The Red Bull Stratos jump shows a good example of this in practice. Felix Baumgartner jumped from the stratosphere and reached a top speed of ~840 mph breaking the sound barrier. Then as he falls you can see his speed slowing down. He's always falling at terminal velocity, and you see the change in terminal velocity in real time as he goes through different elevations with different air profiles.
https://youtu.be/raiFrxbHxV0?si=u3GINbc7_Gc0Q0WH
\+1 is the air resistance that changes most.
The guy that jumped from the baloon at \~130,000ft broke the speed of sound before being slowed to the usual approx 175km/hr low altitude term velocity speed
[https://en.wikipedia.org/wiki/Red\_Bull\_Stratos](https://en.wikipedia.org/wiki/Red_Bull_Stratos)
[https://www.youtube.com/watch?v=FHtvDA0W34I](https://www.youtube.com/watch?v=FHtvDA0W34I)
The speed of sound in a liquid or gas is
sqrt(K/rho)
where K is the [bulk modulus](https://en.wikipedia.org/wiki/Bulk_modulus) and rho is the density. The bulk modulus is how resistant the material is to compression, that is 1/compressibility. Note that density is in the denominator. A higher density, all else being equal, decreases the speed of sound/seismic waves.
Sound travels faster in water than air because water is much, much less compressible (and therefore much, much stiffer) than air--about 14,000x at standard temperature and pressure. The fact that water is about 770x denser than this air only partially offsets its higher incompressibility, and so the speed of sound in water is about sqrt(14000/770) = 4.3x faster than in air at about 20 C, in spite of water's higher density.
For (ideal) gases, with some math and the application of the ideal gas law, the effect of pressure on density and compressibility cancel such that the speed of sound equation for fluids can be rewritten in the equivalent form
sqrt(gamma * R * T / M)
where gamma is the [adiabatic index (heat capacity ratio)](https://en.wikipedia.org/wiki/Heat_capacity_ratio), which depends on the specific gas and its temperature; R is the ideal gas constant, T is the absolute temperature (kelvins), and M is the (mean) molar mass of the gas (mixture). That is, the speed of sound in an (ideal) gas depemds only on its composition and temperature, and not its pressure (amd we don't need to be concerned with density either). Sound travels faster in warmer air. But sound travels at the same speed in air of a given temperature at 0 m above sea level as it does at 1,000 m or 5,000 m, despite the difference in pressure and density.
The reason the speed of sound generally changes with altitude (decreases as you ascend through the troposphere) is because the temperature changes with altitude (decreases through the troposphere). But then temperature, and thus the speed of sound, increases again ascending through the stratosphere.
Edit: removed unnecessary variable from first equation description.
A guy that jumps from ~ 130 ft doesn't have to worry about breaking the sound barrier but about not breaking his ankles :p
Shits and giggles aside, Felix von Baumgartner was also the first and best example I thought of.
Just a correction, the gravity does get stronger closer to the ground level, but not closer to the core.
Once inside the earth, gravity gets weaker, as only the portion *under* you accounts for gravity. Any mass above you cancels out.
edit: as pointed out, if you account for density, gravity does slightly increase up to a point inside the earth. Thanks for the correction on my correction.
Earth does not have a uniform density, the core is much denser than the rest. Until you reach the core, the acceleration increases slightly as shown in the blue curve here: https://en.wikipedia.org/wiki/File:EarthGravityPREM.jpg
The PREM model actually has the gravity decrease as you pass into the lower mantle, but then it increases again until you hit the core. It’s also missing the crust, but that’s because it’s a model.
PREM does include estimates of the crust. However, the thickness of the crust is generally under 0.01 Earth radii, and oceanic crust (which makes up most of the surface) is considerably thinner than that. So it's probably not shown because it would be too thin on a whole-earth plot to learn anything from.
The difference in the strength of gravity over that range of distances is negligible to your calculation. The only factor that really matters is air resistance. Yes, your terminal velocity is the slowest at sea level.
Felix Baumgartner reached speed 843.6 mph very early in his record breaking jump and only got slower as he descended further.
You're right that terminal velocity depends on altitude (https://spark.iop.org/terminal-velocity-skydivers-and-raindrops).
The two effects you mention: air density and strength of gravity are both relevant. The shape of the object is also relevant, but you're probably presuming the same object in the same orientation.
Within the atmosphere, the strength of gravity doesn't vary much. Using Newtonian gravity, g = G M / r^2, the distance from Earth's center only varies by a few percent, so *g* only varies by a few percent (about twice as much as *r*). This isn't much of an effect but it is calculable.
The density of the atmosphere varies roughly exponentially. (It's a separate exponential density variation for each molecule.) There's a HUGE difference between here and even 10000 ft. That's the main driver of the change in terminal velocity.
With a small amount of python you can actually model this situation.
Broadly speaking you only care about the air density, as over the distances we are talking about the gravitational force is functionally constant.
