# Orbit Definition and 106 Discussions

In physics, an orbit is the gravitationally curved trajectory of an object, such as the trajectory of a planet around a star or a natural satellite around a planet. Normally, orbit refers to a regularly repeating trajectory, although it may also refer to a non-repeating trajectory. To a close approximation, planets and satellites follow elliptic orbits, with the center of mass being orbited at a focal point of the ellipse, as described by Kepler's laws of planetary motion.
For most situations, orbital motion is adequately approximated by Newtonian mechanics, which explains gravity as a force obeying an inverse-square law. However, Albert Einstein's general theory of relativity, which accounts for gravity as due to curvature of spacetime, with orbits following geodesics, provides a more accurate calculation and understanding of the exact mechanics of orbital motion.

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1. ### I Change in orbit when mass is doubled

A satellite is orbiting a planet in a circular orbit. The planet's mass doubles instantly. What happens to the orbit of the satellite? I think it would move to an elliptical orbit with major axis equal to the old radius and a minor axis equal to either 1/2 or sqrt(2)/2 times the old radius. I'm...
2. ### I Modeling the Earth and Sun (2 body orbits) using general relativity?

Modeling the time evolution of the sun and earth orbiting each other using ##F = \frac{GMm}{r^2}## is straightforward. However, it appears that modeling the time evolution of the same 2 body system using general relativity seems to be a hard/intractable problem? There was in depth discussion by...
3. ### I Database of binary star data info within 10 PC of Earth

I'm looking for a database of binary stars within 10 PC of Earth, including information such as eccentricity of orbits, their distance from one another, etc. I'm hoping to find a list with this information, or just a collection of pages with this information. I've tried Simbad but I can't find...
4. ### I Is the eccentricity of the lunar orbit constant?

The wikipedia article on Lunar distance contains a confusing graph. The graph seems to suggest that the eccentricity of the lunar orbit is maximal in january and ~july, and minimal in april and ~october. I think the eccentricity should be constant. Is wikipedia right or wrong, or is there some...
5. ### From circular orbit to elliptical orbit

Problem: a particle of mass m is in a circular orbit around a planet at a distance R from the center. The planet mass is M and it's radius is R_0. What is the tangential impulse that will cause the particle to brush against the back of the planet? Describe the orbit. The attempt at solution...
6. ### B Could satellite be geo-stationary away from equatorial plane?

I hope this is okay to ask here. I'm working on a sci-fi short story, and for the purposes of the story I want to have a small ship that maintains its position over a specific location on the Earth's surface. Originally, I thought this would be easy. After all, that's what geostationary...
7. ### Conservation of the Laplace-Runge-Lenz vector in a Central Field

I actually have worked through the solution just fine by taking the derivative of \vec{L}: \frac{d \vec{L}}{dt} = \dot{\vec{v}} \times \vec{M} - \alpha \left(\frac{\vec{v}}{r} - \frac{\left(\vec{v} \cdot \vec{r}\right)\vec{r}}{r^{3}}\right) I permuted the double cross product: \dot{\vec{v}}...
8. ### Stargazing Does an Analemma visualize the Earth's actual orbit around the sun?

An Analemma is the shape that arises from taking a picture of the sun everyday at the same time of the day. This shape also have depth to it since Earth's orbit is elliptical, showing what looks like an wobbly orbit. Isn't this the "real" orbit of Earth around the sun?
9. ### Using Orbital Energy to Calculate Velocity

So what I did first was calculate the initial and final potential energies with Epi=-9.433*10^11 m and Epf = -1.503*10^12 m. Then I found change in potential energy, -5.597*10^11 m. Using this I determined the change in kinetic energy, 5.597*10^11. I then added this change to the initial...
10. ### Converting State Vectors to Keplerian Orbital Elements for Binary Objects

Homework Statement:: I'm working on a personal project to convert objects from a simulation using state vectors for position and velocity to Keplerian orbital elements (semimajor axis, eccentricity, argument of periapsis, etc.). However, the equations I am using do not calculate the...
11. ### I Can I calculate the relative position of a space object with respect to the Earth from this data?

