# Speed of a Meteor

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— Elon Musk

## Introduction

Figure 1: Meteor at Twilight. (Source)

One of my coworkers knows one of my brothers (I have three). My brother and this coworker are friends and their families vacation together. They happened to be at a lake one night in Northern Minnesota together and my brother showed this coworker where to look for satellites and meteors. This coworker stopped by my desk and told me about the great time they had just watching the sky and how interesting it was.

I own a small cabin on a lake in Northern Minnesota. Years ago I showed my brother how to find satellites, planets, and meteors. I love to lay on the dock at night and watch the sky. Because Northern Minnesota is so sparsely populated, the sky is incredibly dark and the stars are so much brighter than in the metropolitan region where I spend most of my time. When people visit me at the cabin, I take them out on the dock and introduce them to the world of meteors, satellites, and planets. It is always a good time.

During a recent discussion on our sky-watching activities, a coworker mentioned that some meteor showers have "fast" meteors and some have "slow" meteors. Why are some meteors fast and others slow? What does fast mean? What does slow mean? This is another example of a Fermi problem and some simple mathematics will give us a feel for what the answer is.

## Background

### Meteor Shower Basics

I am not an expert on meteors, so I needed to do some research. It turns out there are three sources of meteors:

• Asteroid belt
The asteroid belt is the source of the slow-moving meteors, which are assumed to originate from collision between objects in the asteroid belt. The Geminides are a good example of this type of meteor shower.
• Comets
Comets have often been compared to "dirty snowballs" that orbit the Sun. They release rocky material as the heat of the Sun causes them to slowly disintegrate. Comets are the source of the fast-moving meteors. The Leonids are a good example of this type of meteor shower.
• Outside of the Solar System
These are very rare and unpredictable, so they would not be part of any well-known meteor shower. However, their velocity could be very high as they would not be in orbit of the Sun (by definition) and would be following hyperbolic trajectories. I will not be addressing this case here. However, one case has been discovered and it was moving very fast.

### Computing Escape Velocity

All estimates of meteor velocity that I have seen involve a discussion of escape velocity. Escape velocity is the lowest velocity that a body must have in order to escape the gravitational attraction of a particular planet or other object.

We can compute the escape velocity by computing the work that a massive body does on a meteor. Equation 1 gives us the force on the meteor exerted by the gravity of an attracting body.

 Eq. 1 ${{F}_{Meteor}}=G\cdot \frac{{{M}_{Body}}\cdot {{m}_{Meteor}}}{{{r}^{2}}}$

where

We can use Equation 1 to derive Equation 2, which is the work (i.e. energy) performed on the meteor by the gravitational field of the attracting body.

 Eq. 2 ${{E}_{Meteor}}=\int\limits_{\infty }^{{{R}_{Body}}}{-{{F}_{Meteor}}\left( r \right)}\cdot dr=G\cdot \frac{{{M}_{Body}}\cdot {{m}_{Meteor}}}{{{R}_{Body}}}$

where

• EMeteor is the work performed on the meteor by the attracting body.
• RBody is the radius of the attracting body (I am assuming the attracting body is spherical).

Equation 3 equates the kinetic energy of the meteor with the work performed on the meteor by the attracting body.

 Eq. 3 $\frac{1}{2}\cdot {{m}_{Meteor}}\cdot v_{Meteor}^{2}=G\cdot \frac{{{M}_{Body}}\cdot {{m}_{Meteor}}}{{{R}_{Body}}}\Rightarrow {{v}_{Meteor}}=\sqrt{2\cdot \frac{G\cdot {{M}_{Body}}}{{{R}_{Body}}}}$

where vMeteor is the speed of the meteor. We will use Equation 3 to estimate the speed of the meteors entering our atmosphere.

## Analysis

### Asteroid-Based Meteor Shower

In this case, we assume that the meteor has somehow broken free of an asteroid with negligible velocity and has simply fallen to the Earth. This means that its velocity at the surface of the Earth will be the escape velocity from the Earth. Figure 2 illustrates the calculation.

Figure 2: Illustration of Velocity for a Meteor Originating in the Asteroid Belt.

This calculation explains the 11 km/s speed sometimes quoted for slow meteors.

