Question relating to diameters of craters on the moon

[Remon]

Homework Statement

What was the diameter of the object that impacted the moon 3 to 4 billion years ago and created Mare Humorum

Homework Equations

N(t) = N₀(1/2)ⁿ

The Attempt at a Solution

I'm completely lost by this question so I haven't attempted a solution yet but I think I'm suppose to use the half-life equation to find the size of the impact (since it heated the moon's interior by radioactive decay, which directly relates to the half-life equation)
Thanks in advance.

 

[haruspex]

Whatever the method, it is clearly going to depend a lot on other equations and data you have not quoted. If it is to do with radioactive decay, you need some way of assessing how much heat was needed to make the mare as it is today. How big is the mare? How much rock needed to be melted (doesn't that depend on how deep the impactor went?)? How much heat is needed to melt 1m^3 rock? How much fission energy is available in 1m^3 of impactor?

 

[Remon]

Whatever the method, it is clearly going to depend a lot on other equations and data you have not quoted. If it is to do with radioactive decay, you need some way of assessing how much heat was needed to make the mare as it is today. How big is the mare? How much rock needed to be melted (doesn't that depend on how deep the impactor went?)? How much heat is needed to melt 1m^3 rock? How much fission energy is available in 1m^3 of impactor?

Thank you for replying back, but sorry I made a mistake, I asked the professor and he said that there should be no equations used, he told that the textbook has the answer but I read the section in the book (a couple of pages) where it talks about the moon's craters multiple times but I still couldn't find anything, these were his exact words "There is no equation, but the text does explain what you need."
The book does contain a picture I attached of the mare which the prof. talked about but it doesn't seem to help very much

 

[haruspex]

Thank you for replying back, but sorry I made a mistake, I asked the professor and he said that there should be no equations used, he told that the textbook has the answer but I read the section in the book (a couple of pages) where it talks about the moon's craters multiple times but I still couldn't find anything, these were his exact words "There is no equation, but the text does explain what you need."
The book does contain a picture I attached of the mare which the prof. talked about but it doesn't seem to help very much

As you say, the pictures and text you posted don't help. If it's only a couple of pages, can you post the entire text? Are you sure there are no other mentions in the book?

 

[Remon]

As you say, the pictures and text you posted don't help. If it's only a couple of pages, can you post the entire text? Are you sure there are no other mentions in the book?

Ok, I posted 3 pictures I took from the section of the book that talks about craters and Mare Humorum (3 pages in total), but, while looking further, I found another section that talked about impacts (I posted a picture of a page called "page from different section" so you can take a look) and it says near the bottom of the page "that craters are typically about 10 times as wide as the objects that create them", meaning that if I have the diameter of the mare, I can very simply find the diameter of the object that hit it by dividing the diameter of the mare by 10, is it really this simple? I looked up the diameter of the mare and found it to be ≈ 400 km wide, meaning that the diameter of the object that hit it is 40 km wide, and the closest answer I have is 30 km (from the choices I'm given). I'm not entirely sure if this is close enough, especially when the rest of the choices I'm given for the answer are 100, 300, 600, and 1000 km which are obviously much bigger than the answer I got

 

[D H]

I found another section that talked about impacts and it says near the bottom of the page "that craters are typically about 10 times as wide as the objects that create them", meaning that if I have the diameter of the mare, I can very simply find the diameter of the object that hit it by dividing the diameter of the mare by 10, is it really this simple?

It's that simple. Well, almost that simple. Look at your image of the mare. The mare is a bit bigger than the crater. Divide by 10 and then reduce it a bit to account for this apparent fact.

 

[Remon]

It's that simple. Well, almost that simple. Look at your image of the mare. The mare is a bit bigger than the crater. Divide by 10 and then reduce it a bit to account for this apparent fact.

Hmm... that actually makes sense because the crater can't be the exact same size as the impact and then my answer would be closer to 30 km. Thank you

 

[haruspex]

It's that simple. Well, almost that simple. Look at your image of the mare. The mare is a bit bigger than the crater. Divide by 10 and then reduce it a bit to account for this apparent fact.

One of the images is a reconstruction of the original crater, so Remon can just use that.

 

[Remon]

One of the images is a reconstruction of the original crater, so Remon can just use that.

Yeah but there's no scale on it or any information to tell me how wide it is, so the picture doesn't help much, but I looked up its diameter (which was about 400 km) so now its all good :)