Gravity in low-Kerbin orbit (or low-Earth orbit)

[MetricKerbalist]

Hi KSP colleagues,

I should know the answer to this question, but I don't.

Consider a real spacecraft in low-Earth orbit -- oh, perhaps 400 kilometres or whatever.  Similarly, consider a spacecraft in low-Kerbin orbit -- again, perhaps 80 kilometres or whatever.

The craft is well within the planet's gravitational force.  Yet the astronauts or kerbonauts on board are in a state of weightlessness.

How come?

Thank you.

Stanley

[magnemoe]

If you are falling you are not feeling gravity. 
This also applies if you are on an trajectory like an canon ball or the zero g vomit comet planes. 
Orbit is simply that you move so fast you not hitting the ground  
You also get zero g in an suborbital trajectory both in real life and in KSP. 
But you are still in an gravity field or many Earth, Sun and the galaxy

[MetricKerbalist]

Thank you, @magnemoe.  I guess that makes sense.

[FleshJeb]

For a circular orbit, the acceleration due to gravity is equal and opposite to the centripetal acceleration from your motion. You get a net zero.

If you want to have fun with the concept, you can calculate the acceleration of gravity at a particular altitude:

Plug in 9.80665 m/s^2 for g0, 600km for R_e and something like 80km for h

g_h = 7.63 m/s^2

 

Centripetal acceleration is:

So, the required velocity to stay in orbit is:

v = sqrt(a_c * r)

Substitute g_h for a_c, and (R_e + h) for r. In this case r must be in meters and not kilometers.

v = sqrt[g_h * (R_e + h)]

v = 2278.5 m/s for a circular orbit at 80km above Kerbin. You can verify this against the orbital velocity on the navball.

If you like, you can use the cheat menu to put your craft into various perfectly circular orbits and see if it lines up with the calculations.

[MetricKerbalist]

Hi @FleshJeb,

I am going to print out your answer, and go through it line by line.

Thanks.

Stanley

Oh, so that's where the 2278.5 m/s comes from.

[Spacescifi]

1 hour ago, MetricKerbalist said:

Hi KSP colleagues,

I should know the answer to this question, but I don't.

Consider a real spacecraft in low-Earth orbit -- oh, perhaps 400 kilometres or whatever.  Similarly, consider a spacecraft in low-Kerbin orbit -- again, perhaps 80 kilometres or whatever.

The craft is well within the planet's gravitational force.  Yet the astronauts or kerbonauts on board are in a state of weightlessness.

How come?

Thank you.

Stanley

 

Best advice I can give is the ancient predecessor to kerbal.

 

Play space war online in the link.

 

Slow your rocket enough and you notice it fall straight down...just as you and I do (soumding rockets that fly straight up do as well). Fly fast enough sideways and cut thrust and you will be pulled just enough to circle the planet but not enough to fall onto it. Thrust too much and you fly away from the star entirely.

 

Try it! I encourage it. You will see and know firsthand what we are talking about.

Faster than you can complete an orbit in KSP!

https://www.masswerk.at/spacewar/

[MetricKerbalist]

Question, please, @FleshJeb or anyone else.  I am confused.

I just calculated the speed necessary for a circular orbit of 95 km above Kerbin.  I got the answer of 2253.8 m/s.

I thought that orbital velocity should increase with altitude, not decrease.

Edited June 29, 2021 by MetricKerbalist

[HvP]

Our bodies can only feel acceleration when parts of our bodies are pushed or stretched which activates the nerves that sense those forces.

On the ground the surface of the Earth pushes against our feet which transfers that force to our bones, muscles, nerves and inner ear (for balance.)

In orbit both the astronauts and the ship they are in are both in free-fall. Just like in a falling elevator, the person and the thing they are riding in are all falling at the exact same rate in the same direction - floating. So there is nothing to push against and there will also be no feeling of acceleration.

Edited June 29, 2021 by HvP

[FleshJeb]

1 hour ago, MetricKerbalist said:

I thought that orbital velocity should increase with altitude, not decrease.

This would be true if the acceleration due to gravity were a constant, but it's not.

g_h is proportional to 1/r^2, but a_c is proportional to 1/r

This is why space is a counter-intuitive business.

I can derive all this further if it helps.

[kerbiloid]

Making an artificial  gravity is simple.

Just put your craft in orbit, and remove the planet.

The keep it rotating around same point with previous speed.

Edited June 29, 2021 by kerbiloid

[MetricKerbalist]

Hi @FleshJeb,

Please.  I would love to see the derivation.

