Tagged Questions
0
votes
1answer
62 views
Vector cross product of $\mathbf{r}$ and $\ddot{\mathbf{r}}$ in polar coordinates
I'm struggling with the following question:
Question 6 A planet of mass $m$ moves under the gravitational attraction of a central star of mass $M$. The equation of motion of the planet is
...
2
votes
1answer
47 views
Oberth Effect in deep space
Does the Oberth effect only apply when in orbit of a planet or would a rocket generate more and more thrust (if kept on) even in deep space?
Wikipedia explains that the faster the rocket goes, the ...
0
votes
0answers
28 views
Understanding Kepler's $2^{nd}$ law in terms of angular momentum conservation
A) Explain how Kepler's $2^{nd}$ law - "The radius vector from the Sun to a planet sweeps out equal areas in equal time intervals" - can be understood in terms of angular momentum conservation.
I ...
1
vote
2answers
143 views
Semi-major axis and ellipticity of a binary system?
In the image below (source at bottom), it seems to be suggesting that
\begin{equation}
a = a_{1} + a_{2}, \hspace{8cm}(1)
\end{equation}
where $a_{1}$ and $a_{2}$ are the semi-major axis of the ...
4
votes
2answers
115 views
If the moon was rapid enough would it be able to orbit the earth from a close distance?
If the moon was close in orbit that it's surface was like 100 km away from the earth's surface. And it had a large enough angular velocity will it be able to hold orbit?
If this was possible, is ...
0
votes
1answer
63 views
What Speed Would an object need to leave the earth at to reach L1? [closed]
Let's say the Earth is an airless sphere. What speed would an object weighing 1 kg need to leave the surface at in order to get to and be motionless at L1, where the Moon's gravity becomes stronger ...
0
votes
0answers
56 views
How much energy would it take to move the asteroid that has been implicated in the dinosaur extinction by a few centimeters? [closed]
One of the greatest mass extinctions occurred about 65 million years ago, when, along with many other life-forms, the dinosaurs went extinct. Most geologists and paleontologists agree that this event ...
2
votes
2answers
77 views
Generalised Kepler's III law?
I have derived the following equation for the time-derivative of the angle that an orbiting particle subtends with one of the coordinate axes, with the other particle at the origin (this is the focus ...
4
votes
1answer
128 views
How is the equation of motion on an ellipse derived?
I would like to show that a particle orbiting another will follow the trajectory
\begin{equation}
r = \frac{a(1-e^2)}{1 + e \cos(\theta)}.
\end{equation}
I would like to do this with minimal ...
2
votes
1answer
183 views
How can a satellite's speed decrease without its orbital angular momentum changing?
I have no idea what the answer is. I'm supposed to answer it within 3-4 sentences.
2
votes
2answers
81 views
Shoot object into the Sun using minimal energy
Say I want to shoot a cannonball into the Sun with minimal energy (minimal initial velocity relative to Earth).
In which direction do I shoot it?
Let's neglect Earth's gravity, if that would make ...
0
votes
1answer
83 views
Lagrange L4 L5 points and perifocal plane
I have 2 satellites at the L4 and L5 points and these are watching an object. Each satellite provides the angle to the object from its own position from a line parallel to the $\text{x-axis}$ of ...
6
votes
3answers
170 views
Falling through the rotating Earth
Suppose you were standing on the rotating Earth (not necessarily Equator or the poles) and suddenly your body lost the ability to avoid effortlessly passing through solid rock.
Because the earth's ...
2
votes
1answer
111 views
Finding orbital eccentricity
I have this problem: They give me, from a satellite that is in orbit in earth, a value for the period, and the closest height to earth surface, the ask me what the eccentricty of the orbit is. I have ...
0
votes
1answer
167 views
Energy in orbit of satellites around the earth lost?
If the total mechanical energy in a satellite's orbit (assuming circular) is greater when it is closer to the earth, and hence smaller when it is farther from the earth, then we can say that as the ...
0
votes
1answer
148 views
Two moons of Earth?
Hypothetically, suppose there is a situation where the Earth's moon gets neatly sliced into two equal hemispheres, and the force responsible for this slicing also creates a distance between the two ...
6
votes
2answers
186 views
Is the gravitational potential of a planet in orbit always equal to minus the squared velocity?
Say a planet (mass $m$) is orbiting a star (mass $M$) in a perfect circle, so it is in circular motion.
$F=ma$ and the gravitational force between two masses $F=\frac{GMm}{r^2}$ so
...
3
votes
3answers
182 views
Does Kepler's law only apply to planets?
