AER11002 Spacecraft Design Tutorial

A spacecraft executes a Hohmann transfer between two coplanar circular orbits. Assuming impulsive maneuvers and negligible atmospheric drag, which of the following statements regarding the velocity changes ($\Delta V$) and orbital geometry is most accurate?

A single-stage rocket launcher with a dry mass of 80,000 kg has a fuel mass of 600,000 kg and an exhaust velocity of 4,300 m/s. Assuming the required $\Delta V$ to reach orbit is 9,000 m/s, and neglecting gravity losses and atmospheric drag, what is the maximum payload mass the rocket can deliver to orbit, and how does the inclusion of gravity losses typically affect this calculation?

A two-stage-to-orbit rocket launcher has an initial mass of 800,000 kg. The total required $\Delta V$ to reach orbit is 9,250 m/s, with the first stage providing a $\Delta V$ of 4,750 m/s. The exhaust velocity is 4,500 m/s for both stages, and the mass of the empty tank ejected after the first stage is 55,000 kg. Compared to a single-stage-to-orbit rocket with the same initial mass, total $\Delta V$, and exhaust velocity, assess the propellant mass requirements and discuss the primary advantage of using staging in this scenario.

A geostationary satellite is placed in a circular orbit around Earth. Given Earth's mass ($5.972 \times 10^{24}$ kg), the universal gravitational constant ($6.67 \times 10^{-11} Nm^2/kg^2$), and Earth's radius (6,371 km), at what altitude above Earth's surface must the satellite be positioned to maintain geostationary orbit, and what is its orbital speed, considering the effects of third-body perturbations from the Moon and Sun?

A satellite is in an elliptical orbit around Earth with a perigee altitude of 400 km and an apogee altitude of 4,000 km above the surface. Given Earth's mass ($5.972 \times 10^{24}$ kg), the universal gravitational constant ($6.67 \times 10^{-11} Nm^2/kg^2$), and Earth's radius (6,371 km), calculate the initial orbital period. If the orbital period is then increased by exactly 3 hours while maintaining the same ratio between perigee and apogee altitudes, what are the new perigee and apogee altitudes, considering the long-term effects of atmospheric drag?

A deep-space probe is designed to perform a flyby of Jupiter. The mission planners are considering using a gravity assist maneuver to alter the probe's trajectory and increase its speed significantly. Given Jupiter's mass ($1.898 \times 10^{27}$ kg) and the probe's initial velocity relative to Jupiter, derive the maximum possible velocity increase the probe could achieve and under what conditions this maximum is realized, taking into account the effects of Jupiter's atmospheric drag if the probe enters the upper atmosphere.

A satellite is equipped with an electric propulsion system that provides a constant thrust. Describe how the continuous, low-thrust acceleration affects the satellite's orbital elements over time, specifically focusing on the changes in semi-major axis, eccentricity, and inclination, while considering the perturbative effects of solar radiation pressure and Earth's oblateness.

A mission to Mars requires precise targeting for landing a rover on the surface. Discuss how uncertainties in the Mars atmosphere (density variations, winds), spacecraft navigation, and the deployment of a parachute affect the accuracy and precision of the landing, incorporating the use of advanced control systems to mitigate these uncertainties during the terminal descent phase.

A spacecraft is tasked with collecting samples from an asteroid's surface. Formulate a strategy for trajectory design that accounts for the asteroid's irregular shape, gravity field, and rotation, as well as the need to maintain stable orbits or trajectories around the asteroid to allow for precise sample collection, while considering non-gravitational forces such as solar radiation pressure.

A large space station in low Earth orbit (LEO) is subject to long-term atmospheric drag. Analyze the effects of this drag on the station's orbit, including changes in orbital altitude, period, and eccentricity, and evaluate various strategies for orbit maintenance, such as periodic reboosts using onboard thrusters or the deployment of a drag-compensation system, incorporating the impact of solar activity on atmospheric density.

A CubeSat is deployed into a highly elliptical Earth orbit (HEO). Assess the impact of perturbations from the Moon, Sun, and Earth's oblateness on the CubeSat's long-term orbital stability, and propose a control strategy to mitigate these effects while considering the limited resources (power, propellant) available on a CubeSat platform.

For an interplanetary mission, such as a mission to Europa, compare and contrast the use of chemical propulsion, solar electric propulsion (SEP), and nuclear thermal propulsion (NTP) in terms of mission duration, propellant requirements, payload capacity, and overall mission complexity, taking into account the radiation environment around Jupiter and the limitations it imposes on the spacecraft's components.

Develop a closed-loop control system architecture for a spacecraft performing autonomous rendezvous and docking with a target satellite in geostationary orbit (GEO). Describe the necessary sensors (e.g., GPS, star trackers, lidar), actuators (e.g., reaction wheels, thrusters), and algorithms (e.g., Kalman filters, model predictive control) to achieve high precision and reliability, especially during the terminal phase, while accounting for GEO's unique challenges (通信延迟，limited GPS availability, 地球反照率的影响).

Design a thermal management system for a spacecraft destined for a mission to Venus. Analyze the significant challenges posed by Venus's high surface temperature and dense atmosphere, and evaluate different thermal control techniques, such as multi-layer insulation (MLI), heat pipes, radiators, and phase-change materials (PCMs), to maintain the spacecraft's internal components within acceptable temperature ranges, while minimizing weight and power consumption.

Assess the feasibility and implications of constructing a large-scale solar power satellite (SPS) in geostationary orbit (GEO) to wirelessly transmit energy to Earth. Analyze the technical challenges related to orbital assembly, microwave or laser power transmission efficiency, atmospheric effects, potential impacts on the GEO environment (e.g., space debris, radio frequency interference), safety concerns, and economic viability compared to terrestrial renewable energy sources.

Consider a scenario in which a spacecraft must perform an emergency collision avoidance maneuver due to a potential impact with a piece of space debris. Given the limitations in onboard propellant, sensor accuracy, and computation time, formulate an optimal trajectory planning strategy to minimize the probability of collision while minimizing the $\Delta V$ expenditure, taking into account the uncertainties in the debris's orbital parameters and the spacecraft's own position and velocity.

A constellation of small satellites is designed to provide global internet coverage. Analyze the trade-offs between different orbital altitudes (LEO, MEO) and constellation architectures (Walker, Iridium-like) in terms of coverage area, signal latency, power requirements, inter-satellite links, atmospheric drag, radiation exposure, and the cost of deployment and maintenance, while maximizing internet bandwidth and minimizing signal interference.

A spacecraft is equipped with an ion thruster that operates at a very high specific impulse but produces a low thrust force. Formulate an optimal control strategy for guiding the spacecraft from a low Earth orbit (LEO) to a geostationary transfer orbit (GTO) using continuous low-thrust propulsion. The strategy should account for Earth's oblateness, solar radiation pressure, and the ion thruster's limited throttling range, while minimizing the total transfer time and propellant consumption.

Explain the influence of relativistic effects, specifically time dilation and the Shapiro delay, on deep-space navigation and communication, especially during missions involving high-precision ranging and telemetry with distant spacecraft near massive celestial bodies (e.g., the Sun, Jupiter). Furthermore, how does one compensate for these effects in mission planning and real-time operations to ensure accurate positioning and data transmission?