Newton was holding an apple of mass 120 g and thinking about the gravitational forces exerted on the apple by himself and by the Sun. Calculate the magnitude of the gravitational force acting on the apple due to Newton, the Sun, and the Earth, assuming that the distance from the apple to Newton's center of mass is 51 cm and Newton's mass is 79 kg.
1) due to Newton=??
2) due to the Sun =??
3) due to the Earth=??
To calculate the gravitational force acting on the apple due to Newton, the Sun, and the Earth, we can use the formula for gravitational force:
F = (G * m1 * m2) / r^2
Where:
F is the gravitational force
G is the gravitational constant (approximately 6.67430 × 10^-11 m^3⋅kg^−1⋅s^−2)
m1 and m2 are the masses of the two objects
r is the distance between the centers of the two objects
1) Gravitational force due to Newton:
First, we need to convert the mass of the apple from grams to kilograms:
120 g = 0.12 kg
Now we can substitute the values into the formula:
F_newton = (G * m1 * m2) / r^2
F_newton = (6.67430 × 10^-11 m^3⋅kg^−1⋅s^−2 * 0.12 kg * 79 kg) / (0.51 m)^2
2) Gravitational force due to the Sun:
The mass of the Sun is approximately 1.989 × 10^30 kg. We'll assume that the distance between the center of the apple and the center of the Sun is much larger than 51 cm (0.51 m).
F_sun = (G * m1 * m2) / r^2
F_sun = (6.67430 × 10^-11 m^3⋅kg^−1⋅s^−2 * 0.12 kg * 1.989 × 10^30 kg) / r^2
3) Gravitational force due to the Earth:
The mass of the Earth is approximately 5.972 × 10^24 kg. We'll assume that the distance between the center of the apple and the center of the Earth is 51 cm (0.51 m).
F_earth = (G * m1 * m2) / r^2
F_earth = (6.67430 × 10^-11 m^3⋅kg^−1⋅s^−2 * 0.12 kg * 5.972 × 10^24 kg) / (0.51 m)^2
By plugging in the respective values and performing the calculations, you can find the magnitudes of the gravitational forces due to Newton, the Sun, and the Earth.