Question

Comet P/1999 R1 has a perihelion of 0.0570 AU and aphelion of 4.99 AU. Using the results of the previous problem, find its speed at aphelion. (Hint: The expression is for the perihelion. Use symmetry to rewrite the expression for aphelion.)

Reference Problem:
Given the perihelion distance, p, and aphelion distance, q, for an elliptical orbit, show that the velocity at perihelion, vp, is given by vp=√2GMSun(q+p)qp. (Hint: Use conservation of angular momentum to relate vp and vq, and then substitute into the conservation of energy equation.)
(a) ( approx 39.8 , {km/s} )
(b) ( approx 22.3 , {km/s} )
(c) ( approx 42.1 , {km/s} )
(d) ( approx 28.6 , {km/s} )

Answer 1

To find the speed of Comet P/1999 R1 at aphelion, use the expression for the perihelion velocity and substitute the given distances. The speed at aphelion is approximately 22.3 km/s.

Step-by-step explanation:

To find the speed of Comet P/1999 R1 at aphelion, we need to use the expression for the perihelion velocity given in the reference problem and substitute the values of the perihelion and aphelion distances.

The expression for the perihelion velocity, vp, is vp=√2GMSun(q+p)/(qp), where G is the gravitational constant, MSun is the mass of the Sun, and q and p are the aphelion and perihelion distances respectively.

Using the given values of p=0.0570 AU and q=4.99 AU, we can substitute these values into the expression and calculate the velocity at the aphelion.

After substituting the values, the speed at aphelion is approximately 22.3 km/s.