39
votes
Accepted
What assumptions were made about the sphericity of the Moon for the Apollo program?
Edit: I'm going to have to retract part of my answer. The 1967 farside maps made from Lunar Orbiter data show no elevation information.
By the time of Apollo 8, the Lunar Orbiter program had mapped 99%...
- 126k
34
votes
How did theorists determine that the atmosphere attenuates enough to support unpowered orbits?
If 200 miles up counts as a low earth orbit height, then the appreciation is as old as Newton's Principia, that there was no atmosphere left there, and nothing like atmospheric drag to oppose motion.
...
- 1,102
33
votes
Accepted
What causes a satellite's orbit to decay?
If satellites are truly far beyond the atmosphere, their orbits do not decay, except for very small perturbation effects like solar radiation pressure from the Sun or tidal forces from the Moon.
But ...
30
votes
Accepted
How feasible would this mission to Proxima Centauri be?
Unless I am mistaken, the amount of speed a gravitational slingshot can add is less than twice the orbital speed of the planet being used. Mercury's orbital speed is the fastest, at a little over 47 ...
- 10.3k
28
votes
What assumptions were made about the sphericity of the Moon for the Apollo program?
As mentioned in this answer, the far side of the Moon was not unknown by the time of Apollo 11. And in fact the early Soviet probes did send back photos. The first ever view of the lunar far side was ...
- 1,977
24
votes
Accepted
Earth re-entry from orbit by a sequence of upper-atmosphere dips to reduce kinetic energy?
Unpowered re-entry into an atmosphere is about trading orbital energy for heat. If the planet being orbited has radius $R$, then the additional specific energy of an elliptic orbit compared to being ...
- 8,001
21
votes
Accepted
Why does the point of burn on an orbit stay at a constant altitude?
When calculating propulsive manoeuvres, we usually consider them as impulses. That is, happening in a very short time. This is usually a good enough model for chemical rocket engines which deplete ...
20
votes
How did theorists determine that the atmosphere attenuates enough to support unpowered orbits?
The scale height is a useful way to describe how the atmospheric pressure decreases with altitude. From Wikipedia,
For planetary atmospheres, scale height is the increase in altitude for which the ...
- 2,564
18
votes
Accepted
How do we define the aphelion of Earth?
The aphelion is usually considered to be the point of greatest actual separation, so this would include the (very minor!) gravitational effects of other solar system bodies. It's not the slight ...
17
votes
Distance from earth to another planet in solar system
Here's a short answer to get the ball rolling:
However, orbital parameters do not indicate where the body was at a specified date and time to calculate current position...
That's absolutely right, ...
- 148k
13
votes
What causes a satellite's orbit to decay?
The Wikipedia article on orbital decay lists a number of reasons, in addition to atmospheric drag:
Tidal effects
An orbit can also decay by negative tidal acceleration when the orbiting body is large ...
- 179
12
votes
Earth re-entry from orbit by a sequence of upper-atmosphere dips to reduce kinetic energy?
When Does an Orbit Stop Being an Orbit
Low Earth Orbit is (rough) 7.8 km/s. This is the lowest amount of energy you can have in an orbit of the Earth. If you try to create a lower energy orbit, you ...
- 1,548
11
votes
Help with fictional scenario: trapped in Lagrange Point orbit
For The Sun-Earth Lagrange points, trajectories to L3, L4 and L5 are time consuming, in the order of several months even for expensive "fast" trajectories. Regular low energy transfers take ...
11
votes
What's the motion of two connected satellites orbiting the Earth after their separation?
Many good things here, though a few of the assumptions made are not safe.
Before cutting the tether the velocity of two satellites is equal to the one of the system CoM
This can not be assumed. ...
11
votes
Object slowest at periapsis - despite correct position calculation
If I understand correctly, your $p, q$ are essentially cartesian coordinates, and you're trying to get the velocity components in those two orthogonal directions.
However, you're taking the derivative ...
- 148k
10
votes
Accepted
Minimum delta V required to return a piece of metallic asteroid 16 Psyche to Earth?
Given the relatively low inclination of 16 Psyche (3.095°), and the fact that the line of apside is relatively close to the node line anyway, this can be approximated as a planar transfer.
Thus, this ...