Thank you for your consideration.

Stanley

[mikegarrison]

5 hours ago, MetricKerbalist said:

I thought that orbital velocity should increase with altitude, not decrease.

Nope. Orbits are funny. If you burn prograde, you go up. If you go up, you go slower.

It's like a roller-coaster. As you go up (higher orbit) you slow down. As you go down (lower orbit) you speed up.

[cubinator]

12 hours ago, MetricKerbalist said:

Question, please, @FleshJeb or anyone else.  I am confused.

I just calculated the speed necessary for a circular orbit of 95 km above Kerbin.  I got the answer of 2253.8 m/s.

I thought that orbital velocity should increase with altitude, not decrease.

As you go up higher from a planet, you're getting less and less influence from its gravity well. So, you will have less energy staying in orbit. Consider that your low-orbit spacecraft orbits Kerbin within a couple hours, yet the Mun takes several days and Minmus takes even longer. The gravity well looks like this: 

[MetricKerbalist]

44 minutes ago, cubinator said:

As you go up higher from a planet, you're getting less and less influence from its gravity well. So, you will have less energy staying in orbit.

Hi @cubinator and everyone else,

I did a quick check with the KSP wiki, and indeed the farther a planet's orbit from Kerbol the slower its orbital velocity.  And as @mikegarrisonwrote:

7 hours ago, mikegarrison said:

If you go up, you go slower.

So, I certainly don't dispute the fact that a higher orbit leads to a slower orbital velocity.  Thank you all for correcting me on that.

Unfortunately, I do not yet see the logic -- "you will have less energy staying in orbit."  I don't understand what that means.  I am not saying that I therefore conclude that you should go faster in a higher orbit.  I just don't see any cause and effect.  The fact that I don't see it is my fault.  But it isn't clicking yet.

Stanley

[mikegarrison]

Go back to that roller coaster I mentioned. Consider the total energy of the satellite is made up of potential energy (height) and kinetic energy (speed). You can mostly work it out from this.

Another way to think of it is that if you are very far from the planet, you don't feel much of its gravity, so it doesn't take much speed to stay in orbit. But the closer you get to it the more it pulls at you, so the more speed you need to stay in orbit.

Douglas Adams once said that the way to learn to fly is to "throw yourself at the ground and miss". That's more or less what an orbit is. The closer you get to the ground, the faster you have to go in order to miss.

[JoeSchmuckatelli]

16 hours ago, MetricKerbalist said:

Hi KSP colleagues,

I should know the answer to this question, but I don't.

Consider a real spacecraft in low-Earth orbit -- oh, perhaps 400 kilometres or whatever.  Similarly, consider a spacecraft in low-Kerbin orbit -- again, perhaps 80 kilometres or whatever.

The craft is well within the planet's gravitational force.  Yet the astronauts or kerbonauts on board are in a state of weightlessness.

How come?

Thank you.

Stanley

Take the spacecraft in orbit - like the ISS at about 254 miles above the surface.  It's traveling above 17,500 mph... falling sideways fast enough to keep missing the planet, somewhat perpetually.  Just like when you are in a plane traveling 400 mph and you can still get up and walk around in it - you are also going 400mph, but can move relative to the plane itself - the astronauts inside the craft can move relative to the ISS - because they're also moving above 17,500 mph - but can make minor adjustments go slightly faster or slower - just like you do in the plane.

You feel your weight in the plane because neither you nor the plane are actually falling (freely) - instead you stay aloft because of the lift provided by the wings and atmosphere, and the floor supports your weight - thus you are aware of the planet's gravity. You know that if you jump out you will fall to the surface.  However - once you jump - you won't feel the gravity... Only the air rushing past and the planet getting rapidly closer give you any sense of movement. 

In the ISS - because they are falling free they don't feel that.  They are falling free inside or out of the craft.  However if it were possible for a craft to fly at the same altitude at only 400 mph it would feel like being on the plane (you could walk: there would be an 'up' and a 'down' that all passengers agree on).   Jump from that - and you will feel weightless again, until the planet suddenly reminds you that it's really big and hard. 

[MetricKerbalist]

First, I thank everyone for their contributions.  They all helped.

Second, two of the points that @mikegarrisonraised were particularly useful for me:

21 minutes ago, mikegarrison said:

Go back to that roller coaster I mentioned. Consider the total energy of the satellite is made up of potential energy (height) and kinetic energy (speed).

...