Hello, i'm doing a project where the goal is to get the relative position of a space object to the earth, roughly. Basically, i want to say that this object is currently e.g. above New York. The data for any given space object that i have is (It's sourced from an NASA API). The specific...
12. ### Expressing Elliptic Orbitals As Speed Functions.

Hi everyone:) I have spend a couple of days trying to teach myself the math of orbital mechanics and have been able to generate a model of the orbital path of Haley's Comet, incorporating realistic distances and periods using Kepler's second law & ellipsoid functions. This is a GIF of the motion...
13. ### Orbit calculations in the solar system (journey to Mars)

I cannot understand the solution at https://www.aapt.org/physicsteam/2015/upload/E3-2-5-solutions.pdf, because the solution is terse and skip steps (at least i think so). I figured out that the name of this transfer is "Hohmann-Transfer Orbit". A detailed walkthrough would be appreciated. If I...
14. ### Orbital equations in polar coordinates

The equations of motion are: \ddot{r}-r{\dot{\theta}} ^{2} = -\frac{1}{r^{2}} for the radial acceleration and r\ddot{\theta} + 2\dot{r}\dot{\theta}= 0 for the transverse acceleration When I integrate these equations I get only circles. The energy of the system is constant and the angular...
15. ### Satellite Orbit Problems

I just have a question on the problem itself. If I am putting the satellite into orbit 450,000 m above the surface, then would r=6,371,000 m(earth's radius)+450,000 m? And what mass of Earth should I be using, in kg of course.
16. ### I Help With Simple Orbital Modeling

I have yet to decide on values for the mass of the fixed object, M, the mass of the moving celestial body, m, the initial velocity, v, and the distance between the two objects, r. I will most definitely decide on a larger mass M because I would like the celestial body to spiral in towards the...
17. ### Problem about orbital mechanics

I tried it, but I am not getting no of the given answers According to the statement, it is saying that 3 KE (in the orbit ) = ΔUg So, beeing R the radius of the Earth and R2 the radius of the orbit: 3 (1/2)(GMm/r2) = -GMm/r2 - (-GMm/R) Canceling out the GMm: (3/2)(1/r2)= (-1/r2) + (1/R)...
18. ### I Free orbit insertion

Good evening, This week I had a discussion/conversation with one of my coworkers about the posibility of a mass from outer spate that could start orbiting the earth. The issue is, I believe you cannot, whithout a proper change of energy (velocity) start orbiting a celestial body just by coming...
19. ### What is the period of this binary orbit?

Okay, so let's simplify things and look at the ideal case, where the 2 masses are the same. Well, this gives us a sine wave pattern to the orbital velocity. Consequently, the acceleration would follow a cosine wave since the derivative of velocity is acceleration and the derivative of sine is...
20. ### I Frozen orbits of the moon

Quick question for the people to better understand orbital mechanics. Due to large mass concentrations on the moon's surface, there are only four orbital inclinations that a satellite can be at to maintain an indefinite orbit: 27°, 50°, 76°, and 86°. My question is this: If a satellite was...
21. ### Effect of time dilation on a satellite

I've got the start of a plot forming in my mind, and I'm wondering if it's likely to be supported by physics at all. My basic understanding: when astronauts go to the International Space Station, due to the speed at which it is travelling, time passes ever-so-slightly slower for them. This...
22. ### Hohmann transfer orbits

Homework Statement Consider an elliptical orbit of a satellite (of mass m) around the Earth (of mass M >> m). The perigee is at ##r_A## and the apogee at ##r_B##, as measured from the centre of the Earth, itself located at one of the focal points of the ellipse (see Fig. 1). We work in an...
23. ### Why do we need the hyperbolic excess velocity?

$$V_{HE}=\sqrt{\frac{\mu}{a}}$$ What is the rationale for this formula when we can determine the change in velocity from Earth's orbit to transfer orbit using the vis-viva equation? Likewise, what is the use of defining the radius for the sphere of influence for interplanetary transfer...
24. ### I How would the DSG orbit the Moon?

