Question

Scenario #1: The Expanse The Expanse is a science fiction book and television series which is set in a future where space travel is commonplace. In this series, space travelers find ways to replicate the effects of Earth’s gravity by creating apparent weight. There are several ways that they do this: thrust, rotation, and visiting a different planet. When not employing any of these replacements for Earth’s gravity, people are said to be “on the float” with no apparent weight at all. Recall that the magnitude of the acceleration due to gravity near the surface of the Earth is g = 9.8 m/s . 2

Part A: Thrust Gravity (2 points): When a spaceship uses its thrusters to accelerate, a person inside of the ship will experience a net force which gives them an apparent weight. Suppose someone with a mass of 80 kg is on a ship in space (far away from any sources of gravity) that accelerates at ⅓ g. What is their actual weight and their apparent weight?

Part B: Spin Gravity (3 points): Medina is a fictional space station built inside of a cylindrical drum. The drum has a diameter of 960 m and it rotates; the centripetal acceleration from this rotation requires a net force on people inside of the drum and this creates an apparent weight. Draw a free body diagram and a motion diagram for someone standing inside of the drum. If the designers of this space station want to have an acceleration of ⅓ g, what period of rotation must this drum have?

Part C: Alien Planet (4 points): In the series, people land on the fictional planet of Laconia. This planet is similar to Earth in several ways; for one thing, it has the same acceleration due to gravity near its surface. However, there are some important differences: the size of the planet is larger (with a radius r = 9,500 km) and the length of the year is significantly longer (3.1 Earth years). What is the mass of Laconia? Based on what we have learned in this class, what is one possible explanation for Laconia’s year being longer than an Earth year?

Part D: On the Float? (3 points): What’s so bad about being on the float and feeling weightless? Give a plausible reason why people in the series would go to all of the effort to try to replace Earth’s gravity when in space. In your opinion, which of the above methods seems like the best way to create apparent weight and why?

Answer 1

Part A: Inside the space craft as there is no attracting object and the attraction of the ship due to its mass is negligible. So actual weight of person is 0. As ship accelerate forward by g/3 the person get accelerated by -g/3. So apparent weight is W=m.g/3 = 80x9.8/3 = 261.33 newton.

Part B: Centrepetal acceleration = a​​​​​​c= V​​​​​​2/R = g/3 where R is the radius of the drum

Or V​​​​​​2= Rxg/3 = 480x 9.8/3 = 1568

V= √(1568)=39.59

T= 2πR/V = 2xπx(480/39.59) approximately 24π seconds. To draw the diagram it has to specify x and y parameters.

Part C: As the acceleration due to gravity of both planets are same g = GM/R​​​​​​2= Gm/r​​​​​​2 where M and R are mass and radius of earth respectively and m and r that of the new planet. Rearranging the above equation we will get

m = Mx(r​​​​​​2​​​/R​​​​​​2) put r = 9500 km or 9500000 m and R = 6400 km = 6400000 m we get 2.2 times mass of earth. The explanation of longer year will be due to longer orbit of revolution of it.

Part D: The floating will cause food and water to float which is a problem. Floating objects will cause trouble such as short circuiting of the electrical circuits and other damages. Human excretion is very problematic and that is why we need to install special expensive suction devices for it. Pen will not work there and using pencils will cause floating of graphite powder and sometimes they stick on electrical circuits and shorting. Production of gravity by rotation will be the easiest and most eco-friendly way. Because of low requirment of fuel for rotation in space. But special cylindrical shaped spacecraft is required for this to happen. So the possible way we can use now is the thrust method but it require constant acceleration and loss of fuel. Not only that after a certain limit the mass of the rocket starts to increase due to relativity principle and more and more fuel is required. So I suggest the rotation method and this is implemented in the film 'interstellar'.