orbit raising to geo with electric propulsion (question)

[dinos55]

can someone show me how to calculate the deltavs and dry mass of the satellite for an orbit raising to geo from leo wih electric propulsion?

[fourfa]

Do you mean LEO/GEO or LKO/GKO?  Or would that be KKO, or just KO for Kerbalstationary orbit...

[Guest]

45 minutes ago, dinos55 said:

can someone show me how to calculate the deltavs and dry mass of the satellite for an orbit raising to geo from leo wih electric propulsion?

What engine?

What's the satellite's wet mass?

Dry mass?

For GEO it's about 3.9km/s for a circular orbit from 250km (LEO). For Kerbin (KEO), it's about 1.1km/s for a stationary orbit from 80km.

E: You can use Tsiolkovsky's equation to calculate the delta-V of your satellite.

Edited November 6, 2017 by regex

[OhioBob]

For a spiral transfer using constant low thrust (i.e. electric propulsion), the delta-v can be estimated by simply taking the difference between the orbital velocities of the initial orbit and the final orbit.  For GEO it's about 4.7 km/s, and for KEO it's about 1.3 km/s.  This is a little higher than the numbers given by @regex because those are for a two-burn Hohmann transfer.  A spiral transfer doesn't take full advantage of the Oberth effect, so it's a little higher.

Orbital velocity is calculated using, v = SQRT(μ/r), where μ is the gravitational parameter and r is the orbital radius.

[dinos55]

thank you @OhioBob. and what about the change in inclination? how do i calculate the deltav  for electric propulsion? what are the formulas used?

 

@regex thank you! but mostly i want to know what formulas to use and do the calculations to find this results.  

[Guest]

3 hours ago, dinos55 said:

@regex thank you! but mostly i want to know what formulas to use and do the calculations to find this results.  

All spacecraft use the same calculation to find delta-V. Use Tsiolkovsky's equation that I linked above: Natural log of the mass ratio (start mass divided by end mass) multiplied by the exhaust velocity. You get exhaust velocity from isp by multiplying it by 9.80665.

[OhioBob]

3 hours ago, dinos55 said:

thank you @OhioBob. and what about the change in inclination? how do i calculate the deltav  for electric propulsion? what are the formulas used?

I'm not sure how to compute inclination change when using electric propulsion.  For short high-thrust changes, the formulas are,

where the first equation is used to compute the Δv for a stand-only plane change, and the second is the total Δv for a combination altitude change and plane change.  Vi is the initial velocity, Vf is the final velocity, and theta is the plane change.

I'm guessing that for electric propulsion we probably want to use the second equation.  That would mean that a transfer to GEO from a starting inclination of 28.5 degrees (Cape Canaveral) would be about 5.3 km/s.

To compute the Δv of the spacecraft, use Tsiolkovsky's equation as linked to and explained by Regex.
 

Edited November 6, 2017 by OhioBob

[dinos55]

thank you both for your answers! @OhioBob @regex

I would like to ask you something more. How can I find the revolutions that the satellite will do with electric propulsion until it reaches geo from leo? and the total time is t=deltav/acceleration(how do I find the acceleration)?

Thanking you in advance

(sorry for the stupid questions..i am new to orbital mechanics)

[Guest]

1 hour ago, dinos55 said:

I would like to ask you something more. How can I find the revolutions that the satellite will do with electric propulsion until it reaches geo from leo? and the total time is t=deltav/acceleration(how do I find the acceleration)?

I couldn't tell you directly; that is, I lack the math myself, and it would probably involve some sort of integration given that craft mass will vary throughout the burn, but this seems like a pretty good place to start:

http://ccar.colorado.edu/asen5050/projects/projects_2009/stansbury/

[dinos55]

@regex thank you very much!

[OhioBob]

4 hours ago, dinos55 said:

I would like to ask you something more. How can I find the revolutions that the satellite will do with electric propulsion until it reaches geo from leo? and the total time is t=deltav/acceleration(how do I find the acceleration)?

I don't know of a simple way to compute the number of revolutions.  The period of the satellite changes non-linearly as it moves outward so, as Regex said, it will involve some sort of an integration to figure it out.  However, the time it will take should be pretty straightforward.  After you've figured out how much fuel you need to burn to produce the required delta-v (from Tsiolkovsky's equation), you then simply divide the fuel mass by the fuel mass flow rate and that will give you time.  Fuel mass flow rate is compute it as follows:

ṁ = F / (I_sp * g_o)

where ṁ is the mass flow rate (kg/s), F is the thrust (N), I_sp is the specific impulse (s), and g_o is standard gravity (9.80665 m/s²).
 

[dinos55]

@OhioBob thank you again for your help!