A moon orbits a planet in the xy plane, as shown in the figure. You want to calculate the force on the moon by the planet at each location labeled by a letter (A,B,C,D). At each of these locations, what are (a) the unit vector r, and (b) the unit vector F in the direction of the force?

the picture looks like this
B

C Planet A

D

No figure. Cannot copy and paste here.

To find the force on the moon at each location labeled by a letter (A, B, C, D), we need to determine the unit vector r (the direction from the planet to the moon) and the unit vector F (the direction of the force on the moon).

(a) To find the unit vector r:
- For location A, the unit vector r points from the planet to the moon. Since the moon is orbiting the planet, the unit vector r points in the radial direction (from the center of the planet towards the moon).
- For location B, the unit vector r also points in the radial direction, from the center of the planet to the moon.
- For location C, the unit vector r points from the moon to the center of the planet.
- For location D, the unit vector r also points from the moon to the center of the planet.

(b) To find the unit vector F:
- The force on the moon by the planet will always act towards the center of the planet, as it is due to the gravitational attraction between the two. Therefore, at each location (A, B, C, D), the unit vector F will point towards the center of the planet.

Please note that without numerical values or more specific information, we can only provide a general explanation for the unit vectors r and F based on the given setup.

To calculate the force on the moon by the planet at each location labeled by a letter (A, B, C, D), you need to determine the unit vector r (the displacement vector from the planet to the moon) and the unit vector F (the direction of the force).

Here's how you can do that:

(a) To find the unit vector r at each location:
1. Draw the vector from the planet (C) to the moon (A, B, C, D).
2. Measure the magnitude of the displacement vector (the length of the line segment from the planet to the moon) at each location. This will give you the value of the magnitude of r.
3. Divide the displacement vector by its magnitude to obtain the unit vector r.

(b) To find the unit vector F in the direction of the force at each location:
1. Use the right-hand rule to determine the direction of the force. Point your thumb in the direction of the moon's motion around the planet (counterclockwise in the xy-plane).
2. The direction your four fingers curl represents the direction of the force.
3. Normalize the direction vector to obtain the unit vector F.

By following these steps, you can calculate the unit vectors r and F at each location (A, B, C, D) and determine the force on the moon by the planet.