What is the Final Speed of a Horizontally Launched Rocket in Space?

[Vitall]

We got rocket 200km above see level. Horizontal speed is zero. So, it eventually fell on Earth. We will lunch rocket horizontally. What the final speed it will reach?

Pegasus-3 Gross Mass: 985 kg. Empty Mass: 203 kg. Thrust (vac): 3,525 kgf. Isp: 293 sec. Burn time: 65 sec. Propellants: Solid Isp(sl): 240 sec. Diameter: 1.0 m. Span: 1.0 m. Length: 2.1 m. Country: USA.

Should be enough data. If you provide an equation, how you figure out speed, it will be greatly appreciated(so I can calculate speed for different types of rockets). Sorry, not a rocket scientist (tried google, but felt). Excuse my English.

 

[enigma]

Hi Vitall, welcome to PF!

The ideal rocket equation will give you the results without taking drag or gravity losses into account.

$$V_f=I_{sp}*g_0*ln(\frac{m_i}{m_f})$$

g_0 is the sea level acceleration of gravity, Isp is the specific impulse of the engine (a measurement of the "effectiveness" of the motor), m_i is the fueled or gross mass, m_f is the empty mass.

The statistics you have listed are only for the third stage of the pegasus rocket, most likely taken from http://www.astronautix.com/stages/pegasus3.htm . To compute the final speed of the whole rocket, you'll need to take each stage separately, adding the fueled mass into both the final and initial masses, and then dropping the lower stages' mass.

Hope all that made sense. Your english is fine... much better than my attempt at your native language, I'm sure.

 

[Vitall]

Thank you Enigma.

That is perfectly answering my question. The theoretical question was, if we place third stage on Rutan VSS Enterprise spaceship, instead of tourists, what mass we can put on LEO. After some calculation (another forum), we calculated that it might be possible to lunch 20kg/25kg on LEO, but we will need a VERYVERY good hydrogen based third stage, and that is not truly realistic. Thank you for your help once again.