U+K=−Gm1m2/r+1/2 m1 v2,
where m1 and m2 are the masses of two objects, r is the distance between their centers, v is the velocity, and G is the universal gravitational constant.
How can you rearrange the given formula to correctly find m1?
fix your typos, and then just factor out m1 and you have
U+K = m1(1/2 v^2 - Gm2/r^2)
now divide to get m1 all alone
I think -G m1 m2 / r is correct. It is potential energy, not force, integral of 1/ r^2 from infinity to r
To rearrange the formula to find m1, we need to isolate it on one side of the equation.
Let's rearrange the equation step by step:
1. Start with the given formula:
U + K = -G * m1 * m2 / r + 1/2 * m1 * v^2
2. Move the first term containing m1 to the left-hand side by subtracting it from both sides:
U + K + G * m1 * m2 / r = 1/2 * m1 * v^2
3. Next, let's move the last term involving m1 to the right-hand side by subtracting it from both sides:
U + K + G * m1 * m2 / r - 1/2 * m1 * v^2 = 0
4. Now, let's factor out m1 from the remaining terms:
m1 * (G * m2 / r - 1/2 * v^2) = -U - K
5. To solve for m1, divide both sides of the equation by the remaining expression in parentheses (G * m2 / r - 1/2 * v^2):
m1 = (-U - K) / (G * m2 / r - 1/2 * v^2)
Now, you can use the rearranged formula to calculate the value of m1 by substituting appropriate values for U, K, G, m2, r, and v.