Final answer:
The asteroid's speed at its closest approach to the Sun can be calculated using the conservation of angular momentum. The final speed can be found through the relationship (Initial Distance * Initial Speed) = (Final Distance * Final Speed), which yields a result of 77.5 km/s, which doesn't match the answer options given.
Step-by-step explanation:
The student has asked about the speed of an asteroid when it is at its closest approach to the Sun, given that its speed is 15.5 km/s at 2.00 AU. This question can be solved using the conservation of angular momentum, which states that the product of the radial distance and the tangential velocity of the asteroid remains constant for an object in orbit around the Sun (assuming no external torques).
Using this principle, we can set up the following relationship:
- Initial angular momentum (L1): (2.00 AU) * (15.5 km/s)
- Final angular momentum (L2): (0.400 AU) * (Final Speed)
Since L1 = L2, we can solve for the Final Speed as follows:
(2.00 AU) * (15.5 km/s) = (0.400 AU) * (Final Speed)
Final Speed = (2.00 / 0.400) * 15.5 km/s
Final Speed = 5 * 15.5 km/s
Final Speed = 77.5 km/s.
However, this speed is not one of the options provided, which suggests there may be a mistake in the given options or in the problem setup. The student should check the problem and the answer choices again, or provide additional context if available.