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1answer
64 views

Two-body problem - point of closest approach

I am reading through an exercise : One of the hints to solve this problem is that at the point of closest approach the comet's velocity must be tangential only, why is this the case ?
1
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1answer
69 views

Two black holes colliding (classical mechanics)

I had this question come up in my exam where two identical black holes are in orbit around each other. There is a loss of energy via gravitational waves : $$\frac{d E}{d t} = kr^4\omega^6$$ where $k$ ...
-1
votes
1answer
71 views

Barycentre of two planets and calculating velocity shift

I find my self puzzled by this question, and I cant see anything wrong with my derivation, which leads me to believe that there is something I am missing within how the velocity shift is calculated. I ...
-2
votes
1answer
48 views

Spirals in newtonian celestial mechanics?

I know Kepler's laws, Newton's laws, and that conic sections are the trajectories of noncolliding two point masses. But I wonder about a point mass A eventually colliding with point mass B. In ...
0
votes
1answer
54 views

Is the speed of an orbiting object at a given distance enough to uniquely classify an orbit's eccentricity?

As in the title, I am having trouble with part ii and iii of the linked image. So far i have found the semi-major axis and the period of the orbit both using the vis-viva equation along with proving ...
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votes
1answer
328 views

Which Kepler laws might change with the Universal Gravitational Constant?

I was recently asked the following question: Which of the Kepler Laws change if the Universal Constant Of Gravitation is changed? And why? I list the 3 laws of Kepler below: The Law of Orbits: ...
-1
votes
1answer
255 views

Speed at the perihelion [closed]

Hale Bopp has a period of 2400 days, with a mean distance from the sun at 174 AU and 1AU away in perihelion and 357 AU away in aphelion, what is its speed at the perihelion? what formulas do you need ...
1
vote
1answer
50 views

How can I obtain the position of the Earth on the orbit for given date?

I would like to be able calculate (or at least download some time-series data of) the position of the Earth on it's orbit at given date. For my purposes, it would be sufficient to account for the ...
0
votes
1answer
604 views

How to calculate a planet's tangential velocity moving in an elliptic orbit? [duplicate]

Consider a planet of mass $m$ moving around the Sun of mass $M$ in a circular orbit of radius $r$. By equating the centripetal force to $\frac{mv^2}{r}$ to gravitational attraction $\frac{GMm}{r^2}$, ...
4
votes
1answer
250 views

How are the Lagrange points determined?

According to Hyper Physics, there are 5 equilibrium, or Lagrange points of the Earth-Moon system and only 2 of them are said to represent stable equilibrium points. This made me think if there is an ...
0
votes
2answers
330 views

Third law of Kepler [closed]

I can not find any solution to this exercise on the internet. Calculate the mean radius of the orbit of a fictitious planet X, expressed in kilometers and UA, so that its orbital period is 1.9x10 ...
-2
votes
2answers
272 views

How did people get ellipses of Newton's equations of motion and gravitation? [duplicate]

It has become somewhat general knowledge that from Newton's laws of motion and his law of universal gravitation it is possible to verify that the trajectories of the planets are ellipses, i remember ...
1
vote
1answer
70 views

What are the gravitational implications of a planet orbiting a star perpendicular to the star's axis of rotation?

I just read about the planet KELT-9b, and one thing which stuck out to me was the fact that this planet orbits this star parallel to the star's axis of rotation (the article says "perpendicular", but ...
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votes
1answer
88 views

Problem: Spectroscopy of a binary system

The Problem is: For a binary system (2 Stars) with Orbital Period of $P =4.822 days = 416620.8 second$ and inclination $i=90$ and with speeds very less than $3 .10^8 m/s$. Their orbital planes around ...
1
vote
1answer
197 views

The mass and separation of binary system with only information about one star [closed]

If we can observe that a star and an unmeasurable planet are in circular orbit around a common center of mass. If we know the speed of the star to be $100\,m/s$, the mass of the star to be $2 \cdot 10^...
2
votes
1answer
3k views

How to derive inverse square relation in Newton's Law of Gravitation from Kepler's laws?

I read Feynman's Lost lecture a while ago. In that spirit, I'm trying to do a more simplified version of coming up with the inverse square relation. Using Kepler's 2nd, $ A_1 = \frac{1}{2}r_1^2\...
0
votes
2answers
98 views

Angular momentum for planet is constant [closed]

In this excersie we look at the system of the dwarf star Gliese 536. Gliese 536 is 10 Parsec away and has half the mass of the sun. (I guess, they mean our sun). There are hints, that there a so ...
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1answer
113 views

Mass And Gravity (Gravity between Moon and Earth) [closed]

Well I'm still a beginner at the gravity between huge masses ... and the gravity of masses So what i have learned for now is Kepler's 3 laws , and the equations that i have learned are these $${T^...
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votes
1answer
3k views

If two stars of mass $M$ and $2M$ move about their common centre of mass, then they have same angular velocity [duplicate]

Two stars of masses $M$ and $2M$ move in circular motion about their common centre of mass. Which of the following statements is true? A. Both stars move with the same radius. B. Both ...
0
votes
1answer
850 views

Calculating Centripetal Acceleration of Sun about Galaxy [closed]

This is a question from my Mechanics book: Calculate the centripetal acceleration relative to the acceleration due to gravity of: c) the Sun in its rotation about the center of the galaxy (the ...
2
votes
1answer
519 views

Form of acceleration for motion in an ellipse [closed]

I came across the following question: The coordinates of a particle moving in a plane are given by $x(t)=a\cos(pt)$ and $y(t)=b\sin(pt)$, where $a>b$ and $a$ and $b$ are positive constants of ...
1
vote
1answer
415 views

Orbital mechanics : finding eccentricity and semi-major axis

i have a problem. we have a elliptical orbit. Velocities of perigee point and apogee point is given. I have to find the eccentricity and semi major axis. I found eccentricty with conservation of ...
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vote
3answers
239 views

Would it be possible to pull Mars and Earth closer each other?

