Calculate the gravitational force between the Sun and Neptune. The mass of the Sun is 1.99×1030 kg. The mass of Neptune is 1020×1023 kg. The distance between them is 450×1010 m.
We can find the gravitational force between the Sun and Neptune by using the following formula:
F = G * (M1 * M2) / r²
Where:
F is the gravitational force
G is the gravitational constant (6.674×10⁻¹¹ N·(m²/kg²))
M1 is the mass of the Sun (1.99×10³⁰ kg)
M2 is the mass of Neptune (1020×10²³ kg)
r is the distance between them (450×10¹⁰ m)
Plugging the values into the formula:
F = (6.674×10⁻¹¹) * ((1.99×10³⁰) * (1020×10²³)) / (450×10¹⁰)²
F = (6.674×10⁻¹¹) * (20358×10⁵³) / (20250×10²⁰)
F = (6.674×10⁻¹¹) * (20358/20250) * 10³³
F ≈ 1.005 * 6.674 * 10²²
F ≈ 6.70847 * 10²² N
The gravitational force between the Sun and Neptune is approximately 6.70847 * 10²² Newtons.
To calculate the gravitational force between the Sun and Neptune, we can use Newton's Law of Universal Gravitation. The formula for gravitational force is:
F = (G * m1 * m2) / r^2
where F is the gravitational force, G is the gravitational constant (approximately 6.674 x 10^-11 Nm^2/kg^2), m1 and m2 are the masses of the two objects, and r is the distance between the centers of the two objects.
Given:
Mass of Sun (m1) = 1.99 x 10^30 kg
Mass of Neptune (m2) = 1020 x 10^23 kg
Distance (r) = 450 x 10^10 m
Plugging the values into the formula, we get:
F = (6.674 x 10^-11 Nm^2/kg^2 * 1.99 x 10^30 kg * 1020 x 10^23 kg) / (450 x 10^10 m)^2
Now we can simplify the calculation:
F = (6.674 x 10^-11 Nm^2/kg^2 * (1.99 * 1020) x (10^30 * 10^23) kg^2) / (450^2 x 10^20^2) m^2
F = (1.339326 x 10^40 Nm^2/kg^2 * 2.038 x 10^53 kg^2) / (202,500 x 10^40) m^2
To further simplify, we can multiply the numerator and divide by the denominator:
F = (1.339326 x 2.038 x 10^40+53) / 202,500 x 10^-40 m^2
F = 2.728 x 10^93 / (202,500 x 10^40) m^2
Lastly, we can simplify it more by dividing the numerator and denominator by 202,500, which results in:
F = 1.35 x 10^53 N
So, the gravitational force between the Sun and Neptune is approximately 1.35 x 10^53 Newtons.
To calculate the gravitational force between the Sun and Neptune, you 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 Nm^2/kg^2)
m1 is the mass of the first object (the Sun in this case)
m2 is the mass of the second object (Neptune in this case)
r is the distance between the centers of the two objects
Let's substitute the given values into the formula:
F = (6.67430 × 10^-11 Nm^2/kg^2 * 1.99 × 10^30 kg * 102 × 10^23 kg) / (450 × 10^10 m)^2
Now, we can simplify the calculation step by step:
1.99 × 10^30 kg * 102 × 10^23 kg = 2.0298 × 10^53 kg^2
(450 × 10^10 m)^2 = (2.025 × 10^13 m)^2 = 4.100625 × 10^26 m^2
Substitute the simplified values back into the formula:
F = (6.67430 × 10^-11 Nm^2/kg^2 * 2.0298 × 10^53 kg^2) / 4.100625 × 10^26 m^2
Now, divide and cancel out units:
F ≈ 3.24 × 10^22 N
Therefore, the gravitational force between the Sun and Neptune is approximately 3.24 × 10^22 Newtons.