# Ratio of projectile to ejecta mass, shoot the moon.

• Spinnor
In summary, the conversation discussed shooting the surface of the moon with different sized steel balls at high speeds and whether there is a simple formula for the mass of the ejecta based on the mass of the projectile. A helpful website with a calculator and math behind it was shared, and it was discovered that for sizes up to 10 m, the mass of the projectile is roughly proportional to the volume of ejecta, and above that size, the relationship is described by a power law with an exponent less than 1. This is an example of scale invariance, where one picture can be used for a range of projectile masses and ejecta volumes.
Spinnor
Gold Member
Say we shoot the surface of the moon with various sized steel balls of size a cm and larger, say up to a km in size. Say the balls hit the surface of the moon moving at 20,000 mph. Is there a simple formula for the mass of the ejecta as a function of the mass of the projectile? Will the formula depend on whether the projectile hits dust or rock or a combination of the two?

Thanks for any help!

Wow, nice find!

Used the above calculator, seemed buggy for multiple calculations, and got the following result. For a steel projectile striking the moon at 10,000 mph perpendicularly, the mass of the projectile, M, was roughly proportional to the volume, V, of ejecta for sizes from 1 cm to 10 m,

M ≈ V

above that size

M^α ≈ V

Where α is less then 1.

Is the above an example of scale invariance? If I draw a picture of the projectile next to the volume of ejecta I can change the scale but not have to redraw the picture, one picture works for a range of projectile masses and ejecta volume?

I can say that there is indeed a simple formula for the ratio of projectile to ejecta mass. This formula is known as the conservation of momentum, which states that the total momentum of a system remains constant before and after a collision. In this case, the total momentum of the system would be the mass of the projectile multiplied by its velocity, which is equal to the mass of the ejecta multiplied by its velocity.

Therefore, the formula for the ratio of projectile to ejecta mass would be:

(Projectile mass x Projectile velocity) / (Ejecta mass x Ejecta velocity)

This formula would apply regardless of whether the projectile hits dust, rock, or a combination of the two. However, the mass of the ejecta may vary depending on the composition of the surface it is hitting. For example, if the projectile hits a rocky surface, the ejected material may contain larger and denser fragments compared to hitting a dusty surface.

Additionally, the size of the projectile may also affect the ratio of projectile to ejecta mass. A larger projectile would have a greater impact force and may result in a higher ratio of ejecta mass compared to a smaller projectile.

I hope this helps answer your question and provides some insight into the relationship between projectile and ejecta mass during a collision on the surface of the moon.

## 1. What is the significance of the ratio of projectile to ejecta mass in shooting the moon?

The ratio of projectile to ejecta mass is a crucial factor in determining the success of shooting the moon. This ratio determines the amount of energy transferred from the projectile to the ejecta, which ultimately determines the trajectory of the ejecta and its ability to reach the moon.

## 2. How is the ratio of projectile to ejecta mass calculated?

The ratio of projectile to ejecta mass is calculated by dividing the mass of the projectile by the mass of the ejecta. This can be done using either imperial or metric units, as long as the units are consistent.

## 3. What is the ideal ratio of projectile to ejecta mass for shooting the moon?

The ideal ratio of projectile to ejecta mass for shooting the moon depends on various factors such as the distance to the moon, the composition of the projectile and ejecta, and the desired trajectory of the ejecta. Generally, a higher ratio results in a more powerful and accurate shot, but it may also require a larger and more costly projectile.

## 4. Are there any risks associated with shooting the moon using a high ratio of projectile to ejecta mass?

Yes, there are potential risks associated with using a high ratio of projectile to ejecta mass, such as damaging the launching device or causing unintended consequences on the moon's surface. It is important to carefully consider and calculate the necessary ratio to ensure a safe and successful launch.

## 5. Can the ratio of projectile to ejecta mass be adjusted during the launch process?

Yes, the ratio of projectile to ejecta mass can be adjusted during the launch process by altering the amount of propellant or the design of the projectile. However, this should only be done by trained professionals and with careful consideration of the potential consequences.

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