Upon its return voyage from a space mission, the spacecraft has a velocity of 24000km/h at point A, which is 7000km from the center of the earth. Determine the velocity of the spacecraft when it reaches point B, which is 6500km from the center of the earth. The trajectory between these points is outside the effect of the earth's atmosphere.

I solved for the velocity and got 2.63*10^10 and the real answer is 26300km/h. How am I off by such a big factor of 10?

I don't know how you solved it.

INT force.dx from A to b is the added energy.

INT GMe*Ms)/r^2 dr from A to B
GMe*Ms (1/6.5E6 - 1/7.5E6)=
6.67E-11*6.0E24 Ms(2.05E-8)=8.2E6*Ms
now, add that energy to the original KE
ORigal KE= 1/2 m*(6.67E3)^2=2.2E7*m
new KE= 8.2E6M
added it is 3.0 E7*M

M*3.0E7=1/2 M v^2
V= sqrt6E7

V= 2.78E4km/hr instead of 2.63E4km/hr

I didn't get the answer, check my work.

i see where you went wrong. you have 7.5E6 and the second radius and it's supposed to be 7.0E6. yeah that's how i worked the problem. i converted my answer wrong when i went from m/s to km/h thank you for your help!

To determine the velocity of the spacecraft when it reaches point B, we can apply the principle of conservation of angular momentum. This principle states that when there is no external torque acting on a system, the angular momentum of that system remains constant.

To begin, we need to find the angular momentum of the spacecraft at point A. The formula for angular momentum is given by:

L = m * v * r

Where:
L is the angular momentum
m is the mass of the object
v is the velocity of the object
r is the distance of the object from the center of rotation (in this case, the center of the earth)

In this scenario, we are given the velocity of the spacecraft at point A (v = 24000 km/h) and the distance of point A from the center of the earth (r = 7000 km). However, we are not given the mass of the spacecraft, which is necessary for the calculation.

It seems there may have been a mistake in your calculation or the given values.

To correctly solve the problem, we would need the mass of the spacecraft, or some additional information that allows us to determine it. Without knowing the mass, we cannot accurately calculate the angular momentum or the velocity at point B.

Therefore, I apologize, but I cannot provide the correct answer without the necessary information.