Moon Free Fall

Objects are said to be in free fall when the only force acting on them is gravity. Therefore the only force that we need to consider in this situation is the gravity acting on each animal. It's tempting to assume that because the whale has a greater mass than the chihuahua, that it will have a greater acceleration. But it turns out that their acceleration is the same. We can examine the motion of objects in free fall using Newton's Second Law. According to Newton's Second Law, an object's acceleration is: $a= \dfrac{F}{m}$ Now we can plug in for the only force acting, the gravitational force, which is expressed as the weight of an object, or the mass of an object multiplied by gravitational acceleration (of the moon), $g_{moon}.$ $\begin{aligned} &a= \dfrac{F}{m} = \dfrac{W}{m} = \dfrac{mg_{moon}}{m} \\ &a = g_{moon} \\ \end{aligned}$

Thus, all objects have the same acceleration in free fall, regardless of their mass. This was tested in an experiment in 1971 when Commander David Scott of Apollo 15 dropped a feather and a hammer on the moon at the same time. Since the objects have the same acceleration, they hit the ground at the same time.

On moon there is no air resistance and hence both whale and Chihuahua dog are equally pulled by the moon towards itself. $\color{#20A900}\text{It means they are accelerated equally.}$

Galileo conducted several experiments and concluded that the effect of gravity on earthly objects is the same, regardless of the mass of those objects. He argued that in the absence of other forces such as air resistance, all falling objects accelerate towards any surface at the same rate . In the absence of any (significant) resistance to free-fall on the Moon, any two objects should fall at the same rate regardless of mass. Not only whale and Chihuahua dog but every thing will experience an equal acceleration on moon due to the absence of air resistance. Let us take an example of an elephant (1000 Kg) and a boy (10 kg). They both reach the surface of the moon at the same time when released from a same height.

Newton's law of universal gravitation states that:

$F_g = \dfrac {Gm_1m_2}{r^2}$

where

• $F_g$ is the gravitational force acting between two objects,
• $m_1$ and $m_2$ are the masses of the objects
• $r$ is the distance between the centers of their masses of the two objects
• $G$ is the gravitational constant

Let $m_1 = m_{\text{Moon}}$ and $m_2=m_{object}$ , where the object is the whale or chihuahua in this case. By Newton's second law of motion , the acceleration due to gravity of the object $g$ is given by:

$m_{\text{object}}g = \frac {Gm_{\text{Moon}}m_{\text{object}}}{r^2} \implies g = \frac {Gm_{\text{Moon}}}{r^2}$

This means that the acceleration on objects such as whale or chihuahua is independent of their masses. They have the same acceleration so long as they are the same distance from the Moon.

The acceleration each body experiences due to gravitational attraction is independent of their mass And since they're being attracted by the same massive body,their accelerations are the same

This really should have been a sperm whale and a bowl of petunias...

Since it is free fall (no air resistance), they will fall with the same rate of acceleration regardless of their mass.

Note the words FREEFALL and no air resistance .

• If there would have been some air resistance present the bodies would have faced different drags due to their different masses and also due to different body morphology.

• But no air resistance thus no opposing force.Thus the only force that exists now is the gravitational force

  For whale considering its mass to be $M$ :

  $\begin{aligned} &a= \dfrac{F}{M} = \dfrac{W}{M} = \dfrac{Mg_{MOON}}{M} \\ & a = g_{MOON} \\ \end{aligned}$

&

For chihuahua dog considering its mass to be $m$ :

$\begin{aligned} &a= \dfrac{F}{m} = \dfrac{W}{m} = \dfrac{mg_{MOON}}{m} \\ & a = g_{MOON} \\ \end{aligned}$

Gravity pulls us down on earth, and on the moon, gravity is only 1/3 that of Earth, so there's less air resistance. Though YOU might think mass is what matters, it's not the main principle, air resistance & accelaration is. Now we can plug in newtons second law which is A=FM. Next we plug in for the only force acting, our gravitational force, which is expressed as the weight of an object, or the mass of an object multiplied by the gravitational acceleration ( of the moon) g moon.

In a free fall motion the object has only gravity acting on it.and the value of gravity is constant for every object so a=g for both objects

The force of gravity on both objects is different and thus the net force on each object is different. This is because we know that Fg=Fnet ( this is because the only force acting on the objects is Fg). The reason we know that the net force on each object is different is because we know that the force of gravity acting on an object is proportional to its mass. Thus because Fnet=ma where Fnet and m are proportional then we know that for any mass 'a' must be a constant. Thus the two objects both accelerated at the same rate.

Here is a question.

We have two seemingly identical bricks. One is full (a proper brick) and the other one is made from paper and is hollow, therefore the first brick is very heavy while the other one is very light. Their surface roughness is more or less the same.

Now the question is, if we dropped those two bricks from the same height here on Earth (with air resistance) it is clear that the heavy brick will reach the ground first and will reach much higher velocity than the paper one. How is this possible? As stated, all objects in vacuum should reach the same accelerations in freefall, so why are the results different in a non-vacuum environment? To me the only parameter that changes is the absence/presence of the air resistance. But we omitted that by saying the surfaces of the bricks are equal. What am I missing?

I will be very glad to know the answer. Thanks.

Everything is attracted by not only moon's gravity at an equal force but all other objects , there is no air on moon to slow it down

As gravity attracts every object in an equal force unless it is too fluffy or soft for air to slow them down. The whale and the chihuahua will fall at the same time

Unless you are Aristo, we all know that if there's no air resistance both animals would get the same acceleration independently of their mass.

No friction, no resistance to overcome.

Call the Soul of $\frac{Galileo}{Galilei}$ if you cannot answer this...

moon has no air means no air resistance therefore both of them have same acceleration as gravity acts equal on both objects

I was going to post 'Even Galileo could have this one right!' but you know what? That might be construed as mocking Galileo and what he did was one of the most important discoveries ever.

Since there is no drag, all objects will have the same acceleration in free fall.