2}x_{2}}{m_{1}+m_{2}}-x_{1}\right|=\frac{m_{2}}{m_{1}+m_{2}}\left|x_{2}-x_{1}\right|=\frac{m_{2}}{m_{1}+m_{2}}d[/math]
where [math]d[/math] is the distance between bodies 1 and 2.
Now, suppose that the body 1 is the Earth and body 2 is an artificial satellite of 1000Kg whose distance to the center of the earth is 10000Km. As the mass of the Earth is [math]6\times10^{24}[/math]Kg, then the distance of the center of the Earth to the center of mass is about [math]1.6\times10^{-15}[/math]m, which is 1/100.000 of the size of an atom. Then it is obvious that the satellite is in orbit of the Earth, which remais in practice static.
If we consider the Earth and the Moon, thins get a little blurry. The Moon has a mass of [math]7\times10^{22}[/math]Kg and is about 400000Km distant from Earth, so the center of mass is about 5000Km distant from the center of the Earth. This makes it still inside the Earth, which has a radius of 6400Km, so even if the Earth wiggles a bit, it is safe to say that the Moon orbits the Earth.
However, if we consider the Sun, which has a mass of [math]2\times10^{30}[/math]Kg, and is 150,000,000 Km appart from Earth, then the center of mass is “only” 450Km distant from the center of the Sun. Taking into account the much larger distance to the Earth and also that the Sun has a radius of 700,000Km, it is clear that the Earth orbits the Sun and not vice-versa.
Now suppose that the Moon had half the mass of the Earth instead of 1/80. Then, the distance between the center of mass and the center of the Earth would be 130,000Km. We could not say that the Moon orbits the Earth. It would be more appropriate to say that both orbit a point in empty space which is 130,000Km appart from the Earth and 270,000Km appart from the Moon.
So, there is no limit for the object to be bound to Earth by gravity. However, if the object has a very large mass, than it will not make sense to say that it orbits the Earth.
Below around a hundred miles, air drag would disturb the orbit too much to remain there for long. Above around a million miles, the sun’s gravity would disturb the orbit too much to remain there for long.
Earth’s Hill Sphere reaches about 900,000 miles.
Terry Pratchett worked out the celestial mechanics of Discworld, a flat world riding on four elephants riding on a giant turtle. Discworld had one very close, very small sun that orbits it, avoiding the legs of the immense pachyderms.I believe that it also has a small moonlet, but I don't remember it's orbital physics.
I read somewhere that an astrophysics grad student ran the numbers and said that Pratchett's description was wrong, but not insanely wrong.
Terry Pratchett worked out the celestial mechanics of Discworld, a flat world riding on four elephants riding on a giant turtle. Discworld had one very close, very small sun that orbits it, avoiding the legs of the immense pachyderms.I believe that it also has a small moonlet, but I don't remember it's orbital physics.
I read somewhere that an astrophysics grad student ran the numbers and said that Pratchett's description was wrong, but not insanely wrong.
Well, in a two body problem they always orbit around the barycenter of the system. Imagine you are holding both hands with a very massive guy / little boy and you guys just start rotating. The one with bigger mass will move very slightly on the spot with only rotation while the other one just “orbit” around him. In the case of earth and sun the barycenter is extremely close to the centre of the sun because the mass is so big. So theoretically anything can orbit around the Earth but when it gets too big the motion of Earth would also get pretty strange.
Gravity does not know or care where the ground happens to be. Orbits are not affected by the ground. Orbits care about atmospheres, but we’ll ignore that for now.
As far as gravity is concerned, you are not orbiting a planet - you are orbiting a POINT that has mass. That point is the center of gravity. Gravity doesn’t care how far the ground happens to be from that point (ie, gravity does not care about the size of the planet; only its mass).
If the earth were perfectly smooth (6371 km radius), you could orbit a millimeter above the surface. You would need to be moving 28,474 km/hr (17,693 MPH).
Gravity does not know or care where the ground happens to be. Orbits are not affected by the ground. Orbits care about atmospheres, but we’ll ignore that for now.
As far as gravity is concerned, you are not orbiting a planet - you are orbiting a POINT that has mass. That point is the center of gravity. Gravity doesn’t care how far the ground happens to be from that point (ie, gravity does not care about the size of the planet; only its mass).
If the earth were perfectly smooth (6371 km radius), you could orbit a millimeter above the surface. You would need to be moving 28,474 km/hr (17,693 MPH). You would be in freefall, so you would be completely weightless the whole time. If you could maintain that velocity, you would orbit forever. Your own mass is completely irrelevant. You would complete an orbit every 84.3 minutes, BTW.
