Questions tagged [celestial-mechanics]

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Can a satellite be put into orbit such that it will always remain directly over a city? [duplicate]

Isn't it possible if we just set it high enough so that it's angular speed matches with the earth's? I think that the city must be on the equator to make this happen. Am I correct? Please can anyone ...
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Research groups in celestial mechanics [closed]

This Exchange may not be the right place to to ask this question, but I would like to know prominent research groups working in celestial mechanics. Although I'm interested in celestial mechanics, ...
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Books on Celestial Mechanics [duplicate]

My background is mathematics. I would like to study celestial (not classical) mechanics and looking for an appropriate book. I found that somebody has already asked a similar question "How to learn ...
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1answer
250 views

Can the constant $k$ from Kepler's third law be independent of the mass of the planet?

Consider Kepler's third law The square of the orbital period $\tau$ of a planet is directly proportional to the cube of the semi-major axis of its orbit $a$. $\frac{\tau^2}{a^3}=k$ The ...
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Semi-major axis , specific mechanical energy, its period and velocity at Apogee and Perigee and what the difference is [closed]

Hi im needing some help with two questions could you please show the formula and the way its solved?Thanks PS:Could you also explain what the difference of velocity and apogee and perigee? 1.)A ...
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1answer
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Motion under gravitational forces

In a system of particles, can a particle be considered to be attracted to the combined center of mass of the other particles if the Newton's universal law of gravitation is used (the inverse square ...
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5answers
608 views

How can escape velocity and gravitational potential be higher in weaker gravitational fields?

on Earth we have an escape velocity of about 11180 m/s and a gravitational field of g=9.81 m/s^2. It would seem obvious that the escape velocity was higher for stronger gravitational fields. Often it ...
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3answers
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Could the Earth-Moon rotation period equal one Earth year?

I just stumbled on this rather confused QA. The point seems to be if the Earth-Moon rotation period was identical to the Earth-year, then ... ... all three would stay in a line at all times. Could ...
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Orbital period of a satellite in Kerbal Space Program

Let me start off by saying I am really bad at maths and physics, but lately I have been trying to calculate the orbital period of a satellite I have put in orbit around a planet called Kerbin in a ...
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2answers
150 views

How has the world remained in balance?

In the center of our galaxy, there is a Supermassive black hole. We were told in early astronomy units of school that black holes are giant vacuums that will absorb/consume the area around it. My ...
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4answers
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Can the Earth leave orbit if the population of humans and other live forms increases?

I don't know a lot about physics, but this seemed like the correct place to ask my question. I apologize in advance if it is a ridiculous one. It's actually a two part question: If the population of ...
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0answers
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Topic on relativistic celestial mechanics [closed]

I have to do a small 10-15 minutes presentation about celestial mechanics, and I am searching for a topic. As a mathematician my background in physics is not very extensive, but I have some notions ...
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3answers
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Gravity effects when deleting stars or planets

In one of the latest SCIFI movies, they collect a star absorving it entirely in a kind of planet size gun/machine. As mass cannot disappear, I assume it was just concentrated inside their machine (...
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1answer
406 views

Relation between eccentric and true anomalies

If $v$ is the true anomaly and $E$ the eccentric anomaly, how can I show that $$\frac{dv}{dE}=\frac{b}{r}=\frac{\sin v}{\sin E}~?$$
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1answer
436 views

Why do the stars in a binary system, revolve diametrically opposite to each other?

