Hello everyone! Should be obvious it's my first time here. I'm looking for assistance not for myself, but for my girlfriend. She's got a college science class that up until now I was able to help her with, but unfortunately my physics knowledge (one year in high school, eight years ago now) did not cover finding the velocity in an elliptical orbit. 1. The problem statement, all variables and given/known data An asteroid in an elliptical orbit about the Sun travels at 1.2 x 106 m/s at perihelion (the point of closest approach) at a distance of 2.0 x 108 km from the Sun. How fast is it traveling, in m/s, at aphelion (the most distant point), which is 8.0 x 108 km from the Sun? Hint: Use conservation of momentum. I'm hoping that it's just something simple, something that maybe she missed in her notes. From what I can tell: The problem is looking for the velocity of the asteroid at the aphelion of it's orbit, in m/s² We're given the both the distance at perihelion (2 x 108 km) and the distance at aphelion (8 x 108 km), as well as the velocity at perihelion (1.2 x 106 m/s). Further the problem states the asteroid is travelling around "the Sun", which to my mind signifies the problem uses our own sun. 2. Relevant equations This is where we're stuck. From my memories I don't ever recall going over velocities in an elliptical orbit. I've literally got nothing to work with from my own memory, though my intuition states that the problem should contain enough information to solve it. My girlfriend's list of formulas don't seem to include anything using two measures of distance, and two measures of velocity. Due to this, we're stumped. I couldn't seem to find anything which would be immediately helpful after probably twenty minutes of google searching perhaps due to my not knowing proper terms to search for. 3. The attempt at a solution So that's the situation. I'd like to attempt a solution, but neither of us knows where to begin. I'm left with the questions: What is the formula for finding the velocity at aphelion(taking into consideration the conservation of momentum per the question)? Should the gravitational force of the Sun play a role in this equation? (I feel like the problem mentioned the Sun specifically as opposed to any other star in the universe) Is the answer much simpler than I'm making the problem out to be? So to anyone who offers help, thank you very much.