Need some equations to do my calculations.

[Navy2k]

Hi,

what are the equations to calculate:

1. How much dV do I need for a craft to stop completely that weighs around 2000t and is in an 120kmx120km Orbit around Eve.

2. How much thrust do i need to do this manouver within 1 Minute.

Thanks

Ben

P.S. Don't ask

[mhoram]

1. How much dV do I need for a craft to stop completely that weighs around 2000t and is in an 120kmx120km Orbit around Eve.

2. How much thrust do i need to do this manouver within 1 Minute.

Simply look at your current orbital speed: that is about the dV you need to stop your craft.

I have no ship around Eve, so I can not lookup this value, but it can also be calculated via the orbital energy.

You can calculate the thrust as

Thrust = mass * dV / burnduration

[CaptainArchmage]

1. The delta-v requirement does not change with vehicle mass. You will probably have an orbital velocity of 3-4km/s, so you will need to eliminate that completely to come to a stop.

The delta-V you have is given by:

Delta-V = 9.81 * Specific Impulse of Engine * ln((initial mass of ship) / (final mass of ship))

Given that your spaceship has a mass of 2000 tons, assuming you are using the LV-T30 or LV-T34 engines, you will need to have at least 1125 tons of fuel on board to do this.

2. Your acceleration would need to be on average 50-70m/s^2 given the 3-4km/s delta-V. That is quite high.

Edited February 16, 2014 by CaptainArchmage

[Jimbimbibble]

Why can't you just aero-brake? You could use 10% of the fuel and not require ridiculous thrust.

[KvickFlygarn87]

For orbital speed, I'll run a vis-viva equation:

where:

v is the relative speed of the two bodies

r is the distance between the two bodies

a is the semi-major axis

G is the gravitational constant

M is the mass of the central body

For a circular 200km Eve orbit, that is:

r = 200km

a = 900km

G = 9.81 (as always)

M = 1.2244127×10²⁰

Therefore:

v² = 9.81 * 1.2244127²⁰ * (2/200 - 1/900)

I gave vis-viva a shot and failed, someone save me!

[Seret]

What do you actually mean by "stop completely"? Do you mean to land on Eve? It's got an atmosphere like treacle, you shouldn't need much at all.

[Rhomphaia]

For orbital speed, I'll run a vis-viva equation:

http://upload.wikimedia.org/math/d/b/0/db0ddb618d4f68a6a479ccfe2888e215.png

where:

v is the relative speed of the two bodies

r is the distance between the two bodies

a is the semi-major axis

G is the gravitational constant

M is the mass of the central body

For a circular 200km Eve orbit, that is:

r = 200km

a = 900km

G = 9.81 (as always)

M = 1.2244127×10²⁰

Therefore:

v² = 9.81 * 1.2244127²⁰ * (2/200 - 1/900)

I gave vis-viva a shot and failed, someone save me!

Gravitational constant For GM use the gravitational parameter values (Eve 8.1717302×10¹² m³/s²

r is the radius of the point of the orbit you are calculationg,

a is the semi major axis

for a circular orbit this simplifies to 1/a

use meters to keep units constant

for a 200km atltitude a= 900000m

v = 3013.254m/s

[Supernovy]

I gave vis-viva a shot and failed, someone save me!

For a circular orbit, r is identical to a (the semimajor axis of a circle is its radius).

So v² = GM(2/r - 1/r) => v² = GM((2 - 1)/r) => v² = GM/r

v² = 6.67×10^{−11} * 1.2244127×10²³ / (700 000 + 120 000)

v² = 8.1717302×10¹² / 820 000

v² = 9.965⁶

v = 3157 ms^-1

EDIT: Gah! Ninja'd! The difference between my and Rhomphaia's answer can be attributed to different precisions and using different orbit altitudes.

Edited February 16, 2014 by Supernovy

[Navy2k]

Thanks for the calculations.

My Problem is that my craft is rather unwilling to manouver because of weight concerns. So no rcs and little gyros. My idea was to drop this lander in a 90° angle and so have no need to manouver in the atmosphere.

I would dock a 2nd craft for the retro burn and the 90° turn.

Ben

[TheDarkStar]

As long as you can turn a bit and your craft is somewhat stable, try turning with 4x physics warp (use alt + the , or . keys). Also, you're not going to be maneuvering at all the atmosphere of Eve because of how think it is. Without parachutes, you'll easily be going ~80 m/s by the end, and you'll be going straight down, too. Using parachute too early can actually rip your lander apart because of how think the atmosphere is.

Don't forget about Eve's rotation; if you're going at 0 m/s relative to Eve in orbit, you won't be when you reach the ground.

[lammatt]

what do you mean by stop completely?

what is the stopping is referencing to?

do you mean landing?

or do you mean stopping w.r.t a point on the surface of the planet? (aka orbiting @ geostationary height?)

Edited February 16, 2014 by lammatt

[Navy2k]

I meant stoping relative to the ground but not geostationary but free falling

[Seret]

If you're concerned about maneuvering during landing, you still don't need to drop in vertically from orbit. Do a small de-orbit burn that drops your Pe into the atmosphere and let that kill off most of your speed. Then when you're closing in on the ground, burn retro to kill the last of your horizontal velocity and only drop the last little bit vertically.

[Navy2k]

Theres your problem, i don't want to burn retro ;P

[Claw]

Then how are you going to apply this dV to stop your orbital motion if you aren't going to fire retro?

If you are pointing at the surface, then this is a different question.

[Horn Brain]

Thanks for the calculations.

My Problem is that my craft is rather unwilling to manouver because of weight concerns. So no rcs and little gyros. My idea was to drop this lander in a 90° angle and so have no need to manouver in the atmosphere.

I would dock a 2nd craft for the retro burn and the 90° turn.

Ben

That is the most kerbal solution to the problem of targeted deorbiting that I can imagine.

[Navy2k]

Thanks Horn Brain for getting me

Here is an teaser:

Edited February 21, 2014 by Navy2k

[Pds314]

The simple answer is you should make a better lander. Otherwise, figure out a way to get 3 km/s delta-v extra out there with your 2000 tonne craft and then burn it in a minute.

This means an average acceleration of -50 m/s^2, which means you need over 100 mainsails with the added fuel weight.

You could always just add some reaction wheels...

[Pds314]

So yeah. My suggestion is that you make a better lander, like one that can turn for example. You are totally screwing yourself if you try to deorbit an Eve lander like that.