Consider the earth following its nearly circular orbit about the sun. The earth has mass 5.98*10^24 and the sun has mass 1.99*10^30. They are separated, center to center, by r=150 million k.
What is the size of the gravitational force acting on the earth due to the sun?
F=GMsMe/distance^2
To calculate the size of the gravitational force acting on the Earth due to the Sun, we can use Newton's law of universal gravitation:
F = (G * m1 * m2) / r^2
Where:
F is the gravitational force
G is the gravitational constant (approximately 6.67430 x 10^-11 m^3 kg^-1 s^-2)
m1 is the mass of the first object (mass of the Earth)
m2 is the mass of the second object (mass of the Sun)
r is the distance between the centers of the two objects (150 million km)
Let's substitute the given values:
F = (6.67430 x 10^-11 * 5.98 x 10^24 kg * 1.99 x 10^30 kg) / (150 million km)^2
Note: Before performing the calculation, we need to convert the distance from kilometers to meters and the mass from kilograms to standard metric units.
1 million km = 1 x 10^6 km
1 km = 1000 m
1 kg = 1000 grams
F = (6.67430 x 10^-11 * 5.98 x 10^24 kg * 1.99 x 10^30 kg) / ((150 x 10^6 km)^2 * (1000 m/km)^2)
Calculating this expression will give us the size of the gravitational force acting on the Earth due to the Sun.
To determine the size of the gravitational force acting on the Earth due to the Sun, we can use Newton's law of universal gravitation:
F = (G * m1 * m2) / r^2
Where:
F is the gravitational force
G is the gravitational constant (approximately 6.67430 × 10^-11 N(m/kg)^2)
m1 and m2 are the masses of the objects (in this case, the Earth and the Sun)
r is the distance between the centers of the two objects
Given:
m1 = 5.98 * 10^24 kg (mass of the Earth)
m2 = 1.99 * 10^30 kg (mass of the Sun)
r = 150 million km = 150 * 10^6 * 10^3 m = 1.5 * 10^11 m
Plugging the values into the formula:
F = (6.67430 × 10^-11) * (5.98 * 10^24) * (1.99 * 10^30) / (1.5 * 10^11)^2
After performing the calculations, the gravitational force is approximately:
F ≈ 3.52 x 10^22 N