### Comet-Based Meteor Shower

Comets orbit the Sun and the meteors generated by comets move at the velocity of a comet. These meteors really are orbiting the Sun and just happen to slam into the Earth. Figure 3 illustrates the calculation of their velocity.

Figure 3: Velocity of a Meteor Originating from a Comet.

This calculation explains the 42 km/s mentioned in the Wikipedia. The Wikipedia also mentions the peak velocity is 71 km/s, which is the speed of a comet-based meteor slamming heading on into an Earth that is moving at 29 km/s around the Sun.

## Conclusion

I have seen the speed of meteors estimated to be anywhere from 11 km/s to 71 km/s. This post has shown where these numbers come from and they appear to be reasonable.

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### 28 Responses to Speed of a Meteor

1. veda says:

Hi, I am veda, it is very simple calculations but very important basic for all. can we measure the meteors enter in to the atmosphere which were not known where it comes. That time also shall we apply this formulas?. And in fig 2 you have mentioned Msun=2.10^30 kg. but u shows as mass of earth. I think it is mass of earth. Please can u reply this mail.
Thanking u
VEDA

• mathscinotes says:

Hi Veda

Thanks for catching the typo in Figure 2. I have corrected it.

The calculations are for meteors that either come from the asteroid belt or that move like comets. There is no way that I know of to simply estimate the speed of meteors that come in from other sources. All the information that I have seen says that these meteors are very rare and we do not know much about them.

2. A Guy Who Really Sucks At Math says:

I got a headache just reading this. If you could somehow translate this from genius into plebeian wordsmith, I'd be grateful. My ability to add words together and create something meaningful is above average. My ability to do so with numbers is significantly less impressive. To be honest, my computational skills are next to nil, and my patience for the same is even less.

With (semi) Genuine Gratitude,
A Guy Who Really Sucks At Math

• mathscinotes says:

Something tells me that you are not nearly as bad at math as you say:) I do need to make one comment. I have worked with a number of people who said they could not do math. As they worked with me on problems, free of the pressure of school and tests, they have seen some of the beauty of the subject. I have even had people get motivated enough to go be to school and study math-related subjects (one recently got a Masters degree in software).

3. How would you differetionate impact craters from comet craters when comet craters might have originated while both the comet and Earth was at perihelion passage. Let us presume that the perihelion velocity of the comet is about seventy five K miles per hour and Earth's is about 66.5K per hour and the comet is ten million miles from Earth at perihelion. One would presume that the velocity of this type debris would be a lot less than calculating the velocity as an independent action, thus creating a much shallower crater than one from an object hitting the Earth when falling from the Asteroid belt. Ninety percent of lunar craters are shallow as are the presumed craters on the Earth. Does this indicate that the greater number of crater events were objects which impacted from shorter distances .

• mathscinotes says:

Hi Norman,

I certainly would not qualify as a meteor/comet/asteroid expert, but I do that there is a wide range of velocities at which these objects hit the Earth. You are correct that the velocity at impact can be very low. I can give you one example. I saw photograph of a large iron-nickel meteorite (tens of tons range) found in the middle of a desert and there was no crater. An astronomer commented that they believe the meteorite came in horizontally and literally dropped at low velocity into its present position.

mathscinotes

4. I do not believe that one in twenty astronomers or scientist believe that comet tails point away from the Sun due to solar wind. Perhaps the explanation is similar to the 33/1/3 ten inch record disc. A point one inch from the foci moves 6.28 inches per revolution. A point at the edge moves 31.42 inches in the same revolution. Same velocity for both points, different distances. In the case of our record disc we cannot measure the time dilation, too small, but in the case of a comet tail which might stretch ten million miles or more we can visibly see that the head is moving at one velocity and the tail is moving at the same velocity but in a different time synergy. Most scientist know that the solar wind does not have enough force to move a megagram of mass, let alone the tail debris of a comet.

• Dewi Morgan says:

The difference in velocity between a comet and its tail is not even close to relativistic. Nothing in the solar system operates close enough to light speed for relativistic effects to be visible to the eye.

The dynamic pressure of the solar wind is about 10^-6 Newtons per square meter, and that's not counting the charge of the tail particles and the strength of the sun's magnetic field which also has an effect. That's plenty to cause the effect seen.

