# Deflect Asteroid w/ Collisions: Calculating Theta & MJ Interractions

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• dedocta
In summary, the conversation discussed the feasibility of deflecting an asteroid with a collision of ~32MJ of direct energy. The speaker had created an excel spreadsheet to calculate the necessary number of collisions to change the asteroid's trajectory by a certain distance at a certain time. It was noted that energy is not as important as momentum in these calculations and for short timescales, the impact direction does not matter. However, for longer timescales, orbital mechanics must be taken into consideration.
dedocta
TL;DR Summary
I'm looking for a way to calculate how much an asteroids trajectory would change, based off of a collision event.
In short, I was trying to look into feasibility of deflecting an asteroid with a collision of ~32MJ of direct energy. I wanted to know how many collisions are necessary to deflect at a given time out (distance away.)

I found this link, where the collision is perpendicular to the motion of the asteroid:

https://physics.stackexchange.com/q...an-asteroid-with-force-always-perpendicular-tSo, taking the following equation, and with the ideal scenario of a perpendicular collision we are left with an isosceles triangle, where we can solve for Theta based off of the distance away of the asteroid and the distance we want to deflect / modify trajectory.

𝑚(𝑣1^2)(1−cos(𝜃))

I then created an excel spreadsheet to calculate theta based off of the distance away and deflection distance, and asked how many 32MJ interractions it would take to change the trajectory by a certain distance at a certain time of collision. It would appear smaller asteroids it would be possible to change trajectories with this, however, not so much for the lower and upper bounds of the Chicxilub asteroid and another larger current NEO.

Would this be an acceptable way to do this? If so, I've been stuck on where to go next if the collision is not perpendicular, if anyone had any input?

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Energy is largely useless for these calculations. It is all about momentum. A more massive object with the same energy in the asteroid reference frame will have a much larger effect on the orbit.

For short timescales (short compared to an orbit) the impact direction doesn't matter that much for the calculation: You give the asteroid a velocity change v that depends on your impact only, after time t its position will have changed by v*t. For longer timescales you have to consider orbital mechanics. As an extreme case: After one orbit the object will return to where it was, no matter how the impact was (neglecting perturbations by planets or similar). It might return earlier or later, however, that can work as deflection, too.

dedocta

## 1. What is the purpose of calculating theta and MJ interactions when deflecting an asteroid with collisions?

The purpose of calculating theta and MJ interactions is to determine the optimal angle and energy required to successfully deflect an asteroid using a collision. This information is crucial in planning and executing a successful asteroid deflection mission.

## 2. How is theta calculated when deflecting an asteroid with collisions?

Theta is calculated by using the law of conservation of momentum, which states that the total momentum before a collision is equal to the total momentum after the collision. By knowing the mass and velocity of the asteroid and the deflecting object, the angle of deflection can be calculated using trigonometry.

## 3. What is the role of MJ interactions in asteroid deflection?

MJ interactions refer to the combination of the asteroid's mass and velocity, which determines its kinetic energy. This energy plays a crucial role in the success of asteroid deflection, as it determines the amount of force needed to change the asteroid's trajectory.

## 4. How accurate are the calculations for deflecting an asteroid with collisions?

The accuracy of the calculations depends on the accuracy of the input data, such as the mass and velocity of the asteroid and the deflecting object. It is important to use precise and up-to-date data to ensure the accuracy of the calculations.

## 5. Can deflecting an asteroid with collisions cause any potential risks or consequences?

There is always a risk when attempting to deflect an asteroid, as any miscalculations or unexpected factors could potentially cause the asteroid to collide with Earth. It is important to thoroughly assess and plan for all potential risks before attempting an asteroid deflection mission.

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