GM - M mass of earth , G gravitational constant

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SUMMARY

The discussion centers on calculating the maximum distance of a spacecraft from Earth using the formula 1/R[a] = 8GM/R^2*(V[a] + V[b])^2 - 1/R, where G is the gravitational constant, M is the mass of Earth, and R is the distance from the Earth's center. The context involves two spacecraft colliding and merging into a single mass of wreckage. The formula incorporates the velocities of the two spacecraft, V[a] and V[b], and hints at the relationship between orbital mechanics and gravitational forces. The participant seeks clarification on the derivation of the coefficient 8 in the formula.

PREREQUISITES
  • Understanding of gravitational forces, specifically Newton's law of gravitation.
  • Familiarity with orbital mechanics and concepts such as apogee and perigee.
  • Knowledge of basic physics formulas involving mass, distance, and velocity.
  • Ability to manipulate algebraic equations and solve for variables.
NEXT STEPS
  • Research the derivation of the formula for orbital mechanics, focusing on energy conservation principles.
  • Study the implications of the gravitational constant G and its role in celestial mechanics.
  • Explore the concept of apogee in orbital dynamics to understand maximum distances in orbits.
  • Investigate the effects of mass and velocity on the trajectory of colliding spacecraft.
USEFUL FOR

Aerospace engineers, astrophysicists, and students studying orbital mechanics will benefit from this discussion, particularly those interested in spacecraft dynamics and collision scenarios.

dopey9
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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?
 
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Not clear what it is you are looking for. Please state the exact problem you are trying to solve.
 
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).
 
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
 

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