Assuming it happens and that the Deep Space Gateway happens as a base for Moon landing and further exploration. What sort of orbit would it have in relation to this use? I have I-searched but not found any detail. Thanks.
25. ### How much work is done when a satellite is launched into orbit?

Homework Statement A Satellite is brought up into a geostationary orbit (altitude 35800km measured from the surface of the earth). Satellite weights 1000.0kg. How much work is required to bring satellite from a surface of the Earth to geostationary orbit? Homework Equations Newton's law of...
26. ### I Do trojan satellites follow migrating planets?

Some or all of the planets are thought to have migrated long ago under the gravitational influence of Jupiter. Would the trojan matter at their L4 and L5 points have followed during their migration to new orbits? In other words, while the L4 and L5 points are approaching or receding from the...
27. ### Planetary Motion: Orbit Transfers, Hohmann transfer

The thought of increasing a satellite's (for example) speed to allow it to transfer from a "higher energy" elliptical orbit to a "lower energy" circular orbit (in reference to the effective potential energy plot that arises after introducing the concept of an effective mass to simplify the...
28. ### I Question about orbits and Kepler's problem

I've been looking at the Kepler's problem, and it looks like your orbit (elliptic, parabolic or hyperbolic) are given in terms of energy and angular momentum. I was wondering: if I have a central attractive potential (such as the Sun) and a projectile starting from an infinite distance at a...
29. ### B Lowest possible altitude for a Satellite

What is the lowest altitude for a satellite to orbit?
30. ### I How many degrees / radians is one full orbit of the Earth?

One day consists of slightly more than 360° of rotation (360.9856°) on it's axis (due to Earth's orbit around the Sun). I imagine that one orbit is also either > or < 360° around the sun, relative to the motion of the sun around some object. Is this true, or is the orbit of the Earth...
31. ### 2-body problem solution

Homework Statement Two-body problem given as $$\ddot{\textbf{r}}+\frac{GM}{r^2}\frac{\textbf{r}}{r}=0$$ $$\textbf{h}=\textbf{r}\times\dot{\textbf{r}}$$ where the moment of the momentum vector mh Homework Equations The vector solution to the above equation may be obtained by first taking the...
32. ### How to get tangential velocity

I am in the process of making a program that visually shows an elliptical orbit over time. I wish to find the tangential velocity of the satellite in the elliptical orbit based on the variables that I know. Here is what I know: a) The angle relative to the right focus with 0 radians being the...
33. ### I Computational Hohmann Transfer on MapleSoft

Hi, I am trying to recreate an Interplanetary Hohmann transfer orbit from Earth to Mars similar to image A below (the red line). However, Earths orbit is not circular, It is more of an elliptical orbit rather than circular. I was able to successfully plot the orbits of both Earth and Mars...
34. ### B Orbit circularisation/insertion spreadsheet

I am trying to create a spreadsheet that will calculate: The minimum delta-v required to circularise the orbit of a projectile that has been fired horizontally from the Earths surface at a given velocity. Completely ignoring atmospheric drag. See the attached spreadsheet. The steps are...
35. ### Calculating orbits of planets in Solar System

Hi, I am about to write a simple application, simulating in 3D current location of the planets in Solar system. Honestly, I do not know even how to start. Can you please guide me where could I find some good information on planet orbits, current locations and how to make all of the calculations...
36. ### I "Unexpected" Symmetry in Elliptical Orbit

Hello everyone :) Not too long ago, I was thinking about planetary motion around a sun, both with circular orbits and elliptic orbits. However, when thinking a little longer about these two cases in a broader sense, I spotted a big difference which I found quite odd (assume purely classical...
37. ### Having trouble working out centripetal force?