I encountered this question, as I was reading up on Gravity. The author of my textbook says that the stars orbit a common centre which is their center of mass. I somehow think that this fact might ...
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0answers
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Laplace's method to determine orbits

I am trying to do the second problem by Laplace's method, it is in spanish but the only thing that matters are the asteroid's observations and the coordinates of Earth https://freeshell.de/~rgh/arch/...
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1answer
104 views

Can a planet's orbit around a star be simulated? [closed]

Say I know all parameters like density, size, rotational velocity of a planet, could I predict its orbit around a star where I also know parameters of it? I want to design a simple model of the solar ...
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3answers
760 views

How to predict the location of a planet at a given time? [closed]

I am trying to create a simple two-dimensional computer simulation of a planetary system. While I've been able to understand Kepler's Laws of Planetary Motion, I do not know enough about the formulas ...
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1answer
402 views

Gravitational potential of planets

How do you work out the gravitational potential of planets in the solar system? Do orbiting planets have gpe? And what would it be relative to? The equation I know for it is mgh. But what would the ...
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2answers
391 views

Orbital mechanics: will a satellite crash?

For a satellite given an initial speed and position above a planet, I'd like to know whether it will experience an elliptical, circular, parabolic or hyperbolic trajectory, or crash into the planet. ...
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1answer
97 views

The source of work by gravity force [duplicate]

I learn that any work needs a source of energy, the work of gravity force (like keeping the Moon in the orbit by the Earth gravity force) comes from where? Can we find any mass reduction (transform ...
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1answer
100 views

Testing the accuracy of a solar system simulation

I've written a java program to model the solar system, and I need to test its accuracy. What would be some good ways to do that? I've checked for conservation of energy and angular momentum. I'm using ...
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1answer
83 views

Orbital but stationary motion

Is there a place between the Moon and Earth where an object can rest freely and revolve with the Moon? What is that called?
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1answer
750 views

Angular Momentum and Kepler's Second Law

Let me preface by saying that I get the gist of the conservation of angular momentum, at least qualitatively. To better illustrate my question, I will consider the case of a planet orbiting a star. ...
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2answers
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Remotely finding the mass of a satellite

I have a question similar to one I've asked earlier (Calculating mass of an orbiting body with force and acceleration), but without a specific formula... How can you find the mass of a satellite body ...
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2answers
347 views

No energy consumed in planetary motion? [closed]

Most of the orbits of planet are elliptical. How is it then that no energy is consumed?
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3answers
379 views

Elliptical orbit changing as a star's mass increases

I'm studying Kepler's Laws, specifically the orbit of the Earth around the Sun. I know that if the Earth was more massive, the orbit would not be significantly affected. If the Sun was more massive, I ...
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2answers
348 views

Maths of elliptical orbits

I have a simulation of the solar system that currently gives me circular orbits. I'm not 100% sure where I've limited my simulation to this, but probably it starts when I use $$v=\frac{2 \pi r}{T}$$ ...
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1answer
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Find the velocity of three planets about their centre of mass

Just wanted to check if I've done this right, because it isn't working. Mercury: mass $$3.285 \times 10^23\ \mathrm{kg}$$ position: $57,910,000,000\ \mathrm{m}$ from sun Earth: mass $$5.972 \times ...
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0answers
454 views

3-body system centre of mass

I have a three body system of point masses that represent mercury, earth and the sun. I want them to orbit about a common centre of mass, but I think the centre of mass will move. I need the centre of ...
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3answers
317 views

Calculating speed of satellite in vacuum?

Satellite speed is $35\ \mathrm{km/s}$ after burn for $500\ \mathrm{ sec}$ and after some days or months this speed is reduced automatically $34$, $33$, $32$ respectively. Questions: How the ...
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3answers
4k views

What would become of the earth's orbit if half of the sun's mass were suddenly to disappear? [closed]

I shall assume that the sun is at rest, so before the half mass disappear, the orbit of earth is an ellipse.
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2answers
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Why Sun is not able to attract mercury closer?

As sun have a huge amount of attraction pull force , why its not able to pull tiny mercury? Is the whole solar system works in a push and pull network? Why bigger planets like earth, Saturn and ...
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1answer
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What are the orbits of satellites; circular or elliptical? [duplicate]

What are the orbits of satellites; circular or elliptical?
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Questions related to Lagrange points

For me, these two graphs are inherently different. The first graph portrays a "forbidden region" which is completely filled in, the other shows a collection of curves. Whats the difference here? Whats ...
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1answer
521 views

Minimum energy required to remove the satellite from its orbit to infinity?

