Final answer:
By applying Newton's Universal Law of Gravitation and using the given data, the Earth is found to be approximately 1.5 * 10^11 meters from the Sun, with an orbital speed of about 30 km/s.
Step-by-step explanation:
The question at hand involves applying Newton's Universal Law of Gravitation to find the distance between the Earth and the Sun and calculating the tangential speed of the Earth orbiting the Sun. The force of gravity (F) is given by the equation:
F = G * (m1 * m2) / r^2
where G is the gravitational constant (G = 6.674 * 10^-11 N * m^2/kg^2), m1 and m2 are the masses of the two bodies, and r is the distance between their centers. Using the provided mass of the Sun (1.99 * 10^30 kg), the mass of the Earth (5.98 * 10^24 kg), and the force of gravity (3.55 * 10^22 N), we can solve for r.
After rearranging the formula and solving for r, we find that the Earth is approximately 1.5 * 10^11 meters from the Sun.
The tangential speed (v) of the Earth can be found using the formula:
v = sqrt(G * m1 / r)
By substituting the already calculated distance (r) and the known mass of the Sun (m1), we can calculate the Earth's orbital speed, which is approximately 30 km/s.