As far as gravity is concerned, though, you are not orbiting at 1mm above the surface; you are orbiting 6371 km above the center of gravity. Gravity does not know that you are only 1mm from the ground. Gravity does not know (or care) where the ground happens to be.
You could orbit lower, except the ground gets in the way. As with all orbits, the lower it gets, the faster it must become to maintain altitude. A lot of orbital mechanics is counter-intuitive.
Of course, for practical purposes, we can’t reach the velocities necessary to orbit in an atmosphere. The lowest that we can orbit earth is about 160 km above the surface (and even that orbit will require frequent boosting to overcome atmospheric drag).
Yes. Get far enough away, and the competing gravity of the Sun will take over. Now that leaves a lot of room. You might get ten times as far as the Moon. At that distance, the more distant Moon would take years to go around. But solar tidal forces would present a threat. At times, the Sun, the distant moon, and the Earth would be lined up. The distant moon would be a couple million miles, out of 90 million or so miles, nearer to or farther from the Sun.
That would mean about a 5% difference in pull. But 5% of the Sun’s pull? The Sun being about 50 times further from the distant moon than that m
Yes. Get far enough away, and the competing gravity of the Sun will take over. Now that leaves a lot of room. You might get ten times as far as the Moon. At that distance, the more distant Moon would take years to go around. But solar tidal forces would present a threat. At times, the Sun, the distant moon, and the Earth would be lined up. The distant moon would be a couple million miles, out of 90 million or so miles, nearer to or farther from the Sun.
That would mean about a 5% difference in pull. But 5% of the Sun’s pull? The Sun being about 50 times further from the distant moon than that moon’s distance from us would dilute its pull by times 2500, but it outmasses us by thousands of times. So i dont like our odds of holding on long term.
If you out a satellite in orbit it’s going to stay in that orbit unless something affects it.
That can be a rocket engine which can alter the orbit or even escape altogether depending on how much thrust (energy) is used.
But space up there is not a perfect vacuum, there’s a small amount of gas and that will very, very gradually slow the satellite down. And so will solar flares and even radiation pressure if the surface area of the satellite is great enough. As the satellite slows the orbit changes and the gas density very gradually increases as it gets closer to earth.
Synchronous orbits are so h
If you out a satellite in orbit it’s going to stay in that orbit unless something affects it.
That can be a rocket engine which can alter the orbit or even escape altogether depending on how much thrust (energy) is used.
But space up there is not a perfect vacuum, there’s a small amount of gas and that will very, very gradually slow the satellite down. And so will solar flares and even radiation pressure if the surface area of the satellite is great enough. As the satellite slows the orbit changes and the gas density very gradually increases as it gets closer to earth.
Synchronous orbits are so high that this effect is negligible, but the lower the orbit the more pronounced the effect.
T try hinge can stay in orbit for a very long time, but nothing stays forever.
This gets kind of complicated and weird because orbital speeds (we’ll assume perfectly circular orbits) actually get slower the higher up you go. This is why spacecraft catching up to the ISS orbit lower than the ISS; they make the revolution around the earth quicker at a lower orbit because the circle they cover has a smaller circumference. A literal smaller distance to travel. Same idea applies to track races and running on the inside of a track.
so, another thing that complicates orbital velocities is the frame of reference. From earth’s perspective, a geostationary satellite has zero veloci
This gets kind of complicated and weird because orbital speeds (we’ll assume perfectly circular orbits) actually get slower the higher up you go. This is why spacecraft catching up to the ISS orbit lower than the ISS; they make the revolution around the earth quicker at a lower orbit because the circle they cover has a smaller circumference. A literal smaller distance to travel. Same idea applies to track races and running on the inside of a track.
so, another thing that complicates orbital velocities is the frame of reference. From earth’s perspective, a geostationary satellite has zero velocity, it just hangs in the sky above it and doesn’t move. In reality, that geo sat is just orbiting far enough away from the surface of earth that its orbital speed can match the rotation of the earth, so it APPEARS to be motionless.
a satellite in low-earth orbit can be traveling close to 8 km per second (7.8 km/s as per a google search.) That’s just above earth’s atmosphere, though, at about 70–100km. geostationary orbital velocity is much lower, at only 3km/s. That’s still a massive velocity but well below half that of LEO. The biggest difference here is the altitude; LEO happens at about 100km (realistically 200 because lower than that slows quickly to re-enter), GSO happens at 35,800km. That’s almost two and a half orders of magnitude higher up.
the SLOWEST possible orbit, though, is well outside of the geostationary altitude at the edge of the sphere of influence of the earth, where its gravity begins to be matched by that of the sun. Satellites at this altitude appear to move backwards when viewed from earth because their orbits move slower than the rotation of the planet. You’re spinning faster than they orbit! One such satellite is the Russian Spekt-R Satellite, with an apogee of 381,000 km (another order of magnitude above GSO.)
