Find the change in the force of gravity between two planets when their masses remain the same but the distance between them is increased by 10 times.
The force of gravity between two objects is given by the equation:
F = G * ( (m1 * m2) / r^2)
where F is the force of gravity, m1 and m2 are the masses of the two objects, r is the distance between them, and G is the gravitational constant.
If the distance is increased by 10 times (r becomes 10r), the new force of gravity F' becomes:
F' = G * ( (m1 * m2) / (10r)^2)
F' = G * ( (m1 * m2) / 100r^2)
F' = (1/100) * G * ( (m1 * m2) / r^2)
Since the initial force of gravity F is:
F = G * ( (m1 * m2) / r^2)
We can find the relationship between F and F':
F' = (1/100) * F
So, the change in the force of gravity is:
ΔF = F - F'
ΔF = F - (1/100) * F
ΔF = (99/100) * F
The force of gravity has decreased to 1/100 of its initial value when the distance between the two planets increased by 10 times.
To find the change in the force of gravity between two planets when their masses remain the same but the distance between them is increased by 10 times, we need to use the formula for gravitational force:
F = G * (m1 * m2) / r^2
Where:
F is the force of gravity between the two objects
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 planets
r is the distance between the centers of the two planets
Let's denote the initial distance between the two planets as r1, and the final distance as r2, where r2 = 10 * r1.
Given that the masses of the two planets remain the same, we can simplify the formula:
F1 = G * (m1 * m2) / r1^2
Since F2 is the new force of gravity when the distance is increased, we can write:
F2 = G * (m1 * m2) / r2^2
Substituting the value of r2 = 10 * r1 into the equation gives:
F2 = G * (m1 * m2) / (10 * r1)^2
Simplifying further:
F2 = G * (m1 * m2) / 100 * r1^2
We can see that the denominator has increased by a factor of 100 compared to the initial force (F1). Therefore, the force of gravity between the two planets when the distance is increased by 10 times is 1/100 (or 0.01) of the initial force of gravity. This implies a decrease in the force of gravity by a factor of 100.
In summary, when the distance between two planets is increased by 10 times, while their masses remain the same, the force of gravity decreases by a factor of 100.
To find the change in the force of gravity between two planets when their masses remain the same but the distance between them is increased by 10 times, we can use the formula for the force of gravity:
F = G * (m1 * m2) / r^2
Where F is the force of gravity, G is the gravitational constant (approximated to 6.67430 × 10^-11 N(m/kg)^2), m1 and m2 are the masses of the two planets, and r is the distance between them.
Since the masses remain the same, m1 and m2 are constants. Let's assume m1 = m2 = m.
Let's denote the initial distance between the two planets as r1, and the final distance as r2 = 10 * r1.
Now, we can calculate the ratio of the forces of gravity:
F2 / F1 = (G * (m1 * m2) / r2^2) / (G * (m1 * m2) / r1^2)
Canceling out the masses:
F2 / F1 = (1 / r2^2) / (1 / r1^2)
F2 / F1 = (r1^2) / (r2^2)
Since r2 = 10 * r1:
F2 / F1 = (r1^2) / ((10 * r1)^2)
F2 / F1 = 1 / 100
Therefore, the change in the force of gravity between the two planets when their masses remain the same but the distance between them is increased by 10 times is 1/100, or 0.01. So, the force of gravity decreases to 1% of its original value.