Can a Vacuum Pump Simulate Planetary Orbits?

[Echo 6 Sierra]

I was just playing with this little doo-hickey http://www.phy.ntnu.edu.tw/java/circularMotion/circular3D_e.html and was wondering; How is it that Jupiter and Neptune remain in orbit even as large as they are? Is it their mass and that the Suns gravity has THAT much of an influence on them?

 

[Artman]

I may be a little off on this, so if anyone out there knows more about it than I do chime right on in.

Once an object achieves orbit, the forces acting on it are in a kind of equilibrium. The gravity holds them together while their momentum tries to pull them apart. Without outside forces acting on them, such as friction to reduce momentum or an increase or decrease in mass to change the gravity, or another body moving too close and effecting the direction of travel, they should remain that way indefinitely.

Notice also that the planets farther from the sun, (with the possible exception of Pluto) are "Gas Giants," which are larger, but less dense then the rocky planets closer to the sun.

 

[LURCH]

Originally posted by Echo 6 Sierra
I was just playing with this little doo-hickey http://www.phy.ntnu.edu.tw/java/circularMotion/circular3D_e.html and was wondering; How is it that Jupiter and Neptune remain in orbit even as large as they are? Is it their mass and that the Suns gravity has THAT much of an influence on them?

Yes, the Sun's gravity is so strong that even at those great distances, planets are still within its gravity well. However, if I have understood your question correctly, you are wondering why the greater mass of these planets does not cause them to fly off out of their orbits, correct? Well as peculiar as this may seem, when it comes to orbital dynamics, size doesn't matter !

Do you remember hearing the stories about Isaac Newton performing experiments in which two objects, one heavy and one light, were dropped simultaneously? According to the stories, the two objects would hit the ground at the same time. Now there is some debate as to whether Newton ever actually performed these experiments, but no matter; plenty of other people have performed them since. The acceleration of gravity on a free falling object is the same regardless of how heavy the object is.

As Artman has already mentioned, a stable orbit is a state of equilibrium between two forces (well, "pseudo forces", actually). These two forces would be gravitational and centrifugal force. If you increase the mass of the orbiting body, these two forces increase equally, and equilibrium is maintained. So, the only factors required for a stable orbit are altitude and velocity. At any given altitude, an object of any mass must orbit at a particular speed to maintain stability. This means that if we placed a ballpoint pen or a chocolate covered raisin at the same distance from the Sun as the planet Neptune, each object would have to travel at the same speed as the planet does in order to stay in orbit. If any of these objects, the pen, the planet, or the raisin, were to travel slightly faster, they would fly off into space. Slightly slower, and would fall toward the Sun. weird, huh?

 

[Janus]

Originally posted by LURCH
At any given altitude, an object of any mass must orbit at a particular speed to maintain stability. This means that if we placed a ballpoint pen or a chocolate covered raisin at the same distance from the Sun as the planet Neptune, each object would have to travel at the same speed as the planet does in order to stay in orbit. If any of these objects, the pen, the planet, or the raisin, were to travel slightly faster, they would fly off into space. Slightly slower, and would fall toward the Sun. weird, huh?

I'm going to step in here and make a slight correction in order to prevent confusion.

If these object's where to lose or gain some velocity, it does not mean that they will no longer orbit the sun. It means that they will just enter new orbits that are more eliptical than the original.

If they lose velocity, they will shift inot an orbit which passes slighty closer the the Sun and then swings back out to Neptunes orbit . If they gain velocity they will shift to an orbit that swings out fromt he Sun and then returns to Neptune's orbital distance. In both cases they wil return to point of Neptune's orbit where their velocity was changed. Their orbital periods wil be different from Neptune now, so when they return Neptune won't be there, and they won't meet up with Neptune for a number of orbits.

In order for the object to fall into the sun, it wilhave to lose enough velocity (quite a bit) so that its new orbit actually grazes the sun.

To fly off into space, or completely leave orbit from around the Sun, the object would have to gain about .414 times the circular orbital velocity at that distance.