No, sending objects to orbit the Earth would not affect the orbit of the Earth around the Sun. At least not to a noticeable extent.
If the satellite were large enough (in the order of magnitude of the Moon), however, the first order path of the orbit would remain the same, but there would be a higher-frequency, sinusoidal wobbling around it.
Here I made a quick representation. For your eyes only. :
No, sending objects to orbit the Earth would not affect the orbit of the Earth around the Sun. At least not to a noticeable extent.
If the satellite were large enough (in the order of magnitude of the Moon), however, the first order path of the orbit would remain the same, but there would be a higher-frequency, sinusoidal wobbling around it.
Here I made a quick representation. For your eyes only. : )
Orbits are not to scale.
1. The simple orbit is the baseline of the single planet, with no satellites.
2. The composed one is the orbit of the same planet, under the influence of a large satellite.
3. The center of gravity of (planet + satellite) describes again the simple, baseline orbit.
This last point is because the center of gravity of the system composed by:
* the Earth
* the orbiting object (satellite)
would on average remain the same.
Bonus:...
So how can communications satellites remain in orbit over the same spot over the earth, while the Space Shuttle must travel fast enough to orbit the earth every 90 minutes or so, in order to remain in orbit?
Because one thing determines orbital speed and period (i.e. time per orbit) - and that is altitude. Mass doesn't affect it. Orbit occurs when the centrifugal force generated by the rotating object is exactly balanced by the force of gravity at that altitude.
At an altitude of 200 km (a typical altitude for a Space Shuttle mission), a speed of 7.8 km/second is required to maintain orbit. This
So how can communications satellites remain in orbit over the same spot over the earth, while the Space Shuttle must travel fast enough to orbit the earth every 90 minutes or so, in order to remain in orbit?
Because one thing determines orbital speed and period (i.e. time per orbit) - and that is altitude. Mass doesn't affect it. Orbit occurs when the centrifugal force generated by the rotating object is exactly balanced by the force of gravity at that altitude.
At an altitude of 200 km (a typical altitude for a Space Shuttle mission), a speed of 7.8 km/second is required to maintain orbit. This would give a period of 88.3 minutes, just under an hour and a half, per orbit.
But objects at higher altitudes orbit more slowly. At an alititude of 5,000km, the speed required to maintain orbit is only 5.8 km/sec. and the orbital period is 201.1 minutes, or about 3 hours and 20 minutes.
So since the earth itself rotates one revolution per 24 hour period, in order to have an orbit that stays over over one spot on earth (called a "geosynchronous" orbit), we would need an orbit with a 24 period.
It so happens that an altitude of 35,800 km with an orbital speed of 3.2 km/sec is the ONLY altitude and speed combination that will maintain a continous geosynchronous orbit over one spot on earth.
This is what allows communications satellites to effectively "sit" in the same spot in the sky, acting as a relay station to allow television, telephone, radio, internet, and military applications.
Ironically, it may be what is enabling you to read and respond to this very post!
Every object with mass creates a gravitational field. Regardless of the amount of mass, that gravitational field has no end in theory: the force drops off with the square of distance (twice as far = four times less strength), because the field is spreading over an ever-wider sphere and surface area of a sphere is proportional to square of radius (‘distance’) - 4 * Pi * r * r). However, since gravitational waves (or force) travels at the speed of light, in practice, the gravitational field of any object extends as far as light has had time to travel since whatever moment in time you care to thi
Every object with mass creates a gravitational field. Regardless of the amount of mass, that gravitational field has no end in theory: the force drops off with the square of distance (twice as far = four times less strength), because the field is spreading over an ever-wider sphere and surface area of a sphere is proportional to square of radius (‘distance’) - 4 * Pi * r * r). However, since gravitational waves (or force) travels at the speed of light, in practice, the gravitational field of any object extends as far as light has had time to travel since whatever moment in time you care to think of.
In practice though, the gravitational field of the Earth becomes ‘swamped’ by that of the moon (say) if you are much closer to the moon than the Earth (in orbit around it, or walking on its surface). Similarly, the Earth is in orbit around the far more massive sun, yet we on the surface of the Earth feel only Earth’s gravity because locally, Earth’s nearby mass overwhelms the sun’s greater but very distant mass. But if a spaceship travels some way from Earth, it no longer feels “the distant Sun’s gravity PLUS the near Earth’s nearby gravity”; it feels “the distant Sun’s gravity (plus a negligible and diminishing bit of Earth’s)”.
