How Do You Calculate the Impact Speed of an Asteroid?

[Gawdany]

Homework Statement

Suppose an asteroid of mass 3.9e21 kg is nearly at rest outside the solar system, far beyond Pluto. It falls toward the Sun and crashes into the Earth at the equator, coming in at an angle of 30 degrees to the vertical as shown, against the direction of rotation of the Earth. It is so large that its motion is barely affected by the atmosphere.

Mass.asteriod = 3.9e21 kg
Mass.Sun = 2e30 kg
Mass.Earth = 6e24 kg
Distance from Earth to Sun: 1.5e11 m
Grav Constant G: 6.7e-11

Homework Equations

Energy Principle
Using the energy principle to solve for the impact speed, I derive the following equation.
Kast + Use + Uas + Uae = Use
(.5)(3.9e21)v^2 -5.36e33 + Uas +Uae = -5.36e33

The Attempt at a Solution

Using the energy principle to solve for the impact speed, I derive the following equation.

Kast + Use + Uas + Uae = Use
(.5)(3.9e21)v^2 -5.36e33 + Uas +Uae = -5.36e33
My main problem is that I do not know how to calculate the potential energy for Uas and Uae because I do not know the distance from the asteriod and the sun, and the distance from the asteriod to the earth. If anyone can tell me how to figure this out I can easily solve for the impact speed. Please help me. Thanks.

 

[cupid.callin]

This is surely NOT a good question

what is ast se as ae ... you ave used?

 

[Gawdany]

This is surely NOT a good question

what is ast se as ae ... you ave used?

Sorry I thought that would be clear based on the context of the question. Uae = potential energy of the asteriod to the earth, Uas = potential energy of the asteriod to the sun, Use = potential energy of the sun to the earth. Where Grav potential energy = -Gm1m2/r, and my problem is finding the r for the distance from the asteriod and the sun, and the distance from the asteriod to the earth

 

[Gawdany]

So nobody is sure how to answer this question?