My book says that minimum energy required to remove the satellite from its orbit is equal to its total energy (K.E+P.E). But shouldn't it equal to only the potential energy difference of satellite in ...
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2answers
2k views

Does the International Space Station always travels in the same path?

From the 3d visualization http://www.satflare.com/track.asp?q=25544#TOP (the right image with the red line indication the path of the ISS) it looks like always the ISS takes the same path. Is it the ...
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0answers
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What is exactly gravitational potential energy and explain P.E. $= -GMm/r$? [duplicate]

I was studying gravity and I came to know about $P.E.= -\frac{GMm}{r}$ which is derived by $GMm(\frac{1}{\infty} - \frac{1}{r})$ which the work done by the body to displace it from infinity to $r$. ...
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3answers
785 views

What is the distance between two objects in space as a function of time, considering only the force of gravity? [duplicate]

What is the distance between two objects in space as a function of time, considering only the force of gravity? To be specific, there are no other objects to be considered and the objects in question ...
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2answers
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Why does Goldstein's derivation of orbits from Newton's law not yield the orbit consisting of symmetric oscillation along a line thru center of Sun?

Why does Goldstein's derivation of Keplerian orbits from Newton's law of gravity not yield the orbit consisting of symmetric oscillation along a line passing thru the center of the Sun? The fact that ...
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0answers
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Can we use the planets and Sun to fling out a craft at relativistic speeds? [duplicate]

E.g. The Voyager crafts took various assists from the planets. Sun being much more massive, wouldn't a spacecraft gain much more energy from such a flyby on the correct trajectory? If so then what ...
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3answers
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(How) can we determine mid-point on Earth's orbit?

The eccentricity of earth's orbit varies with time, but at present time its eccentricity is roughly mean e (0.0167). The position of equinoxes is far more complicated than I thought and it is not at ...
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1answer
158 views

Acceleration in an elliptical binary system

So I'm having a bit of a problem dealing with binary systems. I'm looking at acceleration in a stellar system and am not sure where to begin. Assuming both stars are of equal masses, they'd be equal-...
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2answers
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Why does using the modified Kepler's 3rd law and using the gravitational parameter yields different results?

$p^2=\frac{2\pi a^3}{\mu}$ ($p$ is the orbital period in seconds) gives slightly different result from $p^2=\frac{4\pi^2}{GM_1}a^3$.
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1answer
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Units in gravitational N-body simulations

I use a code in Python to simulate a binary system interacting through gravity. You can find it here; The code works fine. I am however having problems with the units of length and velocity. I ...
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3answers
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What happens if you slow down a moon?

Let's say you'd put a whooping big rocket engine on the surface of the moon, and slow down its orbital velocity. Not to a complete stop, mind you. Just a bit slower than it was going before (a couple ...
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1answer
440 views

How do I calculate the effect of a prograde, retrograde, radial and anti-radial burn on the orbital elements of a two-dimensional orbit?

My relevant knowledge: This question works in two dimensions, with a two-body problem (see bottom for context). To my understanding, a two-dimensional orbit has the following orbital elements (3D ...
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2answers
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Calculate the Earth’s velocity in its orbit (assumed to be circular) around the Sun [closed]

Data: GM of the Sun: $\text{GM} = 1.327 \times 10^{20} \;\mathrm{m^3 s^{-2}}$ Radius of the Earth’s orbit: $r_{Earth} = 1.496 \times 10^{11} \;\mathrm{m}$ Orbital period of a planet in seconds: $T = \...
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1answer
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Can a natural satellite have a synchronous orbit?

I was thinking about space-elevators and large masses being put into geosynchronous orbit, when I considered the possibility of a natural satellite being in a synchronous orbit. I did a little digging ...