28
So let's break down the answer into bite sized chunks...
How do you transfer a spacecraft from one solar system body to another?
There are two main things you need to do.
Set up an orbit that intercepts the orbit of your target planet/moon.
Time it so that your spacecraft intercepts the target orbit at the same time as the planet/moon you're trying to ...
19
Does pork-chop plots exist for Earth-Moon System?
No, because the concept doesn't make much sense. The Earth-Mars configuration and Mars' eccentricity makes the cost to send a vehicle from Earth to Mars vary by a huge amount. Pork chop plots are a useful way to visualize these huge variations. The cost of sending a vehicle to the Moon on the other hand ...
5
The rotating reference frame is usually preferable over an inertial reference frame when analyzing three-body motion. Two main reasons for this:
The motion is determined by the two primary bodies, so it makes sense to use these to define the reference system
The typical three-body dynamics for which you would use such a reference system, such as Libration ...
5
There are two major issues that I can see.
Whatever you're using to calculate the arcsin is indeed giving you a value in degrees.
The parameters you've provided are basically that of a satellite racing by an object ad a moderate distance, moving far above escape velocity all along its trajectory. It neither gets close enough, nor hangs around long enough ...
4
A few things come to mind:
1) where you put in the radius $8.76×10^{10}$ I think you meant the eccentricity, which for Earth's orbit is about $0.0167$. Putting in a distance parameter there makes the equation dimensionally inconsistent.
2) Do not forget to convert your angles to radians.
3) To deal with the sign: Measure the angle from the initial ...
4
Well, I think this is a good question.
Orbiter 2016 and its 2006 and 2010 predeccessors are fairly realistic spaceflight simulators.
Since you ask about physics:
It has a Newtonian physics engine with adaptive order of integration of linear and angular states (Runge-Kutta and symplectic integrators to order 8)
Dynamic inclusion of gravity sources from ...
3
Brief answer: yes, it's possible. Here's a somewhat scrappy answer: this is pretty much a transcription of what I wrote down when working it out, so it's a bit messy: sorry.
First of all I'll use what I think is the mathematicians' version of spherical polar coordinates (apparently physicists use the two angle names swapped). So starting from a right-...
3
I agree with Ingolifs' answer; you can create a porkchop plot for a transfer between any two orbits. For an Earth-Moon porkchop you could pick either a point on the Earth's surface or a particular low Earth orbit as your start. For example, here's a porkchop plot showing the delta-v required for transfer from Apollo 13's initial Earth orbit to the Moon (...
3
Let's go through this one thing at a time.
First off, your value for $\delta$ is clearly in degrees. With an eccentricity of $200$, the reciprocal $1/e$ is so small it's nearly equal to it's own inverse sine -- in radians. $\delta$ is basically $2/200$ radians $=0.573°$.
Next, realize that geometrically, the eccentricity of a hyperbola equals the center ...
3
Let me put this in a different frame. First recall that magnetic fields also store magnetic energy:
$$
E_{mag} = \int_V H. B\, dV
$$
Now, from Lagrangian mechanics, note that:
$$
L = U-V = E_{mag}+E_{grav}-\frac{mV^2}{2}-\frac{\omega^TI\omega}{2}
$$
And let's forget some dissipative effects and the angular terms for now.
Recalling Euler-Lagrange's ...
3
Dipole-dipole repulsion
The drawing depicts the right idea; if you hold two parallel magnetic dipoles close together there is a strong repulsive force. If you let go, they will fly apart.
In order to imagine what would happen if this was in Earth orbit, let's make the horseshoe magnet an electromagnet. It's the same shape but instead of being made from ...
3
No. What can be done with a magnetic field in Earth's orbit is to torque, or rotate the satellite. But for propulsion of some kind, you would actually need to have some kind of a varying magnetic field, and a tether of some kind. This website talks a bit about how such a thing could work.
2
well, its called a gravity assist. the asteroid took a small amount of earth's velocity and used it to speed up. this is different than skipping off a atmosphere think about skipping a rock on a lake, does it speed up? No. With a gravity assist it's like stealing a bit of energy from the planet to propel your much smaller ship, asteroid whatever it is. ...
2
The equations for the position in a hyperbolic trajectory contain the hyperbolic sinus, cosinus and tangens.
But the other equations, for instance the semi-major axis, energy and hyperbolic excess velocity do not contain hyperbolic functions.
So if you don't want to calculate positions, no hyperbolic functions are used.
I will add a Python program later ...
2
There’s a 2017 federal “Sources Sought” for launch services for TROPICS. The relevant part is:
Therefore, 6 to 8 TROPICS CubeSats will be placed in a constellation formation as described in the three scenarios included in the attached document. All of the CubeSats are identical and must be placed into their operational orbit within 60-days (first ...
2
The probability of collisions over the poles was indeed the reason not to use 90° exactly.
The reason to choose precisely this value might be that at this particular inclination, the Iridium satellites cross the Earth's equator perpendicularly (as seen in an Earth-fixed frame). Back of the envelope:
$$\cos(86.4°) \frac{R_E}{h + R_E} v_{sat} \sim 460 \ \...
1
Is it really true that a polar geosynchronous orbit (displayed in a synodic or rotating frame) is described by Viviani's curve? Can this be demonstrated mathematically?
Yes, and it's simple to show. At least if the satellite is in a perfectly circular orbit, Earth is perfectly spherical and there are no perturbations from any other source. Earth rotates at ...
1
A circular orbit at 400 km height has a period of 1 hour, 32 minutes and 24 seconds. At 302 km it is 1:30:24, only two minutes faster.
If the chaser at 302 km was launched 20 seconds too late, it will need 1/6 of a full orbit to keep up to the target at 400 km, or 15 minutes and 4 seconds. But the target and the chaser are now above the same point on Earth ...
1
To add to Sam's point about accesses, there is also NASA's GMAT free software that allows you to report the accesses.
Alternatively, you can calculate that by yourself. I had no need to calc that before, but I did some related calcs that could be easily transformed into access windows calc. My proposed way is that I would define the ground station of ...
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