Final answer:
The question does not provide enough information to calculate the angular momentum of Mars in its orbit around the Sun. However, we can calculate the ratio between the angular momentum of Earth in its orbit and its rotational angular momentum.
Step-by-step explanation:
The magnitude of the angular momentum of an object in circular motion is given by the product of the object's mass, velocity, and the radius of its orbit. In the case of Mars orbiting the Sun, we need to know the mass of Mars, its velocity, and the radius of its orbit. Unfortunately, the question does not provide this information. However, we can calculate the angular momentum of Earth in its orbit around the Sun and then compare it to the angular momentum of Mars using the given ratio.
To calculate the angular momentum of Earth, we need the mass of Earth, its orbital velocity, and the radius of its orbit. Using the given information that the angular momentum of Earth is 3.77 x 10^6 times larger than its rotational angular momentum, we can set up the following equation:
Angular momentum of Earth in its orbit = 3.77 x 10^6 * Rotational angular momentum of Earth
Given that the rotational angular momentum of Earth is not provided, we cannot calculate the angular momentum of Mars in a circular orbit around the Sun.