Find the change in the force of gravity between two planets when the distance between them is decreased by a factor of 5.
150 billion
Isn't the force inversely proportional to the distance squared?
That's what I believe it is, but I'm not sure... ?
Well it is, so square (1/5) to get the answer
To find the change in the force of gravity between two planets when the distance between them is decreased by a factor of 5, we need to understand the relationship between the force of gravity and the distance between two objects.
The force of gravity between two objects can be calculated using the formula:
F = (G * m1 * m2) / r^2
Where:
- F is the force of gravity
- G is the gravitational constant (approximately 6.674 × 10^-11 N * (m/kg)^2)
- m1 and m2 are the masses of the two objects
- r is the distance between the two objects
When the distance between the two planets is decreased by a factor of 5, it means that the new distance (r') is equal to the original distance (r) divided by 5.
To find the change in force, we need to compare the original force (F) with the new force (F').
Let's assume that the original force of gravity is F, and the new force of gravity is F'.
First, we need to substitute the new distance (r') into the formula:
F' = (G * m1 * m2) / (r'/5)^2
Next, we simplify the formula:
F' = (G * m1 * m2) / [(r/5)^2]
= (G * m1 * m2) / [(r^2)/25]
= (25 * G * m1 * m2) / (r^2)
Now, we can compare F' to F to find the change in force:
Change in force = F' - F
= [(25 * G * m1 * m2) / (r^2)] - [(G * m1 * m2) / r^2]
= [(25 * G * m1 * m2) - (G * m1 * m2)] / r^2
= (24 * G * m1 * m2) / r^2
Therefore, the change in the force of gravity between two planets when the distance between them is decreased by a factor of 5 is given by (24 * G * m1 * m2) / r^2.