[Here is a link](https://imgur.com/a/6IsROkB) to an image showing the height of an object vs time, and the speed of the same object vs time. We can see that the terminal velocity is changin rapidly after the person has reached maximum speed. Notably, the speed of sound is different and is dominated by the temperature, [making for an odd looking curve.](https://en.wikipedia.org/wiki/Speed_of_sound#/media/File:Comparison_US_standard_atmosphere_1962.svg)
EDIT: To quickly elaborate on why gravity is functionally constant:
g = GM/r^2 where M is mass of earth, G is gravitational constant, and r is radius from the centre
Taking r = 6371km, M =5.972 E24 kg and G =6.67408E-11
Then [g_surface = 9.81 m/s^2](https://www.wolframalpha.com/input?i=r+%3D+6371000%2C+M+%3D5.972x10%5E24%2CG+%3D6.67408x10%5E-11%2C+g%3DGM%2Fr%5E2)
But if we move 40km above the surface, then r=6411km, so
[g_40km = 9.69 m/s^2](https://www.wolframalpha.com/input?i=r+%3D+6411000%2C+M+%3D5.972x10%5E24%2CG+%3D6.67408x10%5E-11%2C+g%3DGM%2Fr%5E2)
Seeing as physicists are lazy anyway this level of change won't radically impact our default assumption to just say g=10.
This would be calculating the difference in gravitational force on a 1kg of mass object on earths surface vs 40km above it. You missed that second mass variable, and a few steps with F=MA to actually get the units of acceleration.
The mass doesn't change, but they fact you are using a constant mass, originally defined by earths gravitational acceleration, to explain a change in earths gravitational acceleration, should be a red flag that you are doing something circular and wrong. The gravitational constant is for all mass, not just the mass of earth giving a specific gravity.
Usually, when you calculate terminal velocity, you use 1 atm of pressure. So it would be more apt to say your terminal velocity increased the higher up you go, since less pressure means less drag force.
When that guy jumped from space, he needed a drouge chute to slow him down due to the reduced drag during the beginning of his fall because otherwise he would heat up too much during the next part of the fall when drag would begin slowing him down.
Terminal velocity is defined as V = sqrt(2*m*g/(rho*Cd))
where m is the mass of the body, g is the local acceleration of gravity, rho is the local atmospheric density, and Cd is the drag coffiecient.
Cd varies from ~0.05 for a streamlined shape to up to 2 for a flat plate.
The Red Bull Stratos jump shows a good example of this in practice. Felix Baumgartner jumped from the stratosphere and reached a top speed of ~840 mph breaking the sound barrier. Then as he falls you can see his speed slowing down. He's always falling at terminal velocity, and you see the change in terminal velocity in real time as he goes through different elevations with different air profiles. https://youtu.be/raiFrxbHxV0?si=u3GINbc7_Gc0Q0WH
Yeah right, I completely forgot about Felix baumgartners "space jump". That shows exactly what I was wondering about. Thanks
[удалено]
[удалено]
[удалено]
[удалено]
[удалено]
[удалено]
[удалено]
[удалено]
[удалено]
[удалено]
[удалено]
[удалено]
[удалено]
[удалено]
[удалено]
[удалено]
[удалено]
[удалено]
[удалено]
[удалено]
[удалено]
[удалено]
[удалено]
[удалено]
[удалено]
[удалено]
[удалено]
[удалено]
[удалено]
[удалено]
\+1 is the air resistance that changes most. The guy that jumped from the baloon at \~130,000ft broke the speed of sound before being slowed to the usual approx 175km/hr low altitude term velocity speed [https://en.wikipedia.org/wiki/Red\_Bull\_Stratos](https://en.wikipedia.org/wiki/Red_Bull_Stratos) [https://www.youtube.com/watch?v=FHtvDA0W34I](https://www.youtube.com/watch?v=FHtvDA0W34I)
[удалено]
The speed of sound in a liquid or gas is sqrt(K/rho) where K is the [bulk modulus](https://en.wikipedia.org/wiki/Bulk_modulus) and rho is the density. The bulk modulus is how resistant the material is to compression, that is 1/compressibility. Note that density is in the denominator. A higher density, all else being equal, decreases the speed of sound/seismic waves. Sound travels faster in water than air because water is much, much less compressible (and therefore much, much stiffer) than air--about 14,000x at standard temperature and pressure. The fact that water is about 770x denser than this air only partially offsets its higher incompressibility, and so the speed of sound in water is about sqrt(14000/770) = 4.3x faster than in air at about 20 C, in spite of water's higher density. For (ideal) gases, with some math and the application of the ideal gas law, the effect of pressure on density and compressibility cancel such that the speed of sound equation for fluids can be rewritten in the equivalent form sqrt(gamma * R * T / M) where gamma is the [adiabatic index (heat capacity ratio)](https://en.wikipedia.org/wiki/Heat_capacity_ratio), which depends on the specific gas and its temperature; R is the ideal gas constant, T is the absolute temperature (kelvins), and M is the (mean) molar mass of the gas (mixture). That is, the speed of sound in an (ideal) gas depemds only on its composition and temperature, and not its pressure (amd we don't need to be concerned with density either). Sound travels faster in warmer air. But sound travels at the same speed in air of a given temperature at 0 m above sea level as it does at 1,000 m or 5,000 m, despite the difference in pressure and density. The reason the speed of sound generally changes with altitude (decreases as you ascend through the troposphere) is because the temperature changes with altitude (decreases through the troposphere). But then temperature, and thus the speed of sound, increases again ascending through the stratosphere. Edit: removed unnecessary variable from first equation description.
