Question

Uranus (mass=8.68 x 10²⁵ kg) and its moon miranda (mass=6.59 x 10¹⁹ kg) exert a gravitational force of 2.28 x 10¹⁹ n on each other. how far apart are they?

Answer 1

Using Newton's Law of Universal Gravitation, we rearrange the formula to solve for the distance between Uranus and its moon Miranda given the provided masses and gravitational force. By substituting the values into the rearranged formula, we can then calculate the distance between the two bodies.

Step-by-step explanation:

The question involves calculating the distance between Uranus and its moon Miranda based on the given gravitational force between them. To find the distance, one can use Newton's Law of Universal Gravitation, which states that the force (F) between two masses (m1 and m2) is proportional to the product of their masses and inversely proportional to the square of the distance between their centers (r). The equation is F = G * (m1 * m2) / r^2, where G is the gravitational constant (6.674 x 10-11 N(m/kg)^2).

Given the gravitational force (F = 2.28 x 1019 N), the mass of Uranus (m1 = 8.68 x 1025 kg), and the mass of Miranda (m2 = 6.59 x 1019 kg), the equation can be rearranged to solve for r (the distance between them).

The rearranged equation is r = √[G * (m1 * m2) / F]. Plugging in the values:

• G = 6.674 x 10-11 N(m/kg)^2
• m1 = 8.68 x 1025 kg
• m2 = 6.59 x 1019 kg
• F = 2.28 x 1019 N

We can then calculate the value of r and find the distance between Uranus and Miranda.

Answer 2

To calculate the distance between Uranus and its moon Miranda, we can use Newton's Law of Universal Gravitation. The distance is approximately 9.63 x 10⁶ meters.

Step-by-step explanation:

To calculate the distance between Uranus and its moon Miranda, we can use Newton's Law of Universal Gravitation. The formula for gravitational force is:

F = G * (m₁ * m₂) / r²

Here, F is the force, G is the gravitational constant (6.67430 x 10⁻¹¹ Nm²/kg²), m₁ is the mass of Uranus (8.68 x 10²⁵ kg), m₂ is the mass of Miranda (6.59 x 10¹⁹ kg), and r is the distance between them (unknown).

Plugging in the given force (2.28 x 10¹⁹ N) into the equation, we can solve for r:

2.28 x 10¹⁹ N = (6.67430 x 10⁻¹¹ Nm²/kg²) * (8.68 x 10²⁵ kg) * (6.59 x 10¹⁹ kg) / r²

r² = 9.63 x 10⁶ meters.

Simplifying the equation, we find that the distance between Uranus and Miranda is approximately 9.63 x 10⁶ meters.