Please help me out with the following questions:
1) Two satellites orbit a planet of mass 'M' with Time periods of 3 days and 4.5 days, respectively. If the orbital radius of the first satellite is 2x10^6 m, determine the radius of orbit of the other. (Answer is 2.62x10^6)
2) A mass 'm' is moved from the North pole towards the equator. If the Earth is assumed to be a perfect sphere of radius 'R' , and if the mass moved is exactly 60kg, determine the difference in weight when measured at the North pole and at the equator.
R = 6.4x10^6 m
M of Earth = 6.0x10^24 kg
G = 6.67x10-11
m = 60 kg
( Answer is 2.0 N )
3) An astronaut travels from the Earth towards the moon where he experiences no net force. Determine the distance from the surface of the moon where this phenomenon occurs. Given that,
- the radius of the moon is 1.74x10^6 m
- mass of the moon is 0.0735x10^24 kg
(Answer is 3.71x10^7 m )
Please help me out.. i desperately need the explanation for these quesitons...
3.
ok so the only way I see for solving this question is using knowledge not included in this question....because the radius and mass of moon are not enough (in my opinion). We know that the moon orbits the earth in 28 days, and that the mass of the earth (from question 2) is 6x10
24.
We now have to find the distance between the earth and the moon, we shall assume that the earth and the moon are perfect spheres with all their mass at the cores and that the orbit is a perfect circle so that we can use circular motion and theory of gravitation
G*Me*Mm/r
2=Mm*v
2/r
here Me is mass of earth and Mm is mass of moon.
from my explanation of question 1, you should then see that r(distance between centers of earth and moon)=cube root(G*Me*T
2/4*pi
2). Replacing T as 28 days (converted to seconds, 28*24*3600), we get r to be 3.9*10
8m.
So now we have enough information to solve the question.
since there is no force on the astronaut, he is being pulled with equal but opposite forces from the earth and the moon.
so G*Me*a/R
2=G*Mm*a/r*2
here I use
a to be the mass of the astronaut, R to the the distance from the earth and r to be the distance from the moon,
From the first part of calculations, we see that the distance from the earth to the moon is about 3.9x10
8m,
let say the astronaut is x m from the center of the moon, then he will be (3.9x10
8-x)m from the earth, therefore
Me/(3.9x10
8-x)
2=Mm/x
2ok so simplify the equation,
square root (Me/Mm)=3.9x10
8-x/x
solve for x to get x=38863670
but we must remember that this is the distance from the core of the moon. we must subtract the radius of the moon to get the distance from the surface of the moon.
Therefore, 38863670-1.74*10
6=37123670=3.17*10
7m
If I think of away of solving the question without adding in the extra data I will post it, but I hope this gives you an idea of what is required.
