Mass of an object in orbit

[7499275]

First off I am not sure if this should be in General Discussion or the junkyard, if I have misplaced it mods please if you would be so kind to move it to the correct location thank you!

Anyway I began to think about something while waiting for my game of KSP to load up as it takes around 5-8 minutes somewhere in that area. According to science you need more force to move an object of more mass which is just a given. So if you had a 50 ton space station orbiting Kerbin at 3000m/s it would sustain a steady orbit at its given altitude with the velocity it has right? Well what if you then took 30 tons off that station? Now the station weights in at only 20 tons, would it speed up because it still has the same amount of energy but less mass to move? Therefore it has energy to spare which it then puts into more speed increasing the orbit size?

I do not know if this is how orbits work or not but it made sense in my head at least, because if you remove weight from an object orbiting a body it still has the same amount of energy to push it on the orbital path it has to use it somewhere.

7499275

[tuguley]

Your velocity will remain the same, just the energy of the main station would decrease.

The 30t chunk that falls off, will store that extra energy. Remember, energy is always conserved, so instead of have 1 big station with a lot of kinetic energy, you will have 2 smaller chunks with the energy split between them.

Edited July 17, 2013 by tuguley
typo

[SRV Ron]

Taking mass out of the station won't change its orbital velocity. What will change is the amount of force needed to move that mass to a given speed. It will take 2/5th the amount of fuel to change the velocity of a 20 ton station VS the 50 ton one.

It is something to consider when launching small probes outfitted with heavy nuclear engines in their interplanetary stage VS the far lighter but half as efficient LV-909.

[Vanamonde]

The force of gravitational attraction involves the product of the masses involved, but orbital calculations for artificial objects ignore the mass of the ship/station because it's so much smaller than that of a planet or moon. But to be precise, removing mass from the station side of the system would indeed reduce the mutual gravitational attraction, meaning that the station, if still moving with its previous speed, would shift to a slightly higher orbit. Very slightly higher. This is assuming that for the sake of your thought experiment, that mass is simply vanishing. If instead you merely detached part of the station, the mass of the detached parts would continue to affect the other two bodies in the system. The barycenter of the station parts would keep going on the original trajectory, though things would get complex when the pieces drifted far enough apart for the planet's tidal gradiant to start to affecting them differently. (This is the point where Maltesh usually steps in to tell me what I've gotten wrong or over-looked. )

[WizardlyMouse]

Vanamode, I think you're not thinking about the question right, lol. I don't think OP was talking about the gravitational pull of the objects, but only the orbital velocity of it. Either way, KSP doesn't really model gravity that way.

[Mr Shifty]

Well what if you then took 30 tons off that station? Now the station weights in at only 20 tons, would it speed up because it still has the same amount of energy but less mass to move?

Depends entirely on how you remove it. You can, for instance, remove 30 tons from a vessel by expelling 30 tons of propellant from its rocket nozzle. Or you can remove 30 tons from a vessel by disengaging a docking clamp and decoupling a 30 ton satellite from it.

[Sof]

Short answer is that the energy of the station would change. If you were just to undock a 30 ton fuel tank or something, then both objects would keep the same orbit.

[Dunbaratu]

Short answer: Making the satellite less massive reduces the amount of force gravity pulls on it with but also increases the acceleration effect per unit of force applied to it... in such a way that the two effects cancel each other out exactly and the acceleration due to gravity (and therefore the path the craft follows) remains the same as it was before.

Long Answer:

The definition of Force is:

F = m*a

and the force caused by gravity on mass m1 (a ship) due to being in the proximity of another mass m2 (big planet) is this:

F=G*( (m1*m2)/r^2)

(Where G is a constant)

Therefore if you want to solve for the acceleration on mass 1:

F = m1*a, therefore a = F/m1

And what is F?

F = G*( (m1*m2) / (r^2) )

So:

a = G*( (m1*m2) / (r^2) ) / m1

The m1's cancel each other out and become irrelevant.

a = G*( m2 / r^2 )

Summary: When you are being pulled toward another object due to gravity, your OWN mass doesn't affect how much acceleration you experience but the mass of the object pulling you does.

