Question

An asteroid in an elliptic orbit experiences a close approach to Earth and is given a gravity assist. Given its semi-major axis and eccentricity, the closest point of its orbit to the Sun is at approximately:

A) 0.75 AU
B) 1 AU
C) 1.25 AU
D) 1.5 AU

Answer 1

The perihelion is the closest point of an asteroid's orbit to the Sun. For the asteroid with a given semi-major axis of 3.78 AU and aphelion of 4.95 AU, its perihelion is approximately 2.61 AU.

Step-by-step explanation:

The closest point of an asteroid's orbit to the Sun is called the perihelion. To find the perihelion distance, you need the semi-major axis and the eccentricity of the orbit. Given a semi-major axis of 3.78 AU for the asteroid, the perihelion is one-half the sum of the semi-major axis and the eccentricity. Using the details provided, we do not have the exact value for eccentricity, but we know that the aphelion distance (the farthest point) is 4.95 AU. So, if the sum of aphelion and perihelion distances equals twice the semi-major axis (7.56 AU), the perihelion can be found by subtracting the aphelion distance from twice the semi-major axis.

Calculating the perihelion distance:

7.56 AU - 4.95 AU = 2.61 AU.

Therefore, the closest approach of the asteroid's orbit to the Sun after applying a gravity assist, assuming no significant change in its orbit's eccentricity, would be at the perihelion, which is approximately 2.61 AU.