Orbital Mechanics Questions; Help

[Daniel8520]

Hey guys, understand this is a bit of an ask but I've come to the end of my tether with trying to calculate these. 

If any of you are nerdy enough to give these a go I'd greatly appreciate it. 

http://prntscr.com/d52ktz?

[Gaarst]

Nice try, but we're not doing your homework.

[Daniel8520]

I'll accept formulae, book suggestions and youtube tutorials people know of too.  

[p1t1o]

20 minutes ago, Daniel8520 said:

I'll accept formulae, book suggestions and youtube tutorials people know of too.  

Simple. Google every question.

Google "L4 lagrange" to find out the relationship between earths orbital radius and the radius of the L4 point.

Google "orbital velocity calculator" and find an online calculator that will give you orbital velocities based on masses and altitudes.

Google any variable to find its relationship to known quantities.

Catch my drift?

 

Hint: playing KSP will help immensely in the understanding of all of these variables

Edited November 9, 2016 by p1t1o

[Red Iron Crown]

I can help a bit (I think, the little orbital mech I have is Keplerian rather than n-body):

1. Is the sun mass times G.
2. Not sure, haven't done LaGrange point radii before.
3. Will be the L4 orbit circumference divided by Earth's orbital period.
4. Is a unit conversion of a given in the problem (a_x) from AU to m.
5. Can be calculated using the Vis Viva equation.
6. Is the sum of the science station radius and object radius divided by two.
7. Is twice the answer to 6.
8. Is calculated as negative gravitational parameter divided by twice the semi major axis of the transfer orbit.
9. Vis-viva again.
10. Answer to 9 minus the answer to 3. 
11. I've forgotten angular momentum calcs, sorry.
12. Eccentricity has some calcs here, the e=f/a definition is most useful here (recall that the sun will be at one of the foci of the ellipse)
13. Vis-viva once more.
14. Not sure on this one.

[p1t1o]

58 minutes ago, Red Iron Crown said:

I can help a bit (I think, the little orbital mech I have is Keplerian rather than n-body):

1. Is the sun mass times G.
2. Not sure, haven't done LaGrange point radii before.
3. Will be the L4 orbit circumference divided by Earth's orbital period.
4. Is a unit conversion of a given in the problem (a_x) from AU to m.
5. Can be calculated using the Vis Viva equation.
6. Is the sum of the science station radius and object radius divided by two.
7. Is twice the answer to 6.
8. Is calculated as negative gravitational parameter divided by twice the semi major axis of the transfer orbit.
9. Vis-viva again.
10. Answer to 9 minus the answer to 3. 
11. I've forgotten angular momentum calcs, sorry.
12. Eccentricity has some calcs here, the e=f/a definition is most useful here (recall that the sun will be at one of the foci of the ellipse)
13. Vis-viva once more.
14. Not sure on this one.

I thought #14 was a trick question with the answer being zero - both orbits are stated as co-planar, it is stated that the probe cannot be launched into a different elevation than the launching ship and no inclinations are given for any orbit or object...

[Red Iron Crown]

2 minutes ago, p1t1o said:

I thought #14 was a trick question with the answer being zero - both orbits are stated as co-planar, it is stated that the probe cannot be launched into a different elevation than the launching ship and no inclinations are given for any orbit or object...

The high energy transfer will be intercepting at a point other than its apoapsis, I took this angle to mean the difference between the probe's velocity vector and the object's.

[p1t1o]

23 minutes ago, Red Iron Crown said:

The high energy transfer will be intercepting at a point other than its apoapsis, I took this angle to mean the difference between the probe's velocity vector and the object's.

I assumed that "elevation" references angle to the ecliptic, now Im not sure.

[YNM]

There's actually a bit of flaw in the question regarding fast transfer orbit : generally speaking there'd only be a range of possible orbits and not a fixed one. So I guess it's asking about the minimum eccentricity orbit.