GM - M mass of earth , G gravitational constant

In summary, there is a formula for finding the maximum distance of a spacecraft from Earth, which can be solved by finding the apogee of the spacecraft's orbit. The formula provided is 1/R[a] = 8GM/R^2*(V[a] + V[b])^2 - 1/R, where G is the gravitational constant, M is the mass of the Earth, R is the distance from the center of the Earth, and V[a] and V[b] are the speeds of two spacecrafts. This formula is derived from the equation for the orbit of a mass M[2] around a fixed mass M[1]. However, there is uncertainty about how the number 8 is obtained in the formula
  • #1
dopey9
32
0
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?
 
Physics news on Phys.org
  • #2
Not clear what it is you are looking for. Please state the exact problem you are trying to solve.
 
  • #3
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).
 
  • #4
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
 

Related to GM - M mass of earth , G gravitational constant

1. What is the mass of Earth?

The mass of Earth, commonly referred to as M, is approximately 5.97 x 10^24 kilograms.

2. What is the gravitational constant?

The gravitational constant, denoted by G, is a fundamental constant in physics that represents the strength of the gravitational force between two objects. It has a value of approximately 6.67 x 10^-11 m^3/kg/s^2.

3. How is the mass of Earth related to the gravitational constant?

The gravitational constant plays a crucial role in determining the mass of Earth. The mass of Earth is directly proportional to the gravitational constant, meaning that as the value of G increases, the mass of Earth also increases.

4. Why is the mass of Earth important?

The mass of Earth is important because it is a key factor in determining the planet's gravity, which influences many aspects of our lives such as the rotation of Earth, ocean tides, and the orbit of objects around our planet.

5. How was the mass of Earth and the gravitational constant determined?

The mass of Earth was first determined by Sir Isaac Newton using his laws of motion and gravitation. The gravitational constant, on the other hand, was calculated by Henry Cavendish in the late 18th century through his famous torsion balance experiment.

Back
Top