An astronaut on the Moon simultaneously drops a feather and a hammer. The fact that they land together shows that:

Options

A. no gravity forces act on a body in a vacuum
B. the acceleration due to gravity on the Moon is less than on Earth
C. in the absence of air resistance all bodies at a given location fall with the same acceleration
D. the feather has a greater weight on the Moon than on Earth

Explanation

To solve the question regarding why a feather and a hammer dropped by an astronaut on the Moon land together, we can analyze the options provided and apply our understanding of physics concepts, particularly the effects of gravity and air resistance.

### Step-by-Step Solution:

1. **Understanding the Environment**:
- The Moon has a very thin atmosphere, which means there is almost no air resistance. On Earth, a feather falls slowly due to air resistance, while a hammer falls quickly due to its weight.

**Hint**: Consider the role of air resistance in the motion of falling objects.

2. **Analyzing the Options**:
- **Option 1**: "No gravity forces act on a body in a vacuum."
- This statement is incorrect. Gravity acts everywhere, even in a vacuum. The Moon has gravity, albeit weaker than Earth's.

**Hint**: Remember that gravity is a universal force that acts on all masses.

- **Option 2**: "The acceleration due to gravity on the Moon is less than that on Earth."
- While this statement is true (the Moon's gravity is about 1/6th that of Earth's), it does not explain why the feather and hammer fall together. The acceleration due to gravity affects all objects equally regardless of their mass.

**Hint**: Think about how gravity affects different objects in the same location.

- **Option 3**: "In the absence of air resistance, all bodies at a given location fall with the same acceleration."
- This statement is correct. In the vacuum of the Moon, both the feather and the hammer experience the same gravitational acceleration, leading them to fall at the same rate.

**Hint**: Consider how the absence of air changes the dynamics of falling objects.

- **Option 4**: "The feather has a greater weight on the Moon than on Earth."
- This statement is false. The weight of an object is the product of its mass and the acceleration due to gravity. Since the Moon's gravity is less, the feather's weight on the Moon is also less than on Earth.

**Hint**: Recall the formula for weight and how it changes with gravity.

3. **Conclusion**:
- The correct explanation for why the feather and hammer land together is given by **Option 3**: In the absence of air resistance, all bodies at a given location fall with the same acceleration.

### Final Answer:
The fact that the feather and hammer land together on the Moon shows that in the absence of air resistance, all bodies at a given location fall with the same acceleration.