Two Little Gravity Quizzes

You and the Earth

Your weight is a measure of the force that the Earth exerts on you and that you exert on the Earth. In terms of Newton's Second Law:

F = mg

where g is the acceleration due to gravity, approximately 9.8 m/s². In terms of the mass of the Earth, M, your mass, m, and the radius of the Earth, R (ignoring "big G"), this equation can be written as:

This equation is read as the "force is proportional to the mass of the Earth times the mass of the object (you), and inversely proportional to the radius of the Earth squared." Interestingly, solid spherical bodies act as if all of their mass is concentrated right at the center! Figure out what would happen in a relative sense in the following scenarios (answers given at the end of the quiz):

1. The Earth suddenly doubles in size (radius)
1. Your weight stays the same
2. Your weight doubles
3. You weigh 1/4 as much
4. You weigh 1/2 as much
   
   
2. You eat so much that you now have twice as much mass (Earth stays the same)
1. You weigh twice as much
2. You weigh 4 times as much
3. You weigh the same
4. You weigh 1/2 as much
   
   
3. The Earth is now twice as massive, but your diet leaves you with only 1/2 your original mass
1. You weigh exactly the same as before the changes
2. You weigh 4 times as much
3. You weigh 1/2 as much
4. You weigh 1/4 as much
   
   
4. The Earth balloons to twice its size (radius) and also gains twice its mass
1. Your weight doesn't change
2. You weigh twice as much
3. You weigh 1/2 as much
4. You weigh 4 times as much
   
   
5. The Earth is 1/2 its current size, but twice its current mass.
1. Your weight doesn't change
2. You weigh 8 times as much
3. You weigh 1/8 as much
4. You weigh 1/4 as much

The Sun and the Earth

We can calculate the gravitational force between the Sun and the Earth by using the mass of each object, M_sun and m_earth and the distance between them, D. Again, ignoring "big G," the force is represented by:

Figure out what would happen in a relative sense in the following scenarios (answers given at the end of the quiz):

1. The Sun suddenly moves two times farther away
1. The force stays the same
2. The force doubles
3. The force is 1/4 as much
4. The force is 1/2 as much
   
   
2. The Sun stays in the same place, but the Earth suddenly has twice as much mass
1. The force is twice as much
2. The force is 4 times as much
3. The force is the same
4. The force is 1/2 as much
   
   
3. The Sun is now twice as massive, but the Earth has only 1/2 its original mass
1. The force is exactly the same as before the changes
2. The force is 4 times as much
3. The force is 1/2 as much
4. The force is 1/4 as much
   
   
4. The Earth moves two times farther away and also gains two times its original mass
1. The force doesn't change
2. The force is twice as much
3. The force is 1/2 as much
4. The force is 4 times as much
   
   
5. The Sun goes to 1/2 its current distance, but twice its current mass.
1. The force doesn't change
2. The force is 8 times as much
3. The force is 1/8 as much
4. The force 1/4 as much