10
votes
Help with fictional scenario: trapped in Lagrange Point orbit
It is so easy to die in space…
Being stuck in a Lagrange point is a bit dull: like being adrift in the Sargasso Sea. Isn’t it more exciting to be sucked into a raging hurricane?
A propellant-feed ...
- 18k
10
votes
Accepted
How close do gravitational 2-body hierarchy levels get?
The zone of influence of a larger body over a smaller body is known as the hill sphere. Within this sphere the gravitational attraction of the larger body will dominate its satellite and satellites ...
- 8,974
10
votes
When you burn retrograde, will you reach periapsis sooner or later?
It depends on where you are in your orbit.
Specifically, it depends on where you are in the orbit relative to your periapsis when you start the burn.
Visualizing orbits is difficult at first, but a ...
- 2,734
10
votes
Accepted
In circle orbit, give a delta V to a satellite, how to find final orbit altitude?
To calculate how high your satellite will go, you forgot 1 major thing. The hohmann transfer. I am going to show you how to calculate the transfer from a 600 km circular orbit to another circular ...
- 4,710
9
votes
Help with fictional scenario: trapped in Lagrange Point orbit
While the question asks for a "Lagrange Point orbit" and current answers mention that Halo-type orbits (about Lagrange points) are slow, typically about half of the primary orbit (so of ...
- 148k
9
votes
Is it possible to create an analytical ephemeris from raw position and velocity of a Body?
It's possible, because that's partly how VSOP was made, but the amount of effort involved is immense. What you are describing is at the very least a doctoral thesis, if not several of them.
Why not ...
- 7,778
9
votes
What's the motion of two connected satellites orbiting the Earth after their separation?
Before the tether is cut, the angular velocity of the satellite is given by
$$
\frac{\mu m_1}{r_1^2} + \frac{\mu m_2}{r_2^2} = m_1 \Omega^2 r_1 + m_2 \Omega^2 r_2 = M R \Omega^2,
$$
where $r_1 = R - ...
- 942
9
votes
In circle orbit, give a delta V to a satellite, how to find final orbit altitude?
A single application of all of the allotted delta V will result in an elliptical orbit with a perigee equal to the original altitude. What you want to do instead is to apply a delta V at the start and ...
- 73.2k
9
votes
Accepted
Object slowest at periapsis - despite correct position calculation
As uhoh said, the velocity is the derivative of the position w.r.t. to time, not true anomaly. I.e., if we denote time by $t$, the components of the velocity vector are $\left(\frac{dp}{dt}, \frac{dq}{...
- 2,040
8
votes
Accepted
What is the relationship between the radius of the Hill sphere and escape velocity?
This is where it goes wrong:
$$\Delta v = \sqrt{v_2^2 - v_1^2}$$
You're taking the difference of the squares of the velocities at a low lunar orbit, and the perilune of the transfer orbit.
But really, ...
8
votes
Earth re-entry from orbit by a sequence of upper-atmosphere dips to reduce kinetic energy?
"Earth re-entry from orbit by a sequence of upper-atmosphere dips to reduce kinetic energy?"
A satellite in a long very eccentric elliptical orbit will have a greater energy than one in a ...
- 8,974
7
votes
Accepted
What are "transcritical, pitchfork, period-doubling, torus, and subharmonic bifurcations" in the context of three-body orbits? (e.g. butterflies)
I can attempt an answer by summarizing some of my favorite dissertations. Forgive some of the word vomit below, this is certainly not the most elegant or succinct explanation. I'll give a bit of a ...
- 741
7
votes
Accepted
How do you calculate the characteristics of an orbit of an object launched from a mass driver?
Since we're in an elliptic orbit as soon as we leave the mass driver, we can use the velocity we have to set up the vis-viva equation;
$$v^2 = \mu \cdot \left(\frac{2}{r_{moon}} - \frac{1}{a}\right)$$
...
7
votes
Can electrodynamic tether propulsion use the solar magnetic field?
Some figures I found suggest that 300km above the earth would have a strength around 0.24 gauss (Research India), while the interplanetary field at 1AU is only about 50 micro gauss (Valee). I suspect ...
- 6,667
Only top scored, non community-wiki answers of a minimum length are eligible