What is the formula to find distance between two satellites in space?

[Sangam]

I want to write program to find the distance between two artificial satellites in space every 't' seconds. My initial inputs are initial velocity, masses , radii, position(x,y coordinates) of both the satellites. Then using Pythagoras theorem I can find the initial distance between the 2 satellites.

Then I calculate the force exerted by Satellite 1 on Satellite 2. Using Force/mass i need to find the acceleration and double integrate it to get distance between the 2 satellites. The 2 satellites are continuously revolving in 2 different circular orbit(such that they may collide). I have tried using

linear acceleration = Net force/massOfSat1;

angular acceleration = linear acceleration/radiusOfSat1;

This formula does not give a valid distance as the distance keeps on increasing but I expect that the distance increase and decrease as it is circular motion and the satellites can come near or go far as well . I feel that I am going wrong in using a suitable formula for acceleration.

Your help and suggestions will be greatly appreciated.

[SchweinAero]

1) What are your satellites orbiting around? If it's a third body such as a planet, you actually have two separate systems (planet+sat1) and (planet+sat2) and you can discard the satellites' masses.

2) Are you modelling inclination (that is, 3D)? Because if you aren't, then two satellites on different circular orbits can never collide.

[Sangam]

What are your satellites orbiting around? If it's a third body such as a planet, you actually have two separate systems (planet+sat1) and (planet+sat2) and you can discard the satellites' masses.

2) Are you modelling inclination (that is, 3D)? Because if you aren't, then two satellites on different circular orbits can never collide.

1)The satellites are revolving round the earth. I need to control the satellite 1 based on the force exerted on it by satellite 2 so that satellite 1 does not collide with satellite2.

2)The 2 satellites are in different orbits. same altitude but one orbit is vertical to the earth and other horizontal. so the satellites can collide at the intersection points.

[More Boosters]

Well if it's on 2D you can use the cosine theorem, using their distance to the center of the earth as the sides of the triangle. You'd need to have a polar coordinate system to base your angles on and then take a triangle from that with their relative angles, then calculate the longest side.

[K^2]

Sangam seems to be using Cartesian and simply integrating the forces. It kinds of sounds like he (or she) is forgetting to include force from the primary into the integration. Foce between two satellites alone would be insufficient to maintain orbit, so it would be consistent with distance constantly increasing.

More Boosters is right, though. Distance between two satellites in co-planar circular orbits is perfectly described by law of cosines, with period given by abs(T₁-T₂)/(T₁T₂)

[Sangam]

Sangam seems to be using Cartesian and simply integrating the forces. It kinds of sounds like he (or she) is forgetting to include force from the primary into the integration. Foce between two satellites alone would be insufficient to maintain orbit, so it would be consistent with distance constantly increasing.

More Boosters is right, though. Distance between two satellites in co-planar circular orbits is perfectly described by law of cosines, with period given by abs(T₁-T₂)/(T₁T₂)

Thank you for the reply. I am not able to understand the other forces to be included. "forgetting to include force from the primary into the integration". It would be of great help if you could elaborate on this.(as I know little physics and trying to get this working!!)

[YNM]

In the case of two satellites orbiting a major primary body, with mass of primary consist more than 95% of total mass, it's going to be better if you just consider it two separate limited two-body system (often called one-body system). Else, you'd have to fully simulate the forces and the movement - either it's going to be ridiculously heavy or ridiculously erroneous.

[K^2]

Thank you for the reply. I am not able to understand the other forces to be included. "forgetting to include force from the primary into the integration". It would be of great help if you could elaborate on this.(as I know little physics and trying to get this working!!)

Planet is massive. Artificial satellites are not. If you are considering two satellites orbiting a planet, forget about forces between satellites. The only forces that matter are between the planet (primary) and each of the satellites.

[Sangam]

Planet is massive. Artificial satellites are not. If you are considering two satellites orbiting a planet, forget about forces between satellites. The only forces that matter are between the planet (primary) and each of the satellites.

Ok. Thanks a lot.. Is there any other way to check collision of 2 satellites known their initial positions, masses and initial velocity? I am trying to simulate something similar to this url http://www.science-animations.com/support-files/gravitasieplaneteb.swf.

[John FX]

One thing real world satellites have to consider is relativity and time dilation due to their speed and being in a gravity well.

GPS sats were found to be 15 miles out of places in a very short time until those factors were taken into account.

Don`t know the maths for working it out though.

[Shpaget]

If you have two circular orbits with the same altitude, satellites will either collide on the first intersection or never.

