Luanch angle to put a satellite in an orbit?

[smhni]

I have a Question:

suppose we have a satellite (m=400kg, V0=40m/s) and we want to put it in a 1000km orbit (r=1000km)...what should be the launch angle?


P.S: is this question complete?(For Lack Of A Better Word) .. I mean do we have a formula which relates these parameters.. or perhaps a couple of formulas that relates them...


thx for you help...

 

[rcgldr]

The main goal is to increase speed, so the best path would be nearly horizontal, except that atmospheric drag is much less at higher altitudes, so there needs to be a significant veritcal component during the early part of the path until the atmosphere gets thinner, reducing drag force (along with heat) on the rocket as it's speed increases. Once past the atmosphere, then something similar to a Hohmann transfer orbital path is used, depending on the weight of the target object:

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

 

[D H]

P.S: is this question complete?(For Lack Of A Better Word) .. I mean do we have a formula which relates these parameters.. or perhaps a couple of formulas that relates them...

The question is not complete, and not by a long shot. The ideal launch angle is neither vertical nor horizontal. A horizontal launch won't gain the altitude needed to clear the atmosphere. A vertical launch isn't aligned to gain the requisite horizontal velocity. For the Space Shuttle, the ideal launch angle would be about 78º rather the the 90º vertical alignment.

The Shuttle is not launched at a 78º pitch angle for the simple reason that the vehicle is too danged heavy to be launched at any angle but vertical. It would fall over before it could ever be launched were it oriented at 78º. Vertically-launched vehicles such as the Shuttle have to pitch down to the desired angle soon after launch. Once in this desired attitude, the vehicle maintains a zero angle of attack and follows a gravity turn (google this phrase). The gravity turn let's gravity and aerodynamics turn the vehicle so that by the time the vehicle leaves the atmosphere it is oriented nearly horizontally and has attained orbital velocity.

Vehicles are not launch directly into a 1000 km orbit. The launch vehicle takes the spacecraft to a very low Earth orbit. From that point, upper stages transfer the spacecraft from this insertion orbit to the desired orbit. This is typically done in multiple steps so as to insure that not only is the vehicle in the desired orbit but is also in the right place on that orbit.

 

[smhni]

thanks guys... your answers were very helpful..

 

[PJC01]

I can answer your question by first stating that there is no one specific launch angle that will guarantee a satellite to be placed in a 1000km orbit. The launch angle will depend on various factors such as the location of the launch site, the velocity of the launch vehicle, and the desired orbital parameters. However, there are mathematical formulas and equations that can be used to determine the optimal launch angle for a specific satellite and orbit.

One of the key equations that relates these parameters is the vis-viva equation, which states that the square of the orbital velocity is equal to the gravitational constant times the mass of the central body (in this case, the Earth) divided by the distance from the center of the central body to the satellite. This equation can be used to calculate the required orbital velocity for a specific orbit.

Once the required orbital velocity is known, the launch angle can be determined using trigonometric equations and considering the velocity of the launch vehicle. The launch angle will need to be adjusted to account for the Earth's rotation and the curvature of its surface.

In summary, while there is no single formula that directly relates the launch angle, satellite mass, and orbital distance, there are various equations and principles that can be used to determine the optimal launch angle for a specific satellite and orbit. It is important to consider all the relevant factors and perform calculations to ensure a successful satellite launch and placement in the desired orbit.