Question 1: Define a nebula and explain its role in the formation of stars.

Answer: A nebula is a cloud of gas and dust in space where new stars are formed through gravitational collapse.

Question 2: Describe the process by which a star becomes a black hole at the end of its life cycle.

Answer: A massive star exhausts its nuclear fuel, collapses under gravity, and if sufficiently massive, compresses into a black hole due to intense gravitational pull.

Question 3: Explain how nanotechnology can be used to study distant nebulae.

Answer: Nanotechnology enables the development of highly sensitive sensors and miniature instruments that can be deployed on spacecraft to analyze nebulae at a molecular level.

Question 1: Calculate the escape velocity (v) from a black hole with mass M = 10 times the mass of the Sun (M☉). Use the formula v = sqrt(2GM/R). Given G = 6.674×10⁻¹¹ N·m²/kg², M☉ = 1.989×10³⁰ kg, and the Schwarzschild radius R = 2GM/c², where c = 3×10⁸ m/s.

Answer: Approximately 3×10⁸ meters per second (the speed of light).

Question 2: If a nanobot used in space exploration can operate at a temperature of -200°C, what is this temperature in Kelvin?

Answer: 73 Kelvin.

Question 1: Design a hypothetical experiment using nanotechnology sensors to detect the presence of dust particles indicative of a star's formation in a nebula. Describe the key variables and safety precautions involved.

Answer: The experiment would involve deploying nanoscale sensors within a spacecraft to measure dust particle density and composition. Variables include sensor sensitivity, particle size, and ambient temperature. Safety precautions include radiation shielding, contamination control, and secure attachment of sensors to prevent loss or damage during space travel.

Question 1: A nanotechnology-based telescope detects an unusually high concentration of helium and sulfur in a distant nebula. What does this suggest about the stage of star formation, and how might nanotech advancements improve our understanding?

Answer: It suggests active star formation with nuclear fusion processes. Nanotech advancements could enable more precise analysis of molecular composition and real-time data collection from distant regions.

Question 2: Discuss how nanotechnology could be utilized to develop materials that withstand the extreme conditions near black holes for future space missions.

Answer: Nanotechnology can produce ultra-strong, heat-resistant materials with nanoscale structural control, enabling spacecraft components to endure intense gravitational forces, radiation, and high temperatures near black holes, thus facilitating safer exploration.