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What immediately springs to mind is the Martian moon Phobos, orbiting the planet in 7 hours 39 minutes. That's a fair bit quicker than the 24 hour 37 minute sidereal period of Mars. From the surface of the planet, Phobos and Deimos will therefore appear to cross the sky in opposite directions. Other solar system examples include the small inner Jupiter moons ...


12

Are there any known examples of this situation? Yes! In addition to Phobos mentioned in this answer and from Astronomy SE: How did “oddball” Valetudo, Jupiter's new prograde moon, end up in a wider orbit? Why are most of Jupiter's moons retrograde?


8

Though it's a stretch, GNSS satellites in MEO like GPS, Galileo, GLONASS, etc... are examples of such "moons" orbiting planet Earth, since they're positioned at an altitude lower than geostationary orbit but are still high enough for atmospheric drag to be so low that they can maintain that orbit without needing additional sources of propulsion/...


8

A couple considerations enter here. We do not expect the alignments to occur every 175 years over the long haul. Rather, they are likely to occur in clusters internally spaced by that interval until the alignment is "permanently" lost, and takes a much longer interval to reset. The period of 175 years represents a compromise between multiple ...


4

This answer to How to solve the two-body problem in the ECI frame through numerical integration? says: Instead of a single second order differential equation $$\ddot{\mathbf{r}} = -\frac{\mu}{r^3}\mathbf{r}$$ We can solve the following pair of first order differential equations in parallel $$\dot{\mathbf{v}} = -\frac{\mu}{r^3}\mathbf{r}$$ $$\dot{\mathbf{r}} ...


4

$state=[rx,ry,rz,vx,vy,vz]$ $\dot{state}=[vx,vy,vz,ax,ay,az]$ $a=\dfrac{\mu}{r^2}$ (Newton's universal law of gravitation / two body acceleration in scalar form) Division be zero errors are avoided by using the vector equation for acceleration, since any one of the position components can be equal to zero, but the norm will be a positive number (assuming the ...


4

Working outward, initial measurements were based on measuring angles and a lot of math working from orbital motion which got a consistent model of the solar system, and indeed located planets because the math was inconsistent. This has been fine tuned with LASER measurement to mm accuracy to the moon, and radar measurement of planets out to Saturn. With ...


4

It's quite intentional. There's a significant risk that the vehicle will fail during ascent, and then there's the transition to the "skydiver" orientation and controlled descent using the flaps which had never been tried outside of wind tunnels before these tests. They needed to have the ground impact point be somewhere reasonably safe if things ...


3

This is equivalent to asking whether it's possible for a moon to orbit lower than a geosynchronous orbit, and there are of course satellites in orbit around the Earth that are lower. It's also equivalent to whether it's possible for a planet to rotate slower than its moon orbits, and clearly there's no lower limit on how slowly a planet can rotate (at least ...


3

The Help for Orbital Simulator gives the following for Launches: $\phi$ is the latitude of the launch site. $\lambda$ is the longitude of the launch site. Ω is the ascending node of the orbit. Those three items determine the inclination of the orbit.


2

There are a lot of variables in this question concerning exactly when an abort is required and what has caused the abort. Some Mars mission profiles can use a free return trajectory. If this is used and for whatever reason it becomes necessary to abort, it is relatively easy to return to Earth by applying a small course correction. This will allow the ...


1

You don't start with a departure date--that's one of the answers, not one of the inputs. I don't know a formula for calculating a gravity assist orbit so I will use the easy case and omit Venus, as well as assuming the planets are in circular, coplanar orbits: Find the orbital period of the transfer orbit. For our simple case the orbital radius is (mercury ...


1

If a planet has a large moon that causes significant tides on the planet, then the Moon will spiral inward if it rotates faster than the planet and will then eventually collide with the planet. This is because the tidal bulges caused by the moon are going to be pulled back relative to the moon by the planet's slower angular rotation. Th force of gravity ...


1

...and it got me thinking that a great way to show to people why the Moon is reddish -- when eclipsed by the Earth -- would be if we have a color photograph taken from a spacecraft in the general vicinity. This doesn't help exactly but it's the closest that I could find. The Hubble Space Telescope's near-UV and optical transmission spectrum of Earth as an ...


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