If you reduce the mass of a satellite you won't change the satellite's acceleration toward the planet, but you'll reduce the PLANET's acceleration toward the satellite, which was already so tiny as to be unnoticeable anyway.

[JumpsterG]

I had this same thought experiment a little while back, wondering what would happen if an object magically gained or lost mass instantly while in orbit. Being a fan of the Mass Effect series of games, I found this experiment to be a great excuse to write a plugin to change a ship's mass during flight.

I can verify that while in orbit, increasing or decreasing a craft's mass by a factor of 10 did not change it's orbit in any way. Though, changing mass of vehicles on the ground or in atmosphere proved humorous; Increased mass vehicles would suddenly cave in on themselves and reduced mass vehicles were ridiculously easy to get to orbit. Since the mass (matter?) is being created or destroyed by the plugin, it's not really sound according to physics, but interesting results nonetheless.

I might have to dust off the cobwebs on that plugin, haven't looked at it since .20 came out...

[earth]

the orbit does not change because the mass of your craft is irrelevant in face of the mass of the planet. this is why satellites orbit at the same speed as the iss for example (their theorical speeds are different but ridiculously close).

If both bodies had masses that were no too different, there would be a noticeable change. If the moon were twice heavier, it would fall on earth, because its angular velocity woudnt be enough. By falling i mean getting a lower orbit.

Lets make a thought experiment.

A satellite's mass is basically 0 compared to Kerbin's mass. I dont recall the exact equation for gravity but this means that the total mass is Kerbin's mass.

Gravity pull depends on the total mass and the squared radius if i recall right (and some random constant we dont care about for this). Gravity pull is also equal on both concerned bodies.

F=M/r^2

Now lets say the satellite instantly gains half the weight of kerbin, thats M/2.

F is now 3M/2r^2

What does that mean?

The gravitationnal pull on the satellite is now 1,5 times what it was. The centrifugal force must make for it, because the satellite is in a balance state at all times isnt it? If it does not, its gonna fall towards the ground!

But we only changed the mass and nothing else! And the centrifugal force depends on angular velocity!

So the satellite will fall towards earth, turning its gravitationnal potential energy into kinetic energy aka speed (because the mass of our satellite does not change)

If it can gather enough angular velocity by gaining speed from falling and reducing the radius to be slinged back off the planet, it will hopefully keep a stable elliptical orbit. If not -> boom.

So what happens when you add 500 tons to your 50-ton station?

The exact same thing, except the shift is so slight that i am unsure that 32bit calculations can catch it.

In general, i don't think that KSP accounts for the mass of crafts for calculing the gravitationnal pull of the planets, because it's so irrelevant.

@Steven Mading : i dont get something with your explaination, i do know that gravity's acceleration does depend only on the mass of the other body, but the inertial forces do only depend on the object's mass.... So there would be an actual change actually. Read my post i you wanna know how i ger the thing.

Edited July 19, 2013 by earth

[Epthelyn]

M1 is so small in anything related to spacecraft that it doesn't make any difference.

In fact, if a spacecraft of mass 500t was orbiting Kerbin at 100km (r = 700km, since Kerbin's radius is 600km), the velocity with all parts included would be:

Sqrt((5E22^2*6.67E-11)/((5E22^2+500000)*700000)

2182.72437890947

If you remove the m1:

2182.72437890947

After that point Excel just displayed 0s. If it changed after that, the difference would only be a change of 1 100 billionth for every 500t

You'd need 500,000t to change that 7 to a 6.

Kerbin is quite big.

[Merinsan]

Summary: When you are being pulled toward another object due to gravity, your OWN mass doesn't affect how much acceleration you experience but the mass of the object pulling you does.

If you reduce the mass of a satellite you won't change the satellite's acceleration toward the planet, but you'll reduce the PLANET's acceleration toward the satellite, which was already so tiny as to be unnoticeable anyway.

