Skip to main content
303 votes
Accepted

How did the Apollo computers evaluate transcendental functions like sine, arctangent, log?

Since the Apollo 11 code is on GitHub, I was able to find the code that looks like an implementation of sine and cosine functions: see here for the command module and here for the lunar lander (it ...
supinf's user avatar
  • 2,233
83 votes

Time at 1 g acceleration to travel 100 000 light years

Nonrelativistic solution The variables used will be $x$ for the distance travelled $v$ for velocity $a$ for acceleration ($1~\mathrm{g}$) $t$ for the time $c$ for the speed of light. Non braking ...
Hans's user avatar
  • 3,566
42 votes

How did the Apollo computers evaluate transcendental functions like sine, arctangent, log?

You also asked for the logarithm, so let's do this as well. As opposed to the sine and cosine functions, this one is not implemented with a Taylor series-like approach only. The algorithm is based on ...
dlatikay's user avatar
  • 723
39 votes
Accepted

Person falling from space

Your question is under-specified (you don't give the size or posture of your subject), so I'm assuming an average-sized woman falling in the classic face-down skydiver posture. I'm also modeling this ...
Mark's user avatar
  • 15.3k
37 votes

What is the "pendulum rocket fallacy" as it relates to analogizing a pencil balanced on a finger to maintaining attitude of a hovering rocket?

The pendulum fallacy is the belief that rockets would be passively stable with engines at the top, with the rocket "hanging" from them. The error lies in expecting gravity to pull the body ...
Christopher James Huff's user avatar
34 votes
Accepted

Who developed the mathematics used to correct the trajectory of Apollo 13?

The authors of the paper are Harold A. Hamer, Katherine G. Johnson, and W. Thomas Blackshear. Of these, the name Katherine Johnson might ring a bell with people, as she was one of the protagonists in ...
Ludo's user avatar
  • 14.4k
29 votes
Accepted

How complex was the math and physics necessary to place Apollo 11 on the moon?

Was standard Newtonian mechanics sufficient or were relativistic effects included? Relativistic effects didn't have to be modeled; other sources of error would have swamped the effects of relativity,...
Russell Borogove's user avatar
24 votes

What is the "pendulum rocket fallacy" as it relates to analogizing a pencil balanced on a finger to maintaining attitude of a hovering rocket?

In the inverted pendulum problem: gravity exerts a vertical force on the pendulum, at the center of gravity the support of the pendulum (like the finger under the pencil) exerts a vertical force on ...
njzk2's user avatar
  • 368
17 votes
Accepted

What is the velocity of the ISS relative to the Earth's surface?

JPL Horizons has trajectory data for the International Space Station, SPKID = -125544 Revised: Nov 23, 2022 Trajectory is TLE-based. Predicts run for 4 weeks into future, but are of low accuracy for ...
PM 2Ring's user avatar
  • 2,612
16 votes

What is the "specific impulse"?

If you want to understand how the 'seconds' value fits the greater image, there's this rather contrived definition (which nobody uses because it's contrived and mostly useless but evocative enough.) ...
SF.'s user avatar
  • 55k
14 votes
Accepted

Besides retarded gravitation, anything else to worry about when calculating MU69's orbit from scratch?

This is not a complete answer. It is instead an extended comment to the following: I understand I will have to retard the gravity from each source by its particular light-time, as well as correct ...
David Hammen's user avatar
14 votes

What's the eccentricity of an orbit (trajectory) falling straight down towards the center?

The eccentricity is 1.0. The eccentricity $e$ of an orbit can be found from the radius of apoapse and periapse as: $$e=\frac{r_a-r_p}{r_a+r_p}$$ and the semimajor axis $a$ can as well, from: $$a=\...
kwan3217's user avatar
  • 816
13 votes
Accepted

Why would a slow spiral from a C3 of zero take about 2.4 times as much ΔV as an impulsive maneuver?

If you're in a circular orbit, your velocity is $\sqrt{\mu\over r}$. Escape velocity at that distance is $\sqrt{2\mu\over r}$. So the impulsive $\Delta V$ to reach escape velocity starting from that ...
Mark Adler's user avatar
  • 58.2k
12 votes
Accepted

What are some specific examples of the calculations human "computers" did for the Mercury space program?

