Assume this asteroid has the shape of a sphere. A rock sitting on the

surface of the asteroid has a weight of 100 newtons. What would the weight
of this rock be if it were moved to a distance above the surface equal to
the radius of the asteroid? It may be helpful to draw a picture to better
visualize what is going on. How is the mass of the rock affected by its
change in position?

this is hard to answer, but because it is 80 newtons, the asteroid falls into jupiters hands.

To solve this problem, we need to consider the concept of gravitational force and its relationship with distance. Let's break down the steps to understand how the weight of the rock changes when moved to a distance above the surface equal to the radius of the asteroid:

1. Gravitational Force: The weight of an object on the surface of a celestial body, such as an asteroid, is caused by the gravitational force between the object and the celestial body. The force of gravity is directly proportional to the mass of the object and inversely proportional to the square of the distance between them.

2. Weight on the Surface: When the rock is sitting on the surface of the asteroid, it experiences a gravitational force, which we will call F₁. Let's assume the mass of the rock is 'm'. Therefore, the weight of the rock, which is equal to the force of gravity acting on it, is given by F₁ = m * g, where 'g' represents the acceleration due to gravity.

3. Weight Above the Surface: If we move the rock to a distance above the surface equal to the radius of the asteroid, we need to consider the change in distance from the center of the asteroid.

a. To visualize this, imagine the rock placed on the surface of a sphere. When moved to a distance equal to the radius, it will sit exactly at the outer surface of the sphere.

b. Now, if we calculate the force of gravity acting on the rock at this new position, we need to consider the new distance. The new force of gravity, which we will call F₂, is given by F₂ = m * g₂, where 'g₂' represents the acceleration due to gravity at this new distance.

4. Relationship between Distance and Acceleration due to Gravity: As mentioned earlier, the force of gravity is inversely proportional to the square of the distance between two objects. In this case, when the rock is moved to a distance equal to the radius of the asteroid, the new distance is effectively doubled.

a. The relationship between distances and acceleration due to gravity is given by the equation: g₂ / g₁ = (r₁ / r₂)²

Where:
- g₁ is the acceleration due to gravity on the surface of the asteroid.
- g₂ is the acceleration due to gravity at a distance equal to the radius of the asteroid.
- r₁ is the radius of the asteroid.
- r₂ is the distance above the surface, equal to the radius of the asteroid.

5. Solving for g₂:
Rearranging the equation from step 4, we get g₂ = g₁ * (r₁ / r₂)²

6. Calculating Weight Above the Surface: Using the new acceleration due to gravity (g₂), we can calculate the weight of the rock at the new position. The weight, which is equal to the force of gravity, is given by F₂ = m * g₂.

Now that we understand the steps involved, we can solve the problem by substituting the given values into the equations derived above.