The discussion centers on calculating gravitational force at varying distances from Earth's center using Newton's law of universal gravitation. The formula F = (G * M1 * M2) / R² is established, where G is the gravitational constant (6.67 x 10^-11), M1 is Earth's mass, M2 is the astronaut's mass, and R is the distance from Earth's center. Participants clarify that the force of gravity is inversely proportional to the square of the distance, leading to the equation F1/F2 = R2²/R1². This allows for the calculation of gravitational force at distances of 2R, 5R, 10R, and 17.2R from Earth's center.
PREREQUISITESStudents studying physics, particularly those focusing on gravitational forces, as well as educators seeking to enhance their understanding of universal gravitation principles.
nil1996 said:You don't need Earth's mass and radius and also G.
We have F=GM1M2/R2
As according to your problem M1 and M2 are not going to change
Use F is inversely proportional to R2
F1/F2=R22/R12
oMovements said:I don't understand how you came up with that equation.
nil1996 said:F=GMearthMman/R2
Now according to the problem it is asked to find the force on the man when its distance from the center of Earth is 2R,4R...etc
So in the formula GMearthMman/R2 we are going to change the distance R.Right?
As everything else in the formula is going to remain constant except R
We can say that F is dirctly proportional to 1/R1
so let F1 be the force of gravity on the man at a distance R from the centre of earth.
Let F2 be the force of gravity on the man at a distance R2 from the centre of earth.
So F1=GMearthMman/R2....1
F2=GMearthMman/(R1)2......2
divide equation 1 by 2 you will get my formula.
For your firsr problem R1=2R and F1=634
put in the above equation you will get F2
haruspex said:Please don't post complete solutions. Just give the questioner a nudge in the right direction.