Homework Statement The Russian Mir space station had a mass of 130 tonnes and orbited Earth at an altitude of 480km with an orbital speed of 7621.4m/s. The diameter of Earth is 12 760 km. a) What centripetal force was acting on it? b) Find the value of the acceleration due to...
38. ### I How can General Relativity explain the Moon drifting apart from Earth

According to various sources, the Moon is separating from Earth 4 cm every year. I’ve searched for the explanation and I’ve found the following: The friction the seas and oceans from the Earth make with it’s soil causes the Earth’s rotation to slow down. This causes the Moon to speed up...
39. ### I Changing the ISS's orbital inclination to match the Moon

What is the practical feasibility of changing the International Space Station's orbital inclination to match the orbit of the Moon? Major future missions beyond the Earth-Moon system (ie: space colonization) will likely require in-orbit assembly of components from multiple launches. And...
40. ### Use angular momentum to find the velocity (comet orbit)

Homework Statement A comet orbits the sun. It's position in polar coordinates is given by, $$r(\phi)=\frac{1.8r_0}{1+0.8\cos{\phi}},$$ where ##r_0## is the position at closest approach. Its velocity at this point is given by ##v_0##. Use the concept of angular momentum to find the following...
41. ### Doubling speed in circular orbit to attain elliptical orbit

Homework Statement A satellite is in a circular orbit (radius R) around a planet of mass M. To change the satellite's orbit the engines fire and its speed is suddenly doubled. The engines fire for a very short time. Determine the length of the semi-major axis of the new orbit. Homework...
42. ### Satellites and the Earth's Magnetic Field

So i was just wondering if a satellite's circuitry could be affected by the Earth's own magnetic field inducing a current, if it was moving through it quickly enough (the space station for example), and how it might mess with it? Also considering a satellite is a big hunk of metal, could passing...
43. ### How to calculate ambient temperature in space or in orbit?

How would I go about calculating the ambient temperature in low Earth orbit (LEO) at approximately 400 km? What equations should I be referencing to determine the temperature of sun light side and/or eclipse side? Thanks!
44. S

### Bohr orbit (extremely confused)

Homework Statement Calculate energy of electron in first excited state of hydrogen atom. Homework Equations n=2 when i use E=-13.6 (z/n)^2 and then use E=hc/lamda(wavelength) then wavelength is coming wrong The Attempt at a Solution the correct answer is 6.68 armstrong.
45. A

### Circular orbit - period

Homework Statement An object with mass m is attached to a string with initial length R, and moves on a frictionless table in a circular orbit with center C as shown in the figure. The string is also attached to the center, but its length is adjustable during the motion. The object initially...
46. P

### I Instability of a Rigid Untethered Ring Around a Planet

I had this discussion while driving home to California from a trip to Washington state with a friend. We were discussing the stability of a completely rigid, untethered, ring-structure around Earth, and I did not know how to explain to him that such a thing must be tethered by rigid towers lest...
47. ### Can you change a planet's orbit by reducing its velocity?

My question is, take Mars, say, and install a huge rocket engine on the ground pointing out the planet (obviously) and in the opposite direction of its velocity, so that if it is turned on, the planet is slowed. The rocket starts to work and Mars is slowed. If the loss of velocity goes little by...
48. ### B Inclinations of star orbits in the Milky Way

Do all stars orbit around the black hole in the same plane? Or some stars can have the same orbital radius but slightly different orbital inclinations?
49. ### I Scaling up a mass spectrometer

The essential question is can this tech be scaled up in the vacuum of space to add a substantial tangential acceleration to the orbital velocity vector of a piece of debris such as a speck of paint 1cm^2 in cross section. I am looking to deflect that speck of paint into a container or out of...
50. ### Satellite Motion

Homework Statement A satellite is in a circular orbit around an unknown planet. The satellite has a speed of 1.70 × 104 m/s, and the radius of the orbit is 5.25 × 106 m. A second satellite also has a circular orbit around this same planet. The orbit of this second satellite has a radius of...