Math

[Mission_CDR]

I would like to know more about the physics that this simulator involves. How would you calcualte the velocity that you would need to obatain an orbit with a specific pedigree and apogee altitudes?

http://www.braeunig.us/space/orbmech.htm I have started reading this and I am confused a bit.

7.5 KM/s is the speed that I noted in orbiter whn I was in orbit, lets say the mass of the shuttle was 100,000 KG, and the distance from the center of the earth was 6.800 MegaMeters (6800 KM)

7,500x7,500=100,000G
6,800x6,800

56,250,000=100,000G
46,240,000

56,250,000=0.002162629757785G

26,010,000,000=G (G being the Mass of the earth)

However, http://hypertextbook.com/facts/2002/SamanthaDong2.shtml, says that the mass of the earth is 59,800,000,000,000,000,000,000,000 kg.

What am I doing wrong? Can some one help me to understand this?

 

[Scrooge McDuck]

I would like to know more about the physics that this simulator involves. How would you calcualte the velocity that you would need to obatain an orbit with a specific pedigree and apogee altitudes?

http://www.braeunig.us/space/orbmech.htm I have started reading this and I am confused a bit.

7.5 KM/s is the speed that I noted in orbiter whn I was in orbit, lets say the mass of the shuttle was 100,000 KG, and the distance from the center of the earth was 6.800 MegaMeters (6800 KM)

26,010,000,000=G (G being the Mass of the earth)

The GM in the formula stands for the product of the gravitational constant and Earth's mass. The mass of the shuttle is not needed in the calculation.

GM of Earth = 3.986005x10^14 m^3/s^2

For example, if your orbital altitude is 200 km, then
r = (6378.14 + 200) x 1,000 = 6578140 m

following the calculation:
v = SQRT[ GM / r ] v = SQRT[ 3.986005x10^14 / 6578140 ]
v = 7784 m/s

The Braeunig site you mention is one of my favorites as well, try to look at the examples too.
If your r was 6800, then velocity would be:
v = SQRT[ GM / r ] v = SQRT[ 3.986005x10^14 / 6800000 ]
v = 7656.22 m/s

However, please note that this method is valid for circular orbits only, where Ecc = 0.
If you know, for example, your altitude at Perigee and at Apogee, you can use the calculations described in this example.
It will describe how answer the following example:

An artificial Earth satellite is in an elliptical orbit which brings it to an altitude of
250 km at perigee and out to an altitude of 500 km at apogee. Calculate the velocity of
the satellite at both perigee and apogee.

regards,
mcduck

 

[Mission_CDR]

Ahh, that makes a lot more sense now that I know what GM stands for, I thought it was two different variables G-gravity M-Mass, but now I know, Thanks a lot.

 

[Andy44]

Also, an orbit with a good pedigree comes with papers detailing who it's mother and father and grandparents are.

 

[Mission_CDR]

So let me make sure that I understand completely, If I was orbiting the earth with an orbit of 5 Mega meters (ECC=0) My velocity would be aproximatly 5918.7948 m/s shown by the equation below.

V=SQRT(3.986005x10E15/11,378,140)

V=SQRT(35032131.78955435598...)

V=5918.7948 m/s

Am I right?




That was funny Andy but we aren't talking about life science, lol.

 

[Eagle]

Am I right?

Looks right. Calculated the same radius as you.

fyi Apogee and Perigee are technically for Earth only(which is correct in this context). The more generic terms are Apoapsis and and Periapsis. http://en.wikipedia.org/wiki/Apsis

 

[Ursus]

That was funny Andy but we aren't talking about life science, lol.

He must have thought you were, since you wrote:

How would you calcualte the velocity that you would need to obatain an orbit with a specific pedigree and apogee altitudes?

C'mon... everybody makes typos. Might as well have a little fun with them.

 

[MajorTom]

Guys,

I find this equation most useful for estimating my required final velocity when I want to enter into orbit around my destination planet or moon. Plug in the mass of the object...be it the moon or mars or whatever...and you can come up with the velocity required for a circular orbit at, oh, 100 km or whatever.

