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Results tagged with orbital-mechanics
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user 12448
Orbital mechanics (also called astrodynamics) is the application of ballistics and celestial mechanics to the practical problems concerning the motion of rockets and other spacecraft on an orbital or escape trajectory. For the movements of celestial bodies, use [celestial-mechanics], not this.
1
vote
Accepted
Given orbital parameters and position vector along that orbit, how can I determine the eccen...
From the first equation, we get $\cos\tau = \frac x a + e$. This on its own is not quite enough to find $\tau$, since a given value of $\cos\tau$ usually corresponds to two values of $\tau$ in $[0,2\p …
- 2,120
8
votes
Accepted
Clohessy-Wiltshire/Hill's Equations - F=ma?
Using restricted 3-body problem seems like an overkill for this problem to me. The equations can be deduced in a simpler way. Without going into much details, it goes like this: since the frame is rot …
- 2,120
2
votes
Is the formula for nodal period of a near-Earth satellite given by Wikipedia correct?
This is not a complete answer, but, as far as I can tell:
First, the angular speed in the linked paper is based on the anomalistic period (i.e., the time between two periapsis passages), not the nodal …
- 2,120
2
votes
Obtaining orbital state vectors given two position vectors and an eccentricity
Not a complete answer, but: Let $A$ and $B$ be the two given positions, $O$ the position of the primary body, and $F$ the second focus of the orbit. Then we have $|OA|+|AF| = |OB|+|BF|$ and $|OF| = e( …
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3
votes
Accepted
Secular variation of orbital elements and influence of force components
The formulas (15) and (17) are given under the assumption that both $f_1$ and $f_2$ (the radial and the transverse components of the perturbing force) stay "sensibly constant over one orbital period". …
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13
votes
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Optimal depth for underground flyby?
Assuming a uniform planet with radius $1$ and gravitational parameter $1$, if $V_\infty$ is the speed at infinity and $r$ is the closest approach to the center, then the maximal speed is $V_m = \sqrt{ …
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3
votes
Accepted
Calculating velocity state vector with orbital elements in 2D
Assuming that the direction of the periapsis is the positive direction of the x-axis, then the vector $-a\sin E\cdot \mathbb{i} + b\cos E\cdot \mathbb{j}$ is tangent to the orbit at the point with the …
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4
votes
Accepted
What is the functional form for r(t) for a solar-sail deorbit into the Sun?
This answer assumes that the spacecraft stays in an almost-circular orbit all the time. We have
$$
\frac{dE}{dt} = F_\tau v,
$$
where $E$ is spacecraft's energy (potential + kinetic), $v$ is its speed …
- 2,120
2
votes
Accepted
On the dynamics of two connected objects located at different circular orbits
I'm afraid that your whole approach is wrong due to starting with contradictory assumptions. If the two bodies are connected by a rigid tether, then in general, they will not move in circular orbits, …
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2
votes
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Could a satellite in LEO "pump" or change mass distribution to gain forward momentum?
In theory, you can change your spacecraft's orbit without expending reactive mass, just by moving its parts relative to one another. Instead of a rod and a sphere, let's consider a rod and two identic …
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3
votes
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Help with my tensor tension; how to derive and calculate this rigid body gravity gradient to...
Let $\theta$ be the angle between the direction of the rod and the direction toward the Earth, measured counter-clockwise. Then in the system of coordinates you used to write $I$ as
$$\begin{bmatrix}
…
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0
votes
Does other orbital parameters change on plane alignment impulsive maneuver?
If the only thing you check for is that the Longitude of the Ascending Node is correct, then it guarantees only that your new orbit lies in the correct plane and passes through the point where you do …
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4
votes
Accepted
Pure orbit inclination changing, why delta v differs between vector and numerical approach?
Instead of using the normalized velocity vector, you should first project the velocity vector onto the transverse plane (i.e., take $\mathbf{v} - \frac{\mathbf{v}\cdot \mathbf{r}}{\mathbf{r}\cdot \mat …
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4
votes
Accepted
Reference frames - why do I need to convert to Geocentric Equatorial State Vector to solve e...
I'm not a specialist, but here are my guesses: the geocentric equatorial frame makes it easier to express $\mathbf{v}_{rel}$, the spacecraft's velocity relative to the atmosphere, in terms of $\mathbf …
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4
votes
Accepted
Can "prolateness" be characterized by a $J_2$ coefficient like "oblateness"?
This is an expansion of my comment.
Very roughly speaking, $J_2$ is a measure of the following: if one point is over the body's pole, and another point is over the equator at the same distance $R$ fro …
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