HELP very satellite problem.

[thebomb]

HELP! very urgent! satellite problem.

A 400 kg satellite is going to collide with a smaller 100 kg satellite traveling in the same
orbit but in the opposite direction. Knowing the construction of the two satellites you expect they will become enmeshed into a single piece of space junk. Determine whether the space junk will continue to orbit or crash into Earth.

I am not sure at all what to do with this problem. Any kind of help would be appreciated. Thanks!

 

[ehild]

For simplicity, assume that the orbit is circular, with radius R. What is the speed of the satellite? Does it depend on mass? What is the total energy of a satellite of mass m and traveling along an orbit of radius R?
If the satellites collide and become a single piece, is the speed of this body the same, higher or less than the speed of the original satellites? What is the total energy? What should be the total energy of the junk if it traveled further along the same orbit?

ehild

 

[thebomb]

Thanks! that helps. I will work on it!

 

[masterice]

can anyone help outline this problem? I am not sure where to begin other than the momentum equation. any help is appreciated!

 

[masterice]

bueller? bueller?

 

[thebomb]

So I worked on the problem. Sof far I got...

(400 +100)v = 400v₁ + (100(-v₂))

v_final = 3/5 v_initial

not sure, what to do now...how to figure out the if the 'space junk' is going to stay in orbit or collide with earth?

thanks!

 

[ehild]

What is the force that keeps a satellite on orbit? What force is needed to keep a body on circular track?

ehild

 

[thebomb]

gravitational force!
what equation do I need to use, i am not sure. I kinda need this within like an 40 minutes lol

Thanks for all the help again!

 

[Borek]

Do you know what minimum speed is necessary to put satellite on orbit? Do you know what escape velocity is? Do you know how these are related?

 

[Stonebridge]

The centripetal force on a mass M in orbit at height R is (Mv^2)/R (v is orbital speed)
This force is provided by the Earth's gravitational field. Let's say this has field strength g at the distance R (not same value as on the surface, by the way)
Centripetal force = Mg
Equate the two and rearrange to get a value for R for a given v
Does the value of R depend on v?
If v has changed as a result of the collision, can the junk stay in orbit at the same height?

 

[Drill]

A 400 kg satellite is going to collide with a smaller 100 kg

From this given information, you don't need to know the value of R , since it is equal for both sats , but you can find the relative speeds
v1 = av2 : where a is constant

 

[Borek]

OK, enough time has passed and I think we can get back to the question, as now even giving the final answer will not help the OP

I decided to get back as solving the problem - and browsing wiki articles - I have found an interesting difference in terminology used in English and Polish description of the orbital speeds.

In Poland we use something called "cosmic speeds". Let's assume we have a spherical planet of mass M and radius R. 1^st CS is the one needed for the object thrown horizontally to never fall back on the planet surface. That is

$$v_I = \sqrt{\frac {GM} {R}}$$

2^nd CS is just the escape velocity

$$v_{II} = \sqrt{\frac {2GM} {R}}$$

3^rd CS is the escape velocity for the Solar system, 4^th CS is the escape velocity for our Galaxy.

These definitions make the question relatively easy. Initial v of the satellites was below escape velocity (that is, below 2^nd CS). After collision their speed is below 3/5 v - and as difference between 1^st an 2^nd CS is $\sqrt 2$ after collision satellites must be slower than 1^st CS - so they have to fall on Earth.

Sure, the question can be solved in many ways and there is no need to use 1^st CS idea. However, that was the approach I was aiming at in my previous post - but after browsing wikipedia I have realized that what I wrote can be incomprehensible.

 

[ehild]

A 400 kg satellite is going to collide with a smaller 100 kg satellite traveling in the same
orbit but in the opposite direction. Knowing the construction of the two satellites you expect they will become enmeshed into a single piece of space junk. Determine whether the space junk will continue to orbit or crash into Earth.

This is really an interesting problem. Although the space junk will not stay on the original orbit, it will not fall straight towards the Earth and crash into it, as it has non-zero angular momentum that keeps it on some elliptical orbit. But the crash can happen later, if the nearest point of the orbit is closer to the centre of Earth than its radius. This closest distance can be determined from conservation of energy and angular momentum, and it is proportional to the original radius.

ehild