The burden of travelling between Mars and Earth comes from the distance. If the planets were closer, life could spread to Mars more easily, ensuring the survival of the intelligent lifeforms. What ...
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vote
3answers
650 views

How to calculate transit time for a specific section of an orbit?

I've searched high and low and I haven't been able to find a formula for this. I'm trying to calculate the time it will take to transit through a defined arc length of an elliptical orbit, whose ...
1
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0answers
142 views

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 ...
4
votes
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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0answers
28 views

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/...
1
vote
3answers
751 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 ...
0
votes
2answers
390 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. ...
0
votes
1answer
56 views

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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votes
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.
3
votes
3answers
782 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 ...
1
vote
1answer
247 views

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 ...
1
vote
1answer
437 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
1k views

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 = \...
3
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3answers
7k views

Gravitational Null Point between Earth and Moon

I need help finding the gravitational null point point between the Earth and the Moon, the point beyond which you start falling towards Moon. I am having difficulty in taking into account the orbiting ...
0
votes
1answer
151 views

Is Voyager 2 slowing down?

Voyager 2 will leave the dominating gravitational influence of the Sun for a region where other stars have comparable influence on the craft. By the time it gets that far away, how much will it have ...
0
votes
1answer
92 views

Inverse square law in one dimension [closed]

A point of mass $m$ is at rest at position $b$ and subjected to a force $f(x) = -k x^2$. We are to show that the time required for the particle to reach the origin is $$ \pi \left( \frac{m b^3}{8 k}...
0
votes
2answers
136 views

Deriving the velocity for circular orbital motion

I'm trying to derive the (circular) orbital velocity for a given height from the center of mass of a body, like Earth. First I used the equation of the circle $x^2 + y^2 = r^2$ to get $y = \pm \sqrt{...
1
vote
2answers
189 views

Gravity effect on moving bodies

If we imagine two suns of equal mass, and a small object in their combined center of gravity, which is not moving, it will stay there forever. If the object is displaced a little bit towards one of ...
3
votes
2answers
1k views

How to solve the inverse square law equation of motion

From $$m\boldsymbol{\ddot{r}}=\boldsymbol{\hat{r}} f(r)$$ I can get $$r''-r \theta '^2=-\frac{k}{m r^2}$$ $$2 r' \theta '+r \theta ''=0$$ Now it seems that all the books tells me the method to solve ...
2
votes
0answers
27 views

Orbits of binary pulsars. How to calculate? [duplicate]

If I may ask: How can the orbits of binary pulsar stars, with similar mass, be calculated from Kepler's laws? Considering that both large central masses must be located at their mutual foci. Also, how ...
1
vote
1answer
106 views

Create a star system fit to conic equation

For simulation purposes, I'm trying to create a binary star system. If I have a conic equation such as $ax^2 + by^2 = c$, and the masses of two stars, how would I find the $x$- and $y$- velocity ...
0
votes
1answer
102 views

Kepler's laws: show the planet always stays in the same plane?

I know angular momentum $L=q \times p$ is conserved, where $p=L_{\dot q}$ is linear momentum. How to apply this to a planet orbiting the star, described by the position vector $q$ relative to the star....
2
votes
1answer
297 views

Solving the Kepler problem

I'm trying to solve the Kepler problem using the Lagrangian, $$L = \frac{1}{2} m (\dot{r}^2 + r^2 \dot{\phi}^2) - U(r) $$ which after quite a bit of fiddling with, by noting that the angular ...
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vote
2answers
1k views

Orbital mechanics problem

Here is a problem from the 2009 $F=ma$ contest on orbital mechanics: Two stars, one of mass $M$, the other of mass $3M$, orbit their common center of mass. When the stars are collinear with the ...
2
votes
3answers
6k views

Calculating the velocity of an elliptical orbit

I need an explanation as to why my solution to this problem doesn't work (please do not give me an answer or tell me exactly how to do it as this is a homework question that I need to do myself, hints ...
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vote
2answers
129 views

What is the zero of potential?

A satellite of mass $m$ is travelling at a speed $v_0$ in a circular orbit of radius $r_0$ around a fixed mass at $O$. Taking the zero of potential at $r=\infty$, show that the total energy of the ...
40
votes
8answers
8k views

“Falling upward” - how far you have to be from Earth to start falling to the Moon?

Talking about gravity with my 9 y/o she asked when do we start "falling upward" to the Moon. What is the distance at which the Moon's gravitational attraction is higher than that of the Earth and thus ...
2
votes
0answers
521 views

How to calculate orbital eccentricity from the ratio of satellites' velocities?

I have a problem with working out how to calculate the orbital eccentricity from the ratio of two satellites' linear velocities. We know that two satellites encircles the Earth in two elliptical ...