A.) Suppose you were to get up close to the black hole that is at the center of the Milky Way, our home galaxy. It has a mass measured by the motions of objects nearby that is 4 million times the Sun's mass. Since the Sun has a mass of 2x1030 kg, what is the closest you could get to this thing and have any hope of escaping from it? For comparison, Earth's distance from the Sun is 150 million kilometers. Distance scales this large are often measured in light travel time, so we say 1 light year is the distance light travels in a year, 1 light minute is how far it goes in a minute, and so on. It takes light 8 minutes to reach Earth from the Sun. Hint: What is the Schwarzschild Radius of this black hole? How fast does light travel? a.) about 10 microseconds of light travel time
b.) about 12 million kiometers
c.) about 3km
d.) about 40 secons of light travel time
B.) Suppose hypothetically we put a spacecraft into orbit around the Sun to chase and recover an asteroid. Of course we place a clock on it to control the timing of the on-board computer that will autonomously run the spacecraft, and we synchronized the clock with precision Earth clocks before launch. After 10 years the spacecraft returns with its precious sample, ready to deliver it to anxious aging scientists at home. If on average during its journey it traveled at 30 km/s (that's the Earth's orbital speed around the Sun), what can we say about the clock on the spacecraft when it gets back home.
a.) it will be the same as the clock on Earth
b.) The difference between the clocks depends on its direction of motion compared to Earth, as well as on its speed, so it may either be behind or ahead.
c.) It will be ahead of the clock on Earth, having run fast compared to Earth on is journey.
d.) It will be behind the clock on Earth, having run slow compared to Earth on its journey.