How close will comet come to earth

[scatterbrain8]

I'm given the six orbital parameters for a comet and am asked to find how close it comes to earth, but I'm not sure how to go about this...

Should I calculate the position of the comet and Earth and the comet's perihelion passage? If so, are there equations for this type of thing?

The parameters are a=110 AU, e=0.995, i=89 deg, longitude of the ascending node is 180 deg, argument of perihelion= 0 deg and time of perihelion passage = 2008 March 21

I know it's vernal equinox, but not sure how to quantify the positions...

 

[scatterbrain8]

figured it out, nevermind

 

[Moetasim]

I would approach this question by first understanding the orbital parameters and their significance. The parameter "a" represents the semi-major axis, which is the average distance between the comet and the sun. "e" represents the eccentricity, which describes the shape of the comet's orbit (a perfect circle has an eccentricity of 0, while a highly elliptical orbit has an eccentricity close to 1). "i" represents the inclination, which is the angle between the comet's orbital plane and the plane of Earth's orbit. The longitude of the ascending node and argument of perihelion describe the orientation of the comet's orbit in space. Finally, the time of perihelion passage is the moment when the comet is closest to the sun.

To determine how close the comet will come to Earth, we need to calculate the distance between the comet and Earth at the time of perihelion passage. This can be done using Kepler's laws of planetary motion and the orbital parameters given. Specifically, we can use the equation for the distance of a body from the focus of its elliptical orbit:

r = a(1-e^2)/(1+e*cos(θ))

Where r is the distance between the comet and the sun, a is the semi-major axis, e is the eccentricity, and θ is the true anomaly (the angular distance of the comet from the perihelion point). We can then use this equation to calculate the distance between the comet and Earth at the time of perihelion passage.

Additionally, we can use the time of perihelion passage and the orbital period of the comet to determine the position of the comet and Earth at that time. This can be done using the equation for Kepler's third law:

T^2 = (4π^2/GM)a^3

Where T is the orbital period, G is the gravitational constant, M is the mass of the sun, and a is the semi-major axis. By plugging in the values for the orbital period and semi-major axis given, we can solve for the time of perihelion passage. We can then use this information to calculate the positions of the comet and Earth at that time.

In summary, to determine how close the comet will come to Earth, we need to use the given orbital parameters and equations for Kepler's laws of planetary motion. We can calculate the distance between the comet and Earth at the time