So, there isn’t any end point for Earth’s gravity; gravitational effects are more like “spheres of influence” (actually, it’s more of a lumpy, /somewhat/ spherical shape); as you approach other moons or planets, their ‘sphere(ish) of influence’ becomes increasingly dominant over the Earths. Like the old (very simplified) analogy of putting bowling balls (Sun), footballs (giant planets), tennis balls (Earth), and marbles (moons) on a stretchy surface: the varying-size dents of each object are the sphere(ish) of influences.
In practice then, Earth’s sphere(ish) of inflence extends out to somewhere of the order of the distance of the moon - 250,000 miles. If you put a satellite in orbit around the Earth at 10 times the distance of the moon, the sphere(ish) of influence of Venus, Mars, and Jupiter would relatively quickly affect the orbit and the ship would drop into an orbit around the sun (paralleling Earth but not orbiting it), or end up in some unstable orbit that would result in it hitting Earth or wandering off elsewhere.
There’s no exact answer then but according to:
the Earth’s sphere of influence is calculated to be 577,254 miles, so that’s about twice the Earth-moon distance. Though, obviously, if near the moon, its gravity swamps Earth’s. And although that value might seem very, the concept is not - the number is exact because it comes out of an equation which is intended only to gives a rough idea.
No. You need sideways speed.
Gravity is making you fall towards Earth. If you are going fast enough sideways, you miss the Earth. Gravity can’t pull you down fast enough to make you hit the Earth.
Since gravity is pulling perpendicular to the sideways speed, it doesn’t slow down or speed up the satellite, it just makes it go in a different direction such that the sideways speed stays constant and the satellite keeps falling and keeps missing the Earth.
At least this is true for circular orbits.
No. You need sideways speed.
Gravity is making you fall towards Earth. If you are going fast enough sideways, you miss the Earth. Gravity can’t pull you down fast enough to make you hit the Earth.
Since gravity is pulling perpendicular to the sideways speed, it doesn’t slow down or speed up the satellite, it just makes it go in a different direction such that the sideways speed stays constant and the satellite keeps falling and keeps missing the Earth.
At least this is true for circular orbits.
When STANDING ON EARTH, you are in a SOLAR orbit, not an Earth orbit. If you can move away from the surface at 7miles per second in any direction that does not colide with surface or orbiting objects, you will leave the Earth and never return nor enter Its orbit. Attempting an orbit at slower speed than about 17448 mph will eventually enter earth atmosphere and be destroyed. Lowest safe orbit is about 200 miles because friction from even that super thin air will decellerate and eventually crash to earth. the SST was boosted to an orbit at 250 miles to reduce fuel requirements for readjusting i
When STANDING ON EARTH, you are in a SOLAR orbit, not an Earth orbit. If you can move away from the surface at 7miles per second in any direction that does not colide with surface or orbiting objects, you will leave the Earth and never return nor enter Its orbit. Attempting an orbit at slower speed than about 17448 mph will eventually enter earth atmosphere and be destroyed. Lowest safe orbit is about 200 miles because friction from even that super thin air will decellerate and eventually crash to earth. the SST was boosted to an orbit at 250 miles to reduce fuel requirements for readjusting its speed to maintain the 200 mile high orbit it earlier occupied. Between the highest and lowest speeds mentioned, orbits can be achieved depending on direction that may or not be stable, ending in orbits, hyperbolic paths, bounces off atmosphere, or collisions with Earth.
Thanks for flying Galactic Origin, please remain seated with your seat belts fastened and your tray tables in their full upright and locked position until after warp is attained ! 🛸👽
Approximately 1.5 million kilometers. It is limited by the point at which the influence of the sun's gravity becomes sufficiently stronger than Earth's that any object at that distance would become unbound from Earth & end up in independent orbit around then sun.
That limit applies in general to any system of two bodies, and is called the Hill sphere. It's not actually perfectly spherical, but close enough for most practical purposes, and lies between the L1 & L2 Lagrange points. For circular orbits, the radius of the Hill sphere for any planet or moon can be calculated from
r = a*(m/(3M))^(1/3)
Approximately 1.5 million kilometers. It is limited by the point at which the influence of the sun's gravity becomes sufficiently stronger than Earth's that any object at that distance would become unbound from Earth & end up in independent orbit around then sun.
That limit applies in general to any system of two bodies, and is called the Hill sphere. It's not actually perfectly spherical, but close enough for most practical purposes, and lies between the L1 & L2 Lagrange points. For circular orbits, the radius of the Hill sphere for any planet or moon can be calculated from
r = a*(m/(3M))^(1/3)
Where r is the radius of the Hill sphere, m is the mass of the planet or moon, M is the mass of the sun a planet orbits, or the planet that a moon orbits, and a is the distance from the sun (or planet) to its planet (or moon).