I don't claim to know the math, but I do have an understanding of general physics. The last sentence of your post disproves your math. It's simple not possible for the planet to accelerate towards the satellite while the satellite does not accelerate towards the planet, as it violates the concept of relativity. The planet moves relative to the "stationary" satellite and the satellite moves relative to the "stationary" planet, meaning the acceleration and velocity would need to be consistent between the 2 bodies.

[Ralathon]

I don't claim to know the math, but I do have an understanding of general physics. The last sentence of your post disproves your math. It's simple not possible for the planet to accelerate towards the satellite while the satellite does not accelerate towards the planet, as it violates the concept of relativity. The planet moves relative to the "stationary" satellite and the satellite moves relative to the "stationary" planet, meaning the acceleration and velocity would need to be consistent between the 2 bodies.

I'm sorry but the guy is right.

Gravity pulls on the satellite. Newtons 3th law means that there is an equal force pulling the earth towards the satellite.

The force of gravity is dependent on mass. If you make something twice as heavy the earth will pull on it twice as hard. Since acceleration follows from a = F/m the acceleration towards the earth is constant for the satellite.

So no matter if you make the satellite 10kg or 1000kg, it will always accelerate towards the earth at the same rate.

However, the forces involved will be much lower in the former case. Since the mass of the earth is constant that means the acceleration of the earth towards the satellite is much lower.

I think you're confusing the reference frames here. All this is done from an inertial frame that's separated from both the earth and the satellite. The acceleration of the satellite relative to our FoR is constant while the acceleration of the earth relative to our FoR is variable. You seem to be using either the planet or the sat as your FoR, which is generally frowned upon since both are experiencing acceleration. This means they are non inertial frames of reference and those are always confusing to work with.

[Merinsan]

I'm sorry but the guy is right.

--snip--

Damn it, I knew I'd trip up on something there. You are right, I was using the wrong frame of reference. It's a long time since I read up on relativity. I probably should do a refresher sometime.

[AfailingHORSE]

Summary: When you are being pulled toward another object due to gravity, your OWN mass doesn't affect how much acceleration you experience but the mass of the object pulling you does.

So what would orbits look like if one was to take a noticeable chunk of the planet, say with an comet or so something.

[Ralathon]

So what would orbits look like if one was to take a noticeable chunk of the planet, say with an comet or so something.

If you just magically made Kerbin lighter you'd reduce the force exerted upon satellites. This would reduce the orbital velocity needed for a circular orbit. So it kind of depends on what kind of orbit you started out with and where in that orbit you were when kerbin got lighter.

For example, a satellite in a circular orbit would start to move in an ellipse with periapsis at the point the sat was when kerbin got lighter. A satellite that started out in a elliptical orbit will get more elliptical if it's near periapsis and more circular if it's near apoapsis.

If the mass difference is big enough the system would also send some satellites out of the system. It'd start with highly eccentric orbits with the sats near periapsis. But as you remove more mass even orbits that started out circular would eventually escape.

[AfailingHORSE]

If you just magically made Kerbin lighter you'd reduce the force exerted upon satellites. This would reduce the orbital velocity needed for a circular orbit. So it kind of depends on what kind of orbit you started out with and where in that orbit you were when kerbin got lighter.

For example, a satellite in a circular orbit would start to move in an ellipse with periapsis at the point the sat was when kerbin got lighter. A satellite that started out in a elliptical orbit will get more elliptical if it's near periapsis and more circular if it's near apoapsis.

If the mass difference is big enough the system would also send some satellites out of the system. It'd start with highly eccentric orbits with the sats near periapsis. But as you remove more mass even orbits that started out circular would eventually escape.

God I hope this is modeled in Planetary Annihilation.

[espm400]

God I hope this is modeled in Planetary Annihilation.

Please don't tell me you spent $90 on that backwards priced, early-access game. Yeah it looks cool, and 'll probably take a look when the game comes out proper, but $90 for an alpha is downright outrageous.