Homework 2, Astr 305V, Fall 2018

Due: Tuesday, September 11, 2018

1. We discussed "weightlessness" in class. We also discussed that your weight on Earth is essentially a measure of the force of gravity between the Earth and your body, when you are supported by the Earth's solid surface; the US unit of "lbs" for weight, is indeed in fact a unit of force.

a. The force of gravity between the Moon and an astronaut on the moon's surface will be about 6 times less than that between the Earth and an astronaut standing on the Earth's surface. So the astronaut's scale would indicate a 6 times lower weight on the Moon compared to the Earth.

a. Write down Newton's law of gravity, in one case the formula to calculate your weight on the Moon, and in the other case the formula to calculate your weight on Earth. Explain what is different for the two equations, and what is the same in the two equations.

b. Look up the radius and mass of the Moon and of the Earth and show how the factor 6 difference comes about by comparing the force of gravity on an astronaut when standing on the Earth and when standing on Mars using Newton's law of gravity. Note: you do not need to know the mass of the astronaut to solve this problem, nor the value of the gravitational constant G.

c. A manned spacecraft is on its way to the planet Mars. Once the craft has reached high speed after its launch from Earth, the rockets no longer fire and the craft is coasting on its course to the planet Mars. Are the astronauts weightless during this time?

d. Will the space craft travel towards Mars at constant velocity during this phase of the journey? Explain your answer.

e. Will the space craft travel in a straight line during this phase of the journey? Explain your answer.

f. Describe some of the effects of weightlessness on the human body. How do astronauts in the international space station deal with this?