Question

On 20 August 1977, NASA launched Voyager 2. It now is beyond the edge of the solar

system, in an area known as the Heliosheath. As of 9:00 PM, on 29 September 2020, it
was 11 607 005 809 miles from the earth. We still are communicating with it, though
takes over 17 hours for a radio signal from earth (traveling at the speed of light - this is
so cool!) to reach the craft. It used to be the farthest man-made object from the earth,
but was surpassed by its sister craft, Voyager 1. Incredibly, five of Voyager 2's eleven
scientific instruments still are operating, collecting data, and transmitting it back to earth.
All of the hydrazine that it originally contained to use for thruster operation has been
consumed. Currently, the satellite would weigh 1592 lb if it were on earth. Determine the
force of attraction the earth exerted on Voyager 2 on the 2020 date mentioned previously.

Answer 1

The force of attraction that Earth exerts on Voyager 2 is approximately 2.29 x 10^15 Newtons. This calculation involves Newton's law of universal gravitation, considering the masses of Earth and Voyager 2 (converted from 1592 lb to 721.5 kg) and the distance between them (converted from 11,607,005,809 miles to 18,672,760,956 km).

Step-by-step explanation:

The force of attraction that the Earth exerts on Voyager 2 can be calculated using Newton's law of universal gravitation. According to this law, the force of gravity between two objects is directly proportional to the product of their masses and inversely proportional to the square of the distance between them. In this case, the mass of the Earth is constant, so the force of attraction will depend only on the mass of Voyager 2 and the distance between the Earth and the spacecraft. Since the weight of Voyager 2 on Earth is given as 1592 lb, we can convert this to kilograms by multiplying by the conversion factor 0.4536 kg/lb. Therefore, the mass of Voyager 2 is 1592 lb * 0.4536 kg/lb = 721.5 kg. Given that the distance between the Earth and Voyager 2 is 11,607,005,809 miles, we can convert this to kilometers by multiplying by the conversion factor of 1.60934 km/mile. Therefore, the distance between the Earth and Voyager 2 is 11,607,005,809 miles * 1.60934 km/mile = 18,672,760,956 km. Using the formula for gravitational force, F = (G * mass of Earth * mass of Voyager 2) / (distance between Earth and Voyager 2)^2, where G is the gravitational constant (6.67430 x 10^-11 Nm^2/kg^2), we can calculate the force of attraction: F = (6.67430 x 10^-11 Nm^2/kg^2 * (5.972 x 10^24 kg) * (721.5 kg)) / (18,672,760,956 km)^2. Using this equation, we can find that the force of attraction the Earth exerts on Voyager 2 is approximately 2.29 x 10^15 Newtons.