Space Dynamics - Flight Mechanics & Space Dynamics - Aerospace Engineering Previous Year Questions

An ideal two-stage rocket has identical specific impulse and structural coefficient for its two stages. For an optimized rocket, the two stages have identical payload ratio as well. The payload is 2 tons and the initial mass of the rocket is 200 tons. The mass of the second stage of the rocket (including the final payload mass) is ____ tons.

F and G denote two points on a spacecraft’s orbit around a planet, as indicated in the figure. O is the center of the planet, P is the periapsis, and the angles are as indicated in the figure. If OF = 8000 km, OG = 10000 km, \(\theta_F = 0\) deg, and \(\theta_G = 60\) deg, the eccentricity of the spacecraft’s orbit is ________ (rounded off to two decimal places).

An earth satellite has the instantaneous position vector \(\vec{r}\) and velocity vector \(\vec{v}\) as given below. Here \(\hat{p}\) and \(\hat{q}\) denote the unit vectors along the \(x\) and \(y\) axes of the perifocal frame, respectively. Assume that the value of gravitational parameter is \(398600\ \text{km}^3/\text{s}^2\). Which one of the following trajectories does the satellite follow? \(\vec{r} = (8000\hat{p} + 9000\hat{q})\ \text{km}\) and \(\vec{v} = (-6\hat{p} + 6\hat{q})\ \text{km/s}\)

An earth satellite moves in an elliptical orbit with a perigee altitude of 300 km and an apogee altitude of 3000 km. Assume that the radius of the earth is 6378 km. The eccentricity of the orbit is __________ (rounded off to three decimal places).