If mass does not affect the speed at which they fall, then the mass of the object they are falling towards should not matter either, and yet obviously it does.
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They fell slower because the acceleration due to gravity is considerably smaller (about one-sixth) on the Moon than it is on Earth. This is because the Moon has considerably smaller mass than the Earth.
The way to calculate this acceleration is with this formula:
g = GM / R^2
* g is the acceleration we are trying to calculate.
* G is the gravitational constant.
* M is the mass of the massive body (in this case, the Moon)
* R is the radius of the massive body (the Moon)
As the mass (M) increases, so does the acceleration (g).
The mass of the planet affects the speed, the mass of the object is negligable. The moon’s gravity is lower since it is of less mass. So, after releasing an object, something on Earth would accelerate down at 9.8 meters/second per second whereas something on the moon would only drop down 1.6 meters/second per second.
Edit: fixed math
It’s actually harder to ELI5 this one than it is to use equations.
When an object changes the speed at which it’s moving that is called acceleration. If an object is still and starts moving, it is said to be accelerating.
In order for an object to accelerate, a force must be applied to that object. An object in motion will stay in motion moving in a straight line or will stay at rest unless acted upon by some unbalanced force (Newton’s first law).
When an unbalanced force acts upon an object, the rate at which the speed of that object changes depends on the mass of that object and the magnitude of the force applied to that object (Newton’s second law). Acceleration is determined by the mass of the object and the force applied to that object.
With these 3 things in mind we can look at what it means to drop something. When you drop something it goes from being at rest to moving. Therefore, the object is accelerating. Because the object is accelerating, we know that the object is being acted upon by an unbalanced force (newton’s 1st law). We can find the value of that force by measuring the mass of the object and the acceleration of the object as it falls (newton’s 2nd law). But what is that force?
All objects with mass exert a gravitational force. That is to say all objects with mass apply a force to other objects. When we drop an object we’re seeing gravitational force in action. **The magnitude of that gravitational force depends on the mass of the two objects and the distance they are from each other**.
(This is where the equations would come in handy some I’m just going to hand wave it.)
If you know the gravitational force applied to an object you essentially know the acceleration that will be applied to the object if gravity is the only force acting on that object. When you actually work the math out, you find that the mass of the object in motion gets cancelled out meaning it’s completely irrelevant.
Now with the equations:
The formula for Force is f=ma (Force equals mass time acceleration).
The formula for calculating gravitational force between two objects is f=G(m1*m2r²) (force equals the gravitational constant times the mass of object 1 times the mass of object 2 divided by the distance between the centers of mass squad)
The “f” in each equation here is the actually same value so we can merge these two equations to look like this: m1a=G(m1*m2r²). For the sake of explanation I’ve labeled the smaller object as m1 here. When you solve for acceleration in this equation you find the m1 cancels itself out. Meaning the mass of the smaller object doesn’t matter.
It’s slightly more complicated than that because technically the objects are both accelerating toward each other. But to explain that we have to get into frames of reference and stuff and I’m on mobile, this was hard enough to type out.
They fall the same way on earth UNTIL AIR RESISTANCE BECOMES RELEVANT. Which for a feather, is pretty soon. But if you drop both from let’s say, 5millimeters onto a table, they will fall almost at the same speed. It’s just, with such a dense atmosphere, here on earth most things are slows down by air and the only way to overcome it is to have a big mass, therefore more force pulling the item to the floor. This extra force will help the hammer to win air resistance, for a while. But also a falling hammer will reach a speed at which air resistance will stabilize the fall, it’s called terminal velocity, the speed at which a specific object would stop accelerating because of air drag.
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