They will collide only if the angles between the intersection and both satellites are the same.

[Sangam]

If you have two circular orbits with the same altitude, satellites will either collide on the first intersection or never.

They will collide only if the angles between the intersection and both satellites are the same.

Ok. Thank you for the reply. I am asuming that the circular orbits are perpendicular to each other(one vertical and other horizontal to earth). correct me if am wrong.. I thought that as the satellites revolve, there is change of velocity and there are chances of the 2 satellites coliding if not monitored.

[Cydonian Monk]

Are we talking about an Ideal system or a Real system? In the Ideal two satellites in identical orbits (regardless of inclination) will either collide on the first intersection or never. There is no orbital decay in an Ideal system.

In a Real system, you have to consider many other factors that can warp orbits: The Moon; The Sun; Jupiter; other massive bodies; atmospheric drag; rogue Chinese satellites; leaks; different paint jobs with different UV reflectivity; miniscule differences in mass because Bob in the clean room let a hair get inside one of the satellites; the list goes on. In a Real scenario, you might eventually have a collision, but only because one or both of the orbits has degraded to where the two orbiting bodies are no longer in identical (except inclined) orbits.

Edit: As to andwering the question of interaction between the two in an ideal system, it might not be measureable in a short duration simulation, but will be noticeable long-term (approaching infinity). I would expect libration or some form of oscillation, never a collision if their masses are identical. F=ma should still hold (and the formulas you derive from it), but you're getting into some vector math I've not touched in the last 15 years there.... (Not to mention that, depending on the ratio of the mass of your satellites compared to the mass of the Earth, you're talking about levels of precision that may not be possible with standard tools. Very, very, infinitesimally small numbers for normal satellites.)

Edited September 14, 2015 by Cydonian Monk

[Sangam]

Are we talking about an Ideal system or a Real system? In the Ideal two satellites in identical orbits (regardless of inclination) will either collide on the first intersection or never. There is no orbital decay in an Ideal system.

In a Real system, you have to consider many other factors that can warp orbits: The Moon; The Sun; Jupiter; other massive bodies; atmospheric drag; rogue Chinese satellites; leaks; different paint jobs with different UV reflectivity; miniscule differences in mass because Bob in the clean room let a hair get inside one of the satellites; the list goes on. In a Real scenario, you might eventually have a collision, but only because one or both of the orbits has degraded to where the two orbiting bodies are no longer in identical (except inclined) orbits.

Edit: As to andwering the question of interaction between the two in an ideal system, it might not be measureable in a short duration simulation, but will be noticeable long-term (approaching infinity). I would expect libration or some form of oscillation, never a collision if their masses are identical. F=ma should still hold (and the formulas you derive from it), but you're getting into some vector math I've not touched in the last 15 years there.... (Not to mention that, depending on the ratio of the mass of your satellites compared to the mass of the Earth, you're talking about levels of precision that may not be possible with standard tools. Very, very, infinitesimally small numbers for normal satellites.)

Thank you for the nice explanation. I am considering a real system. I want to develop a simple basic simulator similar to this url http://www.science-animations.com/su...ieplaneteb.swf. That is, monitoring a satellite to avoid collision with nearby satellites/debris using basic physics formula.

What way can this be handled such that it looks realistic(using physics formula) but need not be accurate?

[Shpaget]

You want this for real satellites?

That is going to be an issue. To calculate the minimum distance two satellites will pass by each other you need very precise data. Where do you plan on getting it?

Read up on this collision.

https://en.wikipedia.org/wiki/2009_satellite_collision

A dedicated satellite tracking and close approach alert software miscalculated that event.

There is a saying "garbage in, garbage out", meaning if you input wrong or inaccurate data into your algorithm, you can not expect to get a correct answer.

[Sangam]

You want this for real satellites?

That is going to be an issue. To calculate the minimum distance two satellites will pass by each other you need very precise data. Where do you plan on getting it?

Read up on this collision.

https://en.wikipedia.org/wiki/2009_satellite_collision

A dedicated satellite tracking and close approach alert software miscalculated that event.

There is a saying "garbage in, garbage out", meaning if you input wrong or inaccurate data into your algorithm, you can not expect to get a correct answer.

I am not doing it for real satellites. Just a simulation.. But for simulation i need to get the circular motion and possible collision in animation view. Thats the reason i am using formulas. for example in http://www.science-animations.com/support-files/gravitasieplaneteb.swf they have done a simulation. it is not for real satellites but it follows basic physics rules(formulas)