For instance, the Earth has a orbital velocity of 30 km/s. For an object placed in this orbit to fly off from the sun,(without entering a new orbit around the Sun) it would need to gain an additional 12.42 km/s for a total velocity of 42.42 km/s.

 

[Artman]

Originally posted by Janus
...In order for the object to fall into the sun, it wilhave to lose enough velocity (quite a bit) so that its new orbit actually grazes the sun.

To fly off into space, or completely leave orbit from around the Sun, the object would have to gain about .414 times the circular orbital velocity at that distance.

For instance, the Earth has a orbital velocity of 30 km/s. For an object placed in this orbit to fly off from the sun,(without entering a new orbit around the Sun) it would need to gain an additional 12.42 km/s for a total velocity of 42.42 km/s.

I read that this was actually hard to do when trying to send a probe to Mercury, which as you know is closer to the Sun, it had to use the gravitational pull of the Moon and Venus and large amounts of fuel to overcome it's orbital velocity from Earth and drop in towards the Sun and catch Mercury (which has a high orbital velocity). I think I read that it took more fuel to fly in toward Mercury than out to Mars.

 

[Janus]

Originally posted by Artman
I read that this was actually hard to do when trying to send a probe to Mercury, which as you know is closer to the Sun, it had to use the gravitational pull of the Moon and Venus and large amounts of fuel to overcome it's orbital velocity from Earth and drop in towards the Sun and catch Mercury (which has a high orbital velocity). I think I read that it took more fuel to fly in toward Mercury than out to Mars.

Here's a quick down and dirty formula that helps to calculate that:

[del]V = V_R1( [squ](2R₂/(R₁ + R₂) - 1)

R₁ is the radius of the starting orbit , and R₁ the radius of the destination orbit.

This formula assumes that both orbits are circular, Which isn't strictly true for either Mars or Mercury, but it will at least give you a mean value.

For Mercury, with an oribital distance of 57,910,000 km, you need a [del]V of 7.6 km/sec to do a fly-by of Mercury.

For Mars, at 227,940,000 km, it takes 2.97km/sec for a fly-by.

And both of these are on top of the 11 km/s you need to lift off the surface of the Earth and attain escape velocity.

 

[russ_watters]

To explain it in simpler terms - INERTIA. The resistance to acceleration. A larger planet has a larger gravitational attraction between it and the sun so you might think it would "fall into" the sun unless it orbited faster. But it having more mass means it takes more force to accelerate. The masses in the two equations (gravitational force and acceleration) cancel out and you end up with the exact same acceleration due to gravity.

This is the same as why the acceleration due to gravity of all objects on Earth is the same regardless of mass.

 

[kleinma]

Originally posted by LURCH

Do you remember hearing the stories about Isaac Newton performing experiments in which two objects, one heavy and one light, were dropped simultaneously? According to the stories, the two objects would hit the ground at the same time. Now there is some debate as to whether Newton ever actually performed these experiments, but no matter; plenty of other people have performed them since. The acceleration of gravity on a free falling object is the same regardless of how heavy the object is.

the reason it doesn't work on Earth is due to air resistance... but the apollo 11 astronauts did the experiment on the moon.. and worked as it should... i think it was a penny and feather??

 

[selfAdjoint]

By the way, the legend about dropping weights isn't usually fathered on Newton, but on Galileo. Although of course Newton did do the thought experiment of dropping two weigths - an apple and the Moon!

 

[Phobos]

Originally posted by kleinma
the reason it doesn't work on Earth is due to air resistance... but the apollo 11 astronauts did the experiment on the moon.. and worked as it should... i think it was a penny and feather??

A hammer and a feather maybe?

 

[russ_watters]

Originally posted by kleinma
the reason it doesn't work on Earth is due to air resistance... but the apollo 11 astronauts did the experiment on the moon.. and worked as it should... i think it was a penny and feather??

My junior high physics lab had a vacuum pump and a plexiglass cylinder. It works on Earth too.

 

[kleinma]

Originally posted by russ_watters
My junior high physics lab had a vacuum pump and a plexiglass cylinder. It works on Earth too.

yeah i have seen that experiment on earth... but you have to use the vacuum pump to make it accurate