# GM - M mass of earth , G gravitational constant

1. Jul 13, 2006

### 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?

2. Jul 13, 2006

### Staff: Mentor

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

3. Jul 13, 2006

### HallsofIvy

Unless there is some additional information, there is NO "maximum distance of a space craft 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).

4. Jul 13, 2006

### dopey9

bascailly im 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 spacecrafts
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 spacecrafts collided and where stuck together as one lump of wreckage...this part is continued from another of a question i posted earlier on spacecrafts of which i have solved...but this one iv come close to getting the answer but i dont 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 cant get to it