(This is adapted from my question/answer at Day-to-day tasks of human computers, ala Hidden Figures movie - History of Science and Mathematics Stack Exchange) I was also fascinated by the film Hidden ...
nealmcb's user avatar
  • 711
12 votes
Accepted

Star-shaped artifacts in SAR images of the "Suez Canal traffic jam seen from space"

Discrete Fourier techniques introduce errors in their terms that track with the sinc function. Any target in the image will produce side lobes like those in the following graph. Strong reflections ...
Craeft's user avatar
  • 473
11 votes

Why is specific impulse equivalent to effective exhaust velocity?

Rockets produce thrust by ejecting reaction mass at some velocity. The fundamental quantities involved are mass flow rate and exhaust velocity, thrust is the consequence of these. It's no coincidence ...
Christopher James Huff's user avatar
11 votes
Accepted

Is there a neat formula for hyperbolic Kentucky windage?

Using Perifocal polar coordinates, where the x-axis points from the central body to the periapsis, and the polar equation for conic sections: $$r=\frac{a(1-e^2)}{1+e \cos(f)}$$ Provided parameters $\...
notovny's user avatar
  • 5,449
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 ...
uhoh's user avatar
  • 149k
10 votes
Accepted

In "spacecraft talk" is nadir just a fancy word for "down"?

There are some subtleties here. The fields where the concept of nadir are most important are nadir-pointing Earth observation satellites, satellites formation flying, and rendezvous and proximity ...
David Hammen's user avatar
10 votes
Accepted

What is the highest number of impulses required for an optimal orbital transfer?

Whether you realize it or not, this is a very fundamental and challenging question in astrodynamics. It's personally one of my favorite topics in the field, and has been very rigorously studied by ...
Nick's user avatar
  • 116
10 votes

Is there an intuitive reason for why the shape of the orbit at perigee is the mirror image of that at the apogee?

If we assume Keplerian/Newtonian mechanics, then we can see a way to rendering the same local curvature of the path at perigee and at apogee (terms for orbiting Earth, of course). At both points the ...
Oscar Lanzi's user avatar
  • 8,525
9 votes
Accepted

Deriving the changes in Keplerian Elements induced by small impulses

If we assume a perfect two-body problem, absent perturbations from external bodies or non-spherical gravity sources (i.e., perfect conic orbits with no precession or variation), your constraints ...
Tristan's user avatar
  • 17.3k
9 votes
Accepted

What is the "specific impulse"?

In simplest terms it is just the thrust produced divided by the propellant flow rate. "How much thrust am I getting for the propellant I am expending?" So bigger is better - you are getting more ...
Organic Marble's user avatar
9 votes

Question about the Hohmann Transfer: why does delta-v go down when transferring to a higher orbit?

While the lower destination orbits don't require a big insertion burn, they do need a big circularization burn at apogee of the transfer orbit. The higher the apogee, the longer and skinnier the ...
HopDavid's user avatar
  • 15.8k
9 votes
Accepted

How to calculate the flight path angle, γ, from a state vector?

This is a problem that has plagued groups of people very knowledgeable about orbital dynamics but who learned using different textbooks: there are two different definitions of "flight path angle"!! ...
Tom Spilker's user avatar
  • 18.3k
9 votes
Accepted

Launching east from a mountain on the equator at midnight during a new moon; ranking of each contribution?

Breaking that down: launch due East site in the Ecuadorean Andes sometime before local midnight on a July 4 when there's a new moon Launch due east. With the exception of launch ...
David Hammen's user avatar
9 votes
Accepted

What is the formula for Legendre Polynomials from EGM96 calculated in F447.f program?

This is not a recurrence for a Legendre polynomial $P_{n}(\mu)$ but an Associated Legendre Function (ALF). This1 states much more than is needed here. ALFs are often denoted $P_{n,m}(\mu)$ in ...
Bob Werner's user avatar
  • 1,124
9 votes
Accepted

Why does the eccentricity vector equation always equal -1?

The expression on the right is meant to give the eccentricity vector but the vector notation has been lost. Here it is in this answer: $$ e = {v^2 r \over {\mu}} - {(r \cdot v ) v \over{\mu}} - {r\...
uhoh's user avatar
  • 149k

Only top scored, non community-wiki answers of a minimum length are eligible