Douglas Adams once said that the way to learn to fly is to "throw yourself at the ground and miss". That's more or less what an orbit is. The closer you get to the ground, the faster you have to go in order to miss.

The first point put the issue quantitatively.  As you go higher in orbit, you gain potential energy, but you lose kinetic energy.

Thanks again, everyone.

Stanley

[MetricKerbalist]

Hi KSP colleagues,

Let me please follow up on this topic.

Consider the space stations that you see on science fiction like in 2001: A Space Odyssee.  There we see a torus always in rotation around its own axis.  People on the station walk around as though there were gravity.

Would there be local gravity on the space station?  If so, does the rotation make it happen?  Or is this just fantasy?

Thank you.

Stanley

[Spaceman.Spiff]

3 minutes ago, MetricKerbalist said:

Would there be local gravity on the space station?  If so, does the rotation make it happen?

Yes.
It’s the rotational force creating gravity inside the ring. 

I’m sure others can explain better.  

[HvP]

7 minutes ago, MetricKerbalist said:

Would there be local gravity on the space station?  If so, does the rotation make it happen?  Or is this just fantasy?

The rotation of the space station accelerates anything in contact with the floor through friction. This imparts inertia to someone in contact with the floor. Inertia causes a mass to travel in a straight line - tangent to the rotating circle of the station. But since you would be inside that rotating station the floor curves inward and interrupts your straight line, causing you to remain in contact with the floor, further accelerating you along its inward curve as long as the station keeps spinning.

Do not confuse this with actual gravity, because it isn't. It's centripetal (or centrifugal) force. Microgravity is a real thing because all objects with mass have some small amount of gravity, but that is completely overwhelmed by the centrifugal effect.

Tom Scott has an excellent Youtube video about this -

 

Edited June 29, 2021 by HvP

[Beccab]

2 minutes ago, MetricKerbalist said:

Hi KSP colleagues,

Let me please follow up on this topic.

Consider the space stations that you see on science fiction like in 2001: A Space Odyssee.  There we see a torus always in rotation around its own axis.  People on the station walk around as though there were gravity.

Would there be local gravity on the space station?  If so, does the rotation make it happen?  Or is this just fantasy?

Thank you.

Stanley

It's not local gravity nor fantasy, in reality we have one way to simulate the force of gravity: using a different force in its place. In this case, gravity is created by the centrifugal force that being inside the torus creates, pushing you outwards like, for example, clothes inside the washing machine when it is rotating very fast. That rotation is tuned to the exact speed that allows you to have the quantity of gravity you want, may that be 0.3 G, 1 G or whatever. Another example of this is the "ullage thrust" used in rocket stages when they are in weightlessness: if the tanks of a rocket stage are partially empty, that remaining fuel would float inside the tank and you wouldn't be able to reach it and use it. To prevent this, some upper stages activate ullage motors, which are much smaller and less powerful engines with a separate tank, to "push" the stage forward and simulate gravity for as long as they are active and thus creating acceleration

[MetricKerbalist]

Thank you everyone, in this case especially  @HvP and @Beccab.  That YouTube video was indeed helpful.

[wumpus]

1 hour ago, mikegarrison said:

Douglas Adams once said that the way to learn to fly is to "throw yourself at the ground and miss". That's more or less what an orbit is. The closer you get to the ground, the faster you have to go in order to miss.

This is orbital mechanics in a nutshell.  The only thing to remember is that "the faster you have to go" is angular speed, not linear speed.  And once you enter the atmosphere you have a lot more problems than just missing the ground.

[JoeSchmuckatelli]

2 hours ago, MetricKerbalist said:

Hi KSP colleagues,

Let me please follow up on this topic.

Consider the space stations that you see on science fiction like in 2001: A Space Odyssee.  There we see a torus always in rotation around its own axis.  People on the station walk around as though there were gravity.

Would there be local gravity on the space station?  If so, does the rotation make it happen?  Or is this just fantasy?

Thank you.

Stanley

There should be a tiny bit of gravity given the mass - but so tiny you wouldn't perceive it (especially from the inside).  OTOH - if you have a rotating torus, the centrifugal force can mimic the effect of gravity (giving you a perception of 'up' and 'down' with regard to the inside of the torus) - but someone outside of the torus would not experience the same effect.  (well-except that someone hanging on to the outside is at risk of getting flung off) 

 

It should be remembered that the effect of being pressed against the inside of the rotating torus might seem analogous to feeling gravity on the surface of a planet - but the process is totally distinct. 

Edited June 29, 2021 by JoeSchmuckatelli