What Are Orbital Vectors and How Do I Calculate Them?

[Solistics]

I'm fairly new to astrophysics, but I'm genuienly interested on knowing how to calculate orbits. I've been trying to do so on my own but I just find myself extremely frustrated. I'm trying to figure out what orbital vectors are and how i can calculate them using known orbital parameters. If i can get over this hurdle i should be all set.

thanks.

P.S. any sites that are helpful (lists of equations, sources etc.) would be appreciated.

 

[Stratosphere]

Although I have never attempted to calculate the orbits I would say it would be it would

be a VERY tedious job to do. I would also think that you would need calculus to be able

to calculate accurately.

 

[Solistics]

ok, I'm having difficulties in finding the velocity of the moon from a certain distance from the earth,

the equation I'm using is the vis-viva equation:

v=$$\sqrt({}\mu*(2/r-1/a))$$

$$\mu=GM$$=3.98694E+14

r=radial distance from focus to orbiting object=369397 km (periapsis of moon)
a=semi-major axis=3847487 km

the end value that i got is 45332.04235 m/s !
somethings not right!

 

[D H]

Try as I might I cannot reproduce your result. You are probably doing multiple things wrong.

1. The equation is
   $$v=\sqrt{\mu\left(\frac 2 r - \frac 1 a\right)}$$
   Did you take the square root of the whole thing?
   
   2. μ_E is 398,600.442 km³/s², or 3.98600442×10¹⁴ m³/s².
   A couple of things to note:
   • This value is known very precisely. The error in μ_E is very, very small compared to the error in G. (Almost 9 significant digits versus 4 or so.)
   • UNITS, UNITS, UNITS. You have a number, no units. Lack of attention to units is most likely one of the sources of your error.
2. The Moon's semimajor axis is 384,399 km, not 3847487 km. This is almost certainly another source of your error.

 

[Solistics]

ok, i tried all you suggested however i still have a number of .2454 km/s or 245.5 m/s. I'm not sure this is right because of these values: http://nssdc.gsfc.nasa.gov/planetary/factsheet/moonfact.html"
it says that min. orbital speed is 0.964 km/s. I'm not sure what to think now.

 

[protonchain]

Hi Solistics,

For the moon problem you can assume a circular orbit for which

$$v = \sqrt{\frac{\mu}{r}}$$ or $$v = \sqrt{\frac{G M}{r}}$$

where M is the mass of the Earth + moon. Since the Earth's mass is larger than the moon's mass, we can approximate M to be = the mass of the Earth.

G is $$6.67300×10^{-11} m^{3} kg^{-1} s^{-2}$$ and r = semi-major axis = 384,399 km

Punch in the values for this and you obtain v = 1.018 km/s

The value from wiki is 1.022 km/s, which means we were only off by 0.39%

 

[D H]

First off, I messed up my LaTeX in post #4. Corrected.

protonchain: A couple of points.

Astronomers rarely use G (and planetary masses) for the simple reason that G (and the planetary masses) are not very accurate. G is embarrassing one of the least well-known physical constants (5 decimal places of accuracy). On the other hand, the product G*M can be measured to a very high degree of precision. For example, we know G*M for the Sun to about 12 places of accuracy and for the Earth to about 9 places.

The other point: The Moon's mass is a significant fraction of the Earth's mass. Ignoring it will lead to inaccurate results. A better estimate of the Moon's orbital velocity with respect to the Earth is

$$v=\sqrt{\frac{\mu_E+\mu_M}{a_{M}}} = 1024.5\,\text{km}/\text{s}$$To Solistics:
It looks like you are jumping in over your head. How old are you, and how much high a level have you reached in your physics education? Rather than jumping in like this, I suggest you start with Kepler's laws (google for that). Feel free to ask any questions.

 

[protonchain]

$$v=\sqrt{\frac{\mu_E+\mu_M}{a_{M}}} = 1024.5\,\text{km}/\text{s}$$

Is that a misplaced decimal point? Because it's 1.02 km/s not 1000 km/s

Second of all my error was 0.39%, so I'm well within the limits and it's a good estimate.

 

[D H]

Sorry, misplaced decimal (actually, extra k; that should have been m/s, not km/s). Too fast typing! And yes, it is a reasonably good estimate. Note that you cannot get much better than your estimate if you use G (rather than G*M).

 

[Stratosphere]

I'm fairly new to astrophysics, but I'm genuienly interested on knowing how to calculate orbits. I've been trying to do so on my own but I just find myself extremely frustrated. I'm trying to figure out what orbital vectors are and how i can calculate them using known orbital parameters. If i can get over this hurdle i should be all set.

thanks.

P.S. any sites that are helpful (lists of equations, sources etc.) would be appreciated.

What bodies are you trying to calculate just the Earth and moon?

 

[Solistics]

thanks for the help everyone. I found my problem. It seems like I switched a number in the vis-visa equation, 1/r instead of 2/r. Stupid me . That fixed it. Now my values are exactly like what http://nssdc.gsfc.nasa.gov/planetary/factsheet/moonfact.html" said.

D H I'm interested in where you found the value of mu. At first i did what protonchain did M*G which gave my results a big difference from yours. Knowing how you got that would be great .