Does Kepler's law only apply to planets? If so why doesn't it apply to other objects undergoing circular motion?
By Kepler's law I'm referring to $T^2 \propto r^3$
3
votes
1answer
211 views
How long will it take for a bullet to reach a Geostationary orbit?
I'm curious to know this. Neglect air friction and imagine a bullet that were shot normal to the Earth's surface, from the Equator. I will have to consider the Coriolis effect and so I expect the path ...
1
vote
2answers
99 views
A particle of charge $-e$ orbits a particle of charge $Ze$, what is its orbital frequency?
A point particle $P$ of charge $Ze$ is fixed at the origin in 3-dimensions, while a point particle $E$ of mass $m$ and charge $-e$ moves in the electric field of $P$.
I have the Newtonian equation of ...
2
votes
1answer
162 views
Do Lagrangian points actually maintain a fixed distance?
I was reading on up Lagrangian points and the restricted three-body problem.
From what I was able to tell, the Lagrangian points are 5 points in a two-body system such that a third body would be ...
0
votes
1answer
150 views
Condition for circular orbit
I am a little confused about the condition for circular orbit. Goldstein's Classical Mechanics has the condition for circular orbit as $$f^'=0\tag1$$ where $f^'$ is the effective force. I understand ...
5
votes
2answers
199 views
Why is there this asymmetry between the two foci of an orbital ellipse?
Why does the Earth revolve with the Sun at one of its foci? Does the other focus do nothing? Why is there this asymmetry in our solar system?
1
vote
1answer
118 views
Determining Orbital Velocity
Is there any way to determine the orbital velocity of a point around another stationary point, if I don't know the mass of either of the points but know the force that gravity exerts and the distance ...
2
votes
2answers
485 views
Why is the center-of-mass of 2 bodies at the focus of their elliptical orbits?
Why is the center-of-mass of 2 bodies (which interact only via Newtonian gravity) located at a focus of each of the elliptical orbits?
I know that when there are no external forces, the center of ...
19
votes
1answer
705 views
Why does it take so long to get to the ISS?
I don't understand why when first launched Space X's Dragon capsule had to orbit the Earth many times in order to match up with the ISS? Was this purely to match it's speed, or to get closer (as in ...
1
vote
0answers
367 views
Calculating semi-major axis of binary stars from velocity, position and mass
I'm trying to calculate the 'instantaneous' semi-major axis of a binary system with two equal (known) mass stars for an $N$-body simulation. I know their velocities and positions at a given time, but ...
0
votes
1answer
110 views
How to find the orbit of a moving point object given 3 past passing positions?
How do I find the orbit of a moving point object given 3 past passing positions and the tangents at these passing positions, and given that the orbit is known to be an ellipse?
2
votes
3answers
657 views
Initial vs Constant Orbital Velocity
I am working on some basic physics simulation for a game and need to simulate gravity. I have a system working that is behaving more or less correctly so far, but I want to see if I can send a ...
6
votes
7answers
1k views
How does the earth move?
My son who is 5 years old is asking me a question about how the earth moves around the sun. What answer should I give him?
5
votes
11answers
1k views
Why do we say that the earth moves around the sun?
In history we are taught that the Catholic Church was wrong, because the Sun does not move around the Earth, instead the Earth moves around the Sun.
But then in physics we learn that movement is ...
13
votes
9answers
3k views
Why are orbits elliptical?
Almost all of the orbits of planets and other celestial bodies are elliptical, not circular.
Is this due to gravitational pull by other nearby massive bodies?
If this was the case a two body system ...
11
votes
3answers
2k views
Why are Saturn's rings so thin?
Take a look at this picture (from APOD http://apod.nasa.gov/apod/ap110308.html):
I presume that rocks within rings smash each other. Below the picture there is a note which says that Saturn's rings ...
0
votes
3answers
375 views
Missing something basic about simple orbital mechanics
I seem to be missing something basic.
I've been trying to get a simple orbital simulation working, and my two objects are Earth around the Sun.
My problem is this. I placed the Earth at 93M miles ...
4
votes
2answers
990 views
How to calculate a ballistic trajectory for a suborbital flight?
I'm trying to calculate the initial launch angles and velocity of a projectile (atmosphere's effects can be neglected), assuming that I know the lat/lon coordinates of both the launch and the ...
6
votes
10answers
956 views
Is the distance between the sun and the earth increasing?
M = mass of the sun
m = mass of the earth
r = distance between the earth and the sun
The sun is converting mass into energy by nuclear fusion.
$F = \frac{GMm}{r^2} = \frac{mv^2}{r} \rightarrow r ...