It gives a good guide to delta V, which in turn can help you calculate fuel and thrust (or Isp) required to get you there, etc. etc. Gives you an appreciation for aerobraking rather than using fuel to brake into orbit of your target.:speakcool:

 

[Mission_CDR]

How would you calculate the speed needed to raise your apogee in a 200 km. circular orbit to 300 km. (starting velocity is 7656 m/s) (Your speed at apogee would be slower than if it where a regular 300km circular orbit because your perigree is 100 km lower.)

 

[bujin]

How would you calculate the speed needed to raise your apogee in a 200 km. circular orbit to 300 km. (starting velocity is 7656 m/s) (Your speed at apogee would be slower than if it where a regular 300km circular orbit because your perigree is 100 km lower.)

The Orbital Mechanics page you linked to in your first post explains this under the section "Orbital Maneuvres > Orbit Altitude Changes".

Rp [Radius at Perigee] = 6571000m (200km altitude above mean earth radius)
Ra [Radius at Apogee] = 6671000m (300km altitude)
GM = 4E+14 m^3/s^2

A [Semi-major axis of "transfer" orbit] = (Rp + Ra)/2 = 6621000m

Vp [Velocity at Perigee]
= SQRT(GM * (2/Rp - 1/A))
= SQRT(4E+14 * (3.043677E-7 - 1.510346E-7))
= SQRT(4 * 1.533331E+7)
= SQRT(6.133323E+7)
= 7831.55m/s

Va [Velocity at Apogee]
= SQRT(GM * (2/Ra - 1/A))
= SQRT(4E+14 * (2.998051E-7 - 1.510346E-7))
= SQRT(4 * 1.487705E+7)
= SQRT(5.950821E+7)
= 7714.16m/s

You may want to plug in some more accurate numbers.

 

[Mission_CDR]

The Orbital Mechanics page you linked to in your first post explains this under the section "Orbital Maneuvres > Orbit Altitude Changes".

Rp [Radius at Perigee] = 6571000m (200km altitude above mean earth radius)
Ra [Radius at Apogee] = 6671000m (300km altitude)
GM = 4E+14 m^3/s^2

A [Semi-major axis of "transfer" orbit] = (Rp + Ra)/2 = 6621000m

Vp [Velocity at Perigee]
= SQRT(GM * (2/Rp - 1/A))
= SQRT(4E+14 * (3.043677E-7 - 1.510346E-7))
= SQRT(4 * 1.533331E+7)
= SQRT(6.133323E+7)
= 7831.55m/s

Va [Velocity at Apogee]
= SQRT(GM * (2/Ra - 1/A))
= SQRT(4E+14 * (2.998051E-7 - 1.510346E-7))
= SQRT(4 * 1.487705E+7)
= SQRT(5.950821E+7)
= 7714.16m/s

You may want to plug in some more accurate numbers.

I pluged in some more acurate numbers and here is what I got.

Via=7905.2404952253...m/s
Vfb=7905.1785265348...m/s
Vtxa=7905.27147963...m/s
"DELTA"VA=0.03098440599...m/s

And from what I know about orbiter that is not right.

Did I do something wrong or are the numbers that I used not acuarte enough? The numbers that I used were G=3.986005x10*14. Width of earth=6.37814 Mm

 

[bujin]

I pluged in some more acurate numbers and here is what I got.

Via=7905.2404952253...m/s
Vfb=7905.1785265348...m/s
Vtxa=7905.27147963...m/s
"DELTA"VA=0.03098440599...m/s

And from what I know about orbiter that is not right.

Did I do something wrong or are the numbers that I used not acuarte enough? The numbers that I used were G=3.986005x10*14. Width of earth=6.37814 Mm

Plugging in the same numbers, I get:
Via = 7784.26 m/s
Vfb = 7725.76 m/s

Vtxa = 7813.57 m/s
Vtxb = 7696.56 m/s

DVa = 29.31 m/s
DVb = 29.2 m/s
DVt = 58.5 m/s

 

[Mission_CDR]

I figured out what I did wrong and now I get it, my calculations were for an orbit of 200m and 300m instead of Km. I even calcualted the average speed of the earth assuming that 1AU~150Gm. Then I checked it on google and discovered that my answer was exactly what google said. (29675.98 m/s)

Thanks everybody.