GM - M mass of earth , G gravitational constant

[dopey9]

im trying to find the maximum distance of a spacecraft from the earth, whre GM is used ( M is the mass of the Earth and G is the gravitational constant) ...

i was just wondering if there is a general formual for this?

 

[Doc Al]

Not clear what it is you are looking for. Please state the exact problem you are trying to solve.

 

[HallsofIvy]

Unless there is some additional information, there is NO "maximum distance of a spacecraft from earth". Are you think of the case where the spacecraft is in orbit around the Earth and you are given the position and speed of the spacecraft ? In that case, you could solve for the apogee (point in the orbit farthest from earth).

 

[dopey9]

bascailly I am meant to get to this formula which they have given

1/R[a] = 8GM/R^2*(V[a] + V)^2 - 1/R

where V[a] and V are speeds of two spacecraft s
G is gravitational constant
M is mass of earth
R is the distance from the centre of the earth
R[a] is the max distance of wreckage from the earth...because the two spacecraft s collided and where stuck together as one lump of wreckage...this part is continued from another of a question i posted earlier on spacecraft s of which i have solved...but this one iv come close to getting the answer but i don't know how they got the 8... also i got a hint that a mass M[2] orbits around a fixed mass M[1] according to the formula 1/r=Acos(theta) + G*M[1]*M[2]^2 / L^2

so basically iv been given the formula to derive but iv tried but can't get to it