Newton was holding an apple of mass 273 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 the Sun. (You may enter your calculation using scientific notation.) (Take the mass of the Sun to be 1.99 × 1030 kg1.99 × 1030 kg and the distance from the Sun to be 149.6 × 109 m149.6 × 109 m .)
Question
Newton was holding an apple of mass 273 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 the Sun. (You may enter your calculation using scientific notation.) (Take the mass of the Sun to be 1.99 × 1030 kg1.99 × 1030 kg and the distance from the Sun to be 149.6 × 109 m149.6 × 109 m .)
Solution
To calculate the gravitational force acting on the apple due to the Sun, we can use Newton's law of universal gravitation. The formula is:
F = G * (m1 * m2) / r^2
where:
- F is the force of gravity,
- G is the gravitational constant (6.674 * 10^-11 N(m/kg)^2),
- m1 and m2 are the masses of the two objects (in this case, the apple and the Sun),
- r is the distance between the centers of the two objects.
Let's plug in the values:
m1 (mass of the apple) = 273 g = 0.273 kg (we need to convert grams to kilograms because the gravitational constant G is in terms of kilograms), m2 (mass of the Sun) = 1.99 * 10^30 kg, r (distance from the Sun to the apple) = 149.6 * 10^9 m.
So, the gravitational force F is:
F = (6.674 * 10^-11 N(m/kg)^2) * ((0.273 kg * 1.99 * 10^30 kg) / (149.6 * 10^9 m)^2)
After calculating the above expression, we find that the gravitational force acting on the apple due to the Sun is approximately 0.586 N.
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