Orbit Collision: Find New Earth Orbit Axes (A,B) in Terms of R

In summary, to find the new semi-major and semi-minor axes on the new Earth orbit after a collision with Halley's comet, we need to consider the conservation of angular momentum and the fact that the Earth's new velocity is in the same direction as before. The semi-minor axis may not necessarily remain the same, as the origin of the orbit may no longer be at the previous focus (the sun). The new semi-major axis can be given by the equation a-c = R, where a is the semi-major axis and c is the distance from the origin to the focus.
  • #1
me9900
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Homework Statement


If Halley's comet hits the Earth head on and after the collision the Earth continues to move in its initial direction but with 12% greater speed, find the new semi-major and semi-minor axes on the new Earth orbit in terms of the earth-sun distance (R) for the present circular orbit of the earth.


Homework Equations


F=ma
F=GMm/r^2


The Attempt at a Solution

 
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  • #2
Remember that the Earth's angular momentum is conserved through its orbit.
L = mvr

And consider that, since the Earth's new velocity is in the same direction as before, it would go back to R for its semi-minor axis, due to the fact that the new velocity is in a single coordinate only, and it therefore has no force pushing it tangentially from its original path - it only moves tangential relative to it's old path as it diverges from it due to higher speed.
 
  • #3
I don't necessarily agree with R remaining as the semi-minor axis because the origin of orbit(now an ellipse) isn't at the previous focus (being the sun). However, could R be given by a-c=R or (semi-major axis)-(distance from origin to focus)=R ?
 

Related to Orbit Collision: Find New Earth Orbit Axes (A,B) in Terms of R

1. How does an orbit collision occur?

An orbit collision occurs when two objects in orbit around each other come close enough to collide. This can happen due to gravitational forces or external influences such as a change in the orbit's shape or size.

2. What are the potential consequences of an orbit collision?

The consequences of an orbit collision depend on the size and speed of the objects involved. In some cases, it can result in the destruction of one or both objects. It can also create debris that can be hazardous to other objects in orbit.

3. Can we predict when an orbit collision will occur?

Yes, scientists use mathematical models and computer simulations to predict potential orbit collisions. By monitoring the orbits of objects in space and calculating their trajectories, we can estimate when an orbit collision may occur.

4. How can we prevent an orbit collision?

To prevent an orbit collision, scientists and engineers use various techniques such as adjusting the orbits of objects, using propulsion systems to change the trajectory, or destroying debris that may cause potential collisions.

5. How do we find new Earth orbit axes (A,B) in terms of R?

To find new Earth orbit axes (A,B) in terms of R, we use mathematical equations and data from observations of Earth's orbit. These equations take into account the gravitational pull of the sun and other planets, as well as the Earth's rotation and tilt, to determine the new orbit axes in relation to the distance from the sun, represented by R.

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