Consider the earth following its nearly circular orbit (dashed curve) about the sun.(Figure 2) The earth has mass mearth=5.98×1024kg and the sun has mass msun=1.99×1030kg. They are separated, center to center, by r=93millionmiles=150millionkm.
Fg=(GMeMsun)/r^2
Fg=((6.67*10^-11)(5.98*10^24)(1.99*10^30))/(1.5*10^11)^2
Fg=3.53*10^22
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Well, it seems like the Earth and the Sun are quite the couple. They're really keeping their distance, about 93 million miles or 150 million kilometers apart. But hey, in space, personal space is important, right?
Now, let's talk about their masses. The Earth weighs in at a hefty 5.98 x 10^24 kilograms, while the Sun is truly a heavyweight champ with a mass of 1.99 x 10^30 kilograms. It's like comparing a feather to a five-ton truck!
But despite their size difference, the Earth and the Sun have a pretty stable relationship. The Earth follows its nearly circular orbit around the Sun, like a dance partner who never misses a step. And that's no easy feat considering the gravitational pull between these two cosmic buddies.
So, let's give it up for the Earth and the Sun, showing us that even with astronomical distances and masses, love can still bloom!
To calculate the gravitational force between the Earth and the Sun, you can use Newton's law of universal gravitation equation:
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 (Earth and Sun in this case),
r is the distance between the centers of the two objects.
Now, let's plug in the given values and calculate the gravitational force:
m1 (mass of Earth) = 5.98 × 10^24 kg
m2 (mass of Sun) = 1.99 × 10^30 kg
r (distance between Earth and Sun) = 150 million km = 150 × 10^6 km
First, let's convert the distance from kilometers to meters:
r = 150 × 10^6 km = 150 × 10^9 m
Now, we can substitute the values into the formula:
F = (6.67430 × 10^-11 m^3 kg^-1 s^-2) * (5.98 × 10^24 kg) * (1.99 × 10^30 kg) / (150 × 10^9 m)^2
Simplifying the equation:
F ≈ 3.53 × 10^22 N
Therefore, the gravitational force between the Earth and the Sun is approximately 3.53 × 10^22 Newtons.