Final answer:
The approximate magnitude of the gravitational force exerted by the Sun on the Voyager 1 spacecraft can be calculated using Newton's law of universal gravitation with the known values of the masses of the Sun and Voyager 1, and their separation distance.
Step-by-step explanation:
The question asks for the approximate magnitude of the gravitational force exerted by the Sun on the Voyager 1 spacecraft when they are separated by 17.0 billion kilometers. To solve this, we use Newton's law of universal gravitation, which states that the force of attraction between two bodies is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers. The formula is:
F = G * (m1 * m2) / r^2
Where:
- F is the force of gravity
- G is the gravitational constant, approximately 6.674 x 10^-11 N(m/kg)^2
- m1 and m2 are the masses of the Sun and the spacecraft, respectively
- r is the distance between the centers of the two bodies
Given:
- m1 (mass of the Sun) = 1.989 x 10^30 kg (standard astronomical value)
- m2 (mass of Voyager 1) = 803 kg
- r = 17.0 billion km = 1.7 x 10^10 km = 1.7 x 10^13 m (conversion from km to m)
Plugging in these values:
F = (6.674 x 10^-11 N(m/kg)^2) * (1.989 x 10^30 kg * 803 kg) / (1.7 x 10^13 m)^2
We would perform the multiplication and division to find the approximate force in Newtons (N).