A 981-kg satellite orbits the Earth at a constant altitude of 103-km.
How much energy must be added to the system to move the satellite into a circular orbit with altitude 199 km?
I need answer in MJ
please tell me what formula
You need to do work against gravity to move it to a higher orbit, but you get some back because the kinetic energy will be less at the higher orbit. You have to consider the total energy required.
The total energy (kinetic + potential) for a circular orbit at radius R is
Etotal = (1/2) m V^2 - G M m/R
where G is the universal constant of gravity and M is the mass of the Earth. Since
V^2/R = GM/R^2,
Etotal = (1/2)m*GM/R -GmM/R
= -(1/2)GmM/R
Compute this quantity at R = 103 km and at R = 199 km and take the difference. The work required will be positive.
ok sir is the formula
-(1/2)GmM/R
To calculate the amount of energy required to move the satellite into a circular orbit with a higher altitude, we can use the formula for gravitational potential energy. The formula is:
E = -G * (m * M) / (2 * r)
Where:
E = energy required (in joules)
G = gravitational constant (approximated as 6.674 × 10^-11 N·(m/kg)^2)
m = mass of the satellite (981 kg)
M = mass of the Earth (approximated as 5.972 × 10^24 kg)
r = radius of the orbit (initially 103 km and then 199 km)
Now we can calculate the energy required to move the satellite to the new orbit:
Step 1: Convert the altitudes to meters:
Altitude of initial orbit = 103 km = 103,000 meters
Altitude of final orbit = 199 km = 199,000 meters
Step 2: Calculate the initial radius and final radius:
Initial radius (r1) = radius of Earth + altitude of initial orbit
Final radius (r2) = radius of Earth + altitude of final orbit
Using the average radius of the Earth (approximated as 6,371 km or 6,371,000 meters), we can calculate the initial and final radii:
r1 = 6,371,000 + 103,000 = 6,474,000 meters
r2 = 6,371,000 + 199,000 = 6,570,000 meters
Step 3: Calculate the energy required for each orbit:
Energy required for initial orbit (E1) = -G * (m * M) / (2 * r1)
Energy required for final orbit (E2) = -G * (m * M) / (2 * r2)
Step 4: Calculate the difference in energy to move from initial to final orbit:
Energy difference (ΔE) = E2 - E1
Step 5: Convert the energy difference from joules to megajoules:
Energy difference in megajoules (MJ) = ΔE / (10^6)
Now you can plug the values into the formulas and calculate the energy required.
find the original PE+KE
find the new PE+KE
what is the difference?