The size of your orbit is proportional to the energy of your spacecraft. Use manuever nodes to change the trajectory of your encounter with a planet like Eve, and notice how massively you can change the total size of your orbit (up or down, depending on the direction of the encounter). This implies a significant change in your energy during the encounter. This is from your gentle collision with the planet through its gravity field.
I highly recommend you play Kerbal Space Program if you want to get an intuitive understanding for how it works. But in short, yes, and also if you accelerate towards another orbiting object your own orbit becomes more elliptical such that over sufficient distance you will actually move away from it rather than toward it.
Go play a bit of KSP. NASA employees have stated that Kerbal Space Program has given them an intuition of orbital mechanics that a degree didn't.
And working with things that make you go _slower_ when turning on your engine to push you in the direction of travel needs intuition to even begin. Yes, once you get to the other side of the planet you are orbiting, you are going slower than if you didn't use your engine at all.
Could there be some energy advantage to being in orbit around it? I'm thinking of a scenario where you spend a large amount of energy once get into orbit around the object, but then gain a small amount of energy continuously through something like tidal forces.
Try playing with an online solar system simulator some time. After thousands of orbits, a tiny gravitational nudge can have a huge effect on a system. Also read about the concept of orbital resonances.
Even a small difference in orbits adds up over time. You don't need much fuel for orbital adjustments, as long as you're staying in the same plane.
Say one satellite's orbit is a bit smaller. That means that, over time, they will naturally drift farther and farther apart, until they end up on different sides of the globe. At that point, just raise the smaller orbit slightly.
Kerbal Space Program is really good for understanding stuff like this.
I wrote a small 2D game once, where the Earth is attacked by a swarm of satellites in polar orbits. Your ship is launched from the surface, but after that it's up to you to put yourself in orbit, using thrusters. Thinks Asteroids with gravity. It really taught me a lot about how an orbit's shape changes when thrust is applied in different directions, at different points in an orbit. For example, a good way to circularise an orbit from an elliptical, a small tangential thrust at apogee during each orbit would eventually place the spacecraft in a circular orbit with a radius roughly equal to the apogee distance of the elliptical orbit... or to say it another way, perigee would increase until it equalled apogee...
Anyway, the point being that I never would have understood any of this no matter how many times I read 2010, until I wrote that little game. Some things need to be experienced to really grok.
Is that because you need to decelerate relative to the planet's core to get on an orbit with a smaller radius, so that you can then increase your revolutions per minute at your existing momentum, then accelerate to get back to the orbit the other object's on? I'm trying to visualize the scenario you're describing
Yeah. I have an engineering degree but never really thought much about orbital mechanics.
My first try at KSP I just overbuilt a rocket and aimed it directly at the mun. I missed. Quickload. Back on target, sudden realization that I need about 6000 dV to slow down in time. Watch a Scott Manley video -> instant understanding.
It's definitely one of those things that once you understand it, it's mind boggling how often space is depicted incorrectly.
Think of a very very elliptical orbit, one that's nearly a line and consider what happens when you take a bit of energy off the orbiting object. At perigee, when the energy is almost entirely kinetic, you're mostly just changing the velocity, rather than altitude of the object. At apogee, when the energy is almost entirely potential, it's the other way round - the change is almost entirely one of altitude.
Wait... most of the energy of going into orbit is in accelerating to orbital speed (lateral), not getting away from earth (vertical).
That's true for Low Earth Orbit, but as the radius of a circular orbit increases the kinetic energy decreases and the potential energy increases.
On the surface of the Earth, we have:
-(398600 km^3/s^2 [1]) / (6378 km [2])) = -62.5 km^2/s^2 of potential energy
(0.465 km/s [3])^2/2 = 0.1 km^2/s^2 of kinetic energy
At LEO, we have:
-(398600 km^3/s^2 [1]) / (6678 km [4])) = -59.7 km^2/s^2 of potential energy
(7.8 km/s [5])^2/2 = 30.4 km^2/s^2 of kinetic energy
At GEO, we have:
-(398600 km^3/s^2 [1]) / (42164 km [6])) = -9.5 km^2/s^2 of potential energy
(3.07 km/s [7])^2/2 = 4.7 km^2/s^2 of kinetic energy
Notice how LEO has only 2.8 km^2/s^2 of additional potential energy compared to the surface, but 30.3 km^2/s^2 of additional kinetic energy. However, at GEO there is 53 km^2/s^2 additional potential energy compared to the surface and only 4.6 km^2/s^2 additional kinetic energy.
[1] Earth's gravitational parameter
[2] Earth's equatorial radius
[3] Earth's equatorial rotation speed
[4] A 300 km altitude orbit
[5] Velocity at LEO
[6] GEO radius
[7] Velocity at GEO
Getting into an orbit next to some other small object is kind of hard. In the GIF you can see Hayabusa-2 making multiple orbits below the asteroid's orbit to catch up (lower orbits are faster) before it raises its orbit to the height of the asteroid. Once it reached the asteroid it had to do another correction to the orbit to make sure they stay together.
In comparison, meeting something massive like a planet is very single: go into any orbit that nearly hits the planet, and when you are there slow down enough to let charit gravity pull you into an orbit around that planet.
tl;dr: more gravity makes rondevous easier and quicker
Right, so an orbit implies an amount of kinetic energy which you need to lose to lower your orbit; and losing kinetic energy in a frictionless environment requires some kind of propulsion.
I've been playing the Kerbal Space Program (KSP) game lately; it's funny how when you actively use orbital mechanics, thinking about them is easier.
This fourth dimension observation is cool and likely very useful mathematically, but it's also kinda obvious (at least after playing KSP) that if you subtract the time/gravity element from an orbit, it becomes circular. It's equivalent to saying that if you subtract out the gravity effects of the planet you're orbiting, your orbital speed is constant, which just makes sense intuitively.
Calling this observation a fourth dimension is useful, but perhaps unnecessarily complicated for the simple concept.
Everything else is going to be small and average out over time. And if you manage to pick up a bit of energy orbiting a tiny object you'll quickly just get ejected at its (small) escape velocity. Whatever that gives you, it won't be worth the cost of matching orbits to start with. Better to come in hot and slingshot.
Solar wind / radiation pressure is probably the next best free ride since that adds up over time continuously and is everywhere.
Everyone should play KSP. :)
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