The principles of comet tail formation are reasonably well known and non-contentious at this point, and I can do little better than to point you to the wiki page on it: https://en.wikipedia.org/wiki/Comet_tail

5. veda says:

Hi,
How are you, after this article would u investigate or research on meteors. My friend says in tropical region have data lacking for meteors, is it correct? if it is correct or not , why it is? I have a small doubt, where more meteors are fallen, what about meteors falling in the tropical region. How many meteor radars are close to the tropical region. I hope you will give reply to my mail.
Thanking you
veda

• mathscinotes says:

Hi veda,

I have no data on research currently being done on meteors. I am just an engineer who is trying to use basic math to learn a few things.

mathscinotes

________________________________

6. hy, so im doing an investigation of meteorites and crater shapes as a year 12 physics assesment and i was wondering if you could forward this investigation by using the given velocity to come up with a theoridical Crater shape ( diameter, depth) and the matter propultion due to the impact. thank u.
BTW, as a mathematitian u could also investigate the logistic degradation of meteor matter, to find the model of loss mass and substitute this into equation 4 to come up with the perfect model.

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8. Stathakis Vasilis says:

I have been trying to figure out a similar problem and cannot figure it out or I am not sure of my results. I would appreciate your input if you find it interesting. The problem is to calculate the distance a meteorite would travel in a certain amount of time if it is on a collision course with earth (taking into account that gravity is not constant) . I think your calculation could work and will try to work it out.

• Hello, well since we don't have any numbers, i will just point out the things that is needed.
if you would like to find the attractive pull of the earth from 0 to 9.82 then simply use
g=(Gm)/d^2 where d is the distance at which u want to find g.
hint, use excel and find the distance where g=0 and then simply create an extremely long column where u can see the gravity increasing as distance decreases.

Now things to take into consideration are; the meteors size, total mass, mass loss due to deterioration, and from what you are saying you are looking for the velocity and acceleration of the meteor, so, simply ask your self how far away is the meteor? How big (size and mass) is it? and also try to use excel and the formula for velocity to connect it all to give a close and relevant answer for the velocity or a specific meteor (constant) at any distance (start to collision). i hope that this helps

• Stathakis Vasilis says:

guillaume aveline . Thanks for your reply. I had not thought of using excel. I guess you are a real engineer with the "just do it" approach. I was going on a little more involved path (actually integrating and integrating again).

• oh well thanks, i just finished school but from your reply i seem to have been helpful, and i hope that you reach your aim and beyond. hehe

if you didn't understand think of writing a scientific report.
hehe

9. Elizabeth Brown says:

Thanks for asteroid and comet origins. I see slow moving objects often which could be police helicopters. Now I know meteorites arent just fast.

• mathscinotes says:

If you see slow moving objects in the sky, you may be looking at satellites. Sometimes, you will see an object moving across the night sky at a constant rate with a variable light intensity. That could be a tumbling satellite. I see them all the time.

mathscinotes

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11. A kid who loves math says:

Hey, I'm trying to figure out the velocity of a falling thing (It's basically a pole with a cone on top) I can't figure out where the numbers go.
Here is some stuff to know.
Mass of my object: 1,701 kg
Volume = 0.15m^3
I also want to know whether my thing will burn up when it's falling
(Hint: the melting point of lead is 327.5C and 621.5F)

• A kid who loves math says:

Also it's 220 miles/ 354056 meters above the surface (That's 6,371,000 meters above the center of the Earth) The attracting body is Earth

12. Ray Novotny says:

Hi everyone. If I could strobe a meteor, Could the speed be more accurately determined? Ray

• mathscinotes says:

Strobe with known period, plus some range or angle information would do it. I think most of them are burning up around 80 km to 120 km, which is called the meteoric region. If you assume an altitude, get some angle info, and know the period of the strobe, you can generate an estimate.

mathscinotes

13. Ray Novotny says:

Thanks for the response. If you have a minute feel free to look at a video with the meteor. Thanks again, Ray

• mathscinotes says:

Very cool. Thanks for sharing.

mathscinotes

14. Anonymous says:

Hello! Thank you for you article. I believe that Rearth is in fact the radius of the Earth, and not the diameter. This is wrong in the image.

Cheers!

• mathscinotes says:

Thank You! I have corrected the error.

mark

15. namgay says:

i am thinking if you could solve more on equation 2 because i am confused how did you get R instead of r square at the end