Gravitational Constant

[george7378]

Hi everyone,

I have a question about the gravitational constant:

6.67300 × 10-11 m3 kg-1 s-2



What do the 'm', the 'kg' and the 's' mean?

Thanks.

 

[Urwumpe]

*No comment*

:n00b:

http://ts.nist.gov/WeightsAndMeasures/Metric/metrsty3.cfm

 

[RisingFury]

m - meter
kg - kilogram
s - second

 

[Andy44]

Urwumpe has it. Units of measurement. Without which the constant is useless.

 

[george7378]

Thanks - I don't think I phrased it very well - meant to ask what they apply to (I guess 'kg' is body mass and 'm' is radius - maybe I'm wrong).

 

[Notebook]

This is what I think you are after:

http://en.wikipedia.org/wiki/Dimensional_analysis

N.

 

[jedidia]

well, they ARE the unit of the gravitational constant. It's just a bit abstract a unit, I admitt. If you take the unit for velocity, for example, it is m/s, or m * s^-1, which is meters per second.

The unit of Gravity is acceleration, which is m/s^2, or meters per seconds squared, which is already a bit abstract, since we're not used to imagining squared seconds (as we are for example used to thinking about square meters).

The unit of the gravitational constant is therefore m^3/kg/s^2, or cubic meters per kilogram per square-second. The unit is a result of the operations that lead up to the gravitational constant. Although it looks scary, there's really nothing to it... it's just a unit. You have a kilogram of stones, a meter per second of velocity, or a cubic meter per kilogram per squaresecond of gravitational constant. (we could rename the whole unit into something else, and noone would wonder. For example, go look up the definition of a newton-meter...)

 

[george7378]

Right - thanks.

I have another question which isn't really related to this, but doesn't need a new thread;

How do I get two azimuth values (one for ascending node and one for descending node) from the following formula:

azimuth = arcsin (cos (inclination) / cos (latitude))?

Thanks.

---------- Post added at 17:42 ---------- Previous post was at 17:14 ----------

Never mind - I found it:

(90 - asc) + 90.

 

[insanity]

remember that you're going to need to swap between degrees and radians for azimuth calculations.

If you're writing a program, the DGIV manual describes a slick equation to get the job done:
You need a few variables: inclination, latitude, current speed (for Earth, 410 m/s is good), and final orbital altitude (which you can convert into orbital speed)

Then you'll need to swap the degrees into radians, setup the equations from the manual, swap back to degrees and you have the answer for the northern track solution. For the southern track solution, subtract 180 degrees from the northern track solution. Round it off to two decimal places and you have two solutions that take are pretty dang good

 

[george7378]

Thanks for the tips insanity - that is a great equation. I was using the 'rough' calculation before, but now I have integrated the more accurate one. Also, I found a useful header file which allows you to use degrees in C++.

How do I convert orbitel velocity to altitude (I assume they are proportional)?

Thanks.

 

[insanity]

Thanks for the tips insanity - that is a great equation. I was using the 'rough' calculation before, but now I have integrated the more accurate one. Also, I found a useful header file which allows you to use degrees in C++.

How do I convert orbitel velocity to altitude (I assume they are proportional)?

Thanks.

Easy! We need a two variables: Mass of Central Body and the radius between the satellite and the central body (which is just the radius of the body plus altitude). We get to use the gravitational constant here, too!

The equation is: [math]
v=\sqrt\frac{GM}{R}
[/math]

Remember that units are essential to keep track of, and that in doing calculations like these some dimensional analysis may be necessary

 

[george7378]

Thanks - I'll keep that in mind. For this one, I think I'll stick with a direct entry of the velocity, since it is easily available from within Orbiter and requires entry of one value only (as opposed to radius and mass, which may require an internet search).

Thanks again!

 

[Urwumpe]

How do I convert orbitel velocity to altitude (I assume they are proportional)?

Not directly. The important formula is the vis Viva integral.

http://en.wikipedia.org/wiki/Vis-viva_equation

As you can see, at r=a (circular orbit case) the formula gets reduced to

v² = µ/a

(I assume you know µ=GM)