What is the approximate Delta V to take a body from an apogee of 43,000km to 66,000km. Assume a separated mass of 4850 kg.
To calculate the approximate Delta V required to take a body from one orbit to another, we can use the formula:
ΔV = √[(2μ / r1) - (μ / (r1 + r2))]
Where:
- ΔV is the required change in velocity (Delta V) in meters per second (m/s)
- μ is the standard gravitational parameter of the central body, which can be calculated by multiplying the gravitational constant (6.67430 x 10^-11 m^3/kg/s^2) by the mass of the central body. For Earth, the standard gravitational parameter is approximately 3.986 x 10^14 m^3/s^2.
- r1 is the initial radius or altitude of the body (apogee in this case) in meters
- r2 is the final radius or altitude of the body (perigee in this case) in meters
Before calculating the Delta V, we need to convert the given apogee and perigee altitudes from kilometers to meters:
Apogee (r1) = 43,000 km = 43,000,000 meters
Perigee (r2) = 66,000 km = 66,000,000 meters
Now we can substitute these values into the formula to find the Delta V:
ΔV = √[(2 * 3.986 x 10^14) / 43,000,000) - (3.986 x 10^14) / (43,000,000 + 66,000,000))]
Simplifying the equation, we get:
ΔV = √[(7.972 x 10^14 / 43,000,000) - (7.972 x 10^14) / (109,000,000)]
Solving this equation, we find:
ΔV ≈ 9,272.2 m/s
Therefore, the approximate Delta V required to take the body from an apogee of 43,000 km to 66,000 km is approximately 9,272.2 m/s.