How to find orbital velocity when an object is at height h from earth'...
The orbital velocity formula is given by :
Vórbit = √GM/R
G - gravitational constant,
M - mass of the body at center,
R - radius of the orbit
orbital velocity formula is applied to calculate the orbital velocity of the any planet if mass M and radius R are known .
orbital velocity is expressed in meter per second ( m/sec).
How to find orbital velocity when an object is at height h from earth'...
Orbital Velocity at a Height h from Earth's Surface
To determine the orbital velocity of an object at a height h from the Earth's surface, we need to consider the gravitational force acting on the object and the centripetal force required to keep it in orbit.
1. Gravitational Force:
The gravitational force between the object and the Earth can be given by the equation:
F = G * (m1 * m2) / r²
where F is the gravitational force, G is the gravitational constant (approximately 6.67 x 10^-11 N m²/kg²), m1 is the mass of the object, m2 is the mass of the Earth, and r is the distance between the object and the center of the Earth.
2. Centripetal Force:
The centripetal force required to keep the object in orbit can be calculated using the equation:
F = (m * v²) / r
where F is the centripetal force, m is the mass of the object, v is the orbital velocity, and r is the distance between the object and the center of the Earth.
3. Equating the Forces:
To find the orbital velocity, we can equate the gravitational force and the centripetal force:
G * (m1 * m2) / r² = (m * v²) / r
4. Canceling Mass:
Since the mass of the object cancels out, we can rearrange the equation to solve for the orbital velocity:
v² = (G * m2) / r
5. Height from Earth's Surface:
The distance r in the equation can be expressed as the sum of the Earth's radius (R) and the height (h):
r = R + h
6. Calculating Orbital Velocity:
Substituting the value of r into the equation, we get:
v² = (G * m2) / (R + h)
Taking the square root of both sides of the equation gives us the orbital velocity:
v = √((G * m2) / (R + h))
Summary:
To find the orbital velocity of an object at a height h from the Earth's surface, we use the equation v = √((G * m2) / (R + h)), where G is the gravitational constant, m2 is the mass of the Earth, R is the Earth's radius, and h is the height from the Earth's surface. This equation allows us to calculate the speed required for an object to maintain a stable orbit at a given height.