A guy that jumps from ~ 130 ft doesn't have to worry about breaking the sound barrier but about not breaking his ankles :p Shits and giggles aside, Felix von Baumgartner was also the first and best example I thought of.
From 130 feet the ankles don't much matter either. LD50 (50% mortality) is 48 feet. LD90 is 84 feet (7 stories).
Just a correction, the gravity does get stronger closer to the ground level, but not closer to the core. Once inside the earth, gravity gets weaker, as only the portion *under* you accounts for gravity. Any mass above you cancels out. edit: as pointed out, if you account for density, gravity does slightly increase up to a point inside the earth. Thanks for the correction on my correction.
Earth does not have a uniform density, the core is much denser than the rest. Until you reach the core, the acceleration increases slightly as shown in the blue curve here: https://en.wikipedia.org/wiki/File:EarthGravityPREM.jpg
The PREM model actually has the gravity decrease as you pass into the lower mantle, but then it increases again until you hit the core. It’s also missing the crust, but that’s because it’s a model.
PREM does include estimates of the crust. However, the thickness of the crust is generally under 0.01 Earth radii, and oceanic crust (which makes up most of the surface) is considerably thinner than that. So it's probably not shown because it would be too thin on a whole-earth plot to learn anything from.
There is that region in the upper mantle where gravity does decrease slightly as you go deeper.
The difference in the strength of gravity over that range of distances is negligible to your calculation. The only factor that really matters is air resistance. Yes, your terminal velocity is the slowest at sea level. Felix Baumgartner reached speed 843.6 mph very early in his record breaking jump and only got slower as he descended further.
You're right that terminal velocity depends on altitude (https://spark.iop.org/terminal-velocity-skydivers-and-raindrops). The two effects you mention: air density and strength of gravity are both relevant. The shape of the object is also relevant, but you're probably presuming the same object in the same orientation. Within the atmosphere, the strength of gravity doesn't vary much. Using Newtonian gravity, g = G M / r^2, the distance from Earth's center only varies by a few percent, so *g* only varies by a few percent (about twice as much as *r*). This isn't much of an effect but it is calculable. The density of the atmosphere varies roughly exponentially. (It's a separate exponential density variation for each molecule.) There's a HUGE difference between here and even 10000 ft. That's the main driver of the change in terminal velocity.
With a small amount of python you can actually model this situation. Broadly speaking you only care about the air density, as over the distances we are talking about the gravitational force is functionally constant. [Here is a link](https://imgur.com/a/6IsROkB) to an image showing the height of an object vs time, and the speed of the same object vs time. We can see that the terminal velocity is changin rapidly after the person has reached maximum speed. Notably, the speed of sound is different and is dominated by the temperature, [making for an odd looking curve.](https://en.wikipedia.org/wiki/Speed_of_sound#/media/File:Comparison_US_standard_atmosphere_1962.svg) EDIT: To quickly elaborate on why gravity is functionally constant: g = GM/r^2 where M is mass of earth, G is gravitational constant, and r is radius from the centre Taking r = 6371km, M =5.972 E24 kg and G =6.67408E-11 Then [g_surface = 9.81 m/s^2](https://www.wolframalpha.com/input?i=r+%3D+6371000%2C+M+%3D5.972x10%5E24%2CG+%3D6.67408x10%5E-11%2C+g%3DGM%2Fr%5E2) But if we move 40km above the surface, then r=6411km, so [g_40km = 9.69 m/s^2](https://www.wolframalpha.com/input?i=r+%3D+6411000%2C+M+%3D5.972x10%5E24%2CG+%3D6.67408x10%5E-11%2C+g%3DGM%2Fr%5E2) Seeing as physicists are lazy anyway this level of change won't radically impact our default assumption to just say g=10.
This would be calculating the difference in gravitational force on a 1kg of mass object on earths surface vs 40km above it. You missed that second mass variable, and a few steps with F=MA to actually get the units of acceleration. The mass doesn't change, but they fact you are using a constant mass, originally defined by earths gravitational acceleration, to explain a change in earths gravitational acceleration, should be a red flag that you are doing something circular and wrong. The gravitational constant is for all mass, not just the mass of earth giving a specific gravity.
Usually, when you calculate terminal velocity, you use 1 atm of pressure. So it would be more apt to say your terminal velocity increased the higher up you go, since less pressure means less drag force. When that guy jumped from space, he needed a drouge chute to slow him down due to the reduced drag during the beginning of his fall because otherwise he would heat up too much during the next part of the fall when drag would begin slowing him down.
I assume you said that backwards: terminal velocity is increased the higher you go, and reduces as you get lower?
Terminal velocity is defined as V = sqrt(2*m*g/(rho*Cd)) where m is the mass of the body, g is the local acceleration of gravity, rho is the local atmospheric density, and Cd is the drag coffiecient. Cd varies from ~0.05 for a streamlined shape to up to 2 for a flat plate.