a) What is the magnitude of the gravitational force that the Sun exerts on Saturn?
b) What is the magnitude of the gravitational force that Saturn exerts on the Sun?
To find the magnitude of the gravitational force between two objects, we can use Newton's Law of Universal Gravitation. The formula is:
F = (G * m1 * m2) / r^2
Where:
F is the magnitude of the gravitational force
G is the gravitational constant (approximately 6.673 × 10^-11 N(m/kg)^2)
m1 and m2 are the masses of the two objects
r is the distance between the centers of the two objects
a) To find the magnitude of the gravitational force that the Sun exerts on Saturn, we need to know the masses of the Sun and Saturn, as well as their distance. The mass of the Sun is approximately 1.989 × 10^30 kg, and the mass of Saturn is approximately 5.683 × 10^26 kg. The average distance between the Sun and Saturn is approximately 1.429 × 10^9 kilometers (or 1.429 × 10^12 meters).
Plugging these values into the formula, we get:
F = (6.673 × 10^-11 N(m/kg)^2 * 1.989 × 10^30 kg * 5.683 × 10^26 kg) / (1.429 × 10^12 m)^2
Calculating this expression will give us the magnitude of the gravitational force that the Sun exerts on Saturn.
b) To find the magnitude of the gravitational force that Saturn exerts on the Sun, we can use the same formula and plug in the masses of Saturn and the Sun, as well as the same distance. However, it's important to note that this gravitational force will be equal in magnitude but opposite in direction to the force calculated in part a). This is due to Newton's third law of motion, which states that for every action, there is an equal and opposite reaction.