An m = 43 kg mass instrument package is put into orbit at an altitude above the Earth of A = 23000 km. What is the kinetic energy of this satellite in Joules?
F = G m Me/(h+Re)^2
so let R = 2.3*10^7 + RE
centripetal a = v^2/R
so
F = m a = m v^2/R = mG Me/R^2
or
m v^2 = m G Me/R
and
.5 mv^2 = .5 m G Me/R
But how do I get it to Joules? thanks
That is in Joules if you use
m in kg
G = 6.67*10^-11 N m^2/kg^2
Me = 5.98 * 10^24 kg
Re = 6.38 * 10^6 meters
To calculate the kinetic energy of a satellite, we need to know its mass and velocity. However, the given information only includes the mass of the satellite package and the altitude above the Earth. To find the satellite's velocity, we can use the concept of gravitational potential energy and the law of conservation of energy.
First, let's find the gravitational potential energy (PE) of the satellite at altitude A. The formula for gravitational potential energy is:
PE = m * g * h
where m is the mass of the satellite, g is the acceleration due to gravity, and h is the height or altitude.
Since we know the mass of the satellite (m = 43 kg) and the altitude (A = 23000 km = 23,000,000 m), we can calculate the gravitational potential energy (PE) using the standard value of the acceleration due to gravity (g = 9.8 m/s^2):
PE = 43 kg * 9.8 m/s^2 * 23,000,000 m
Next, we can use the law of conservation of energy to find the kinetic energy (KE) of the satellite. The law of conservation of energy states that the sum of potential energy and kinetic energy remains constant. Therefore, the sum of the gravitational potential energy (PE) and kinetic energy (KE) will be equal to each other.
PE + KE = Total Energy
Since the satellite is in orbit, the total energy is equal to zero (assuming no external forces are acting on the satellite):
PE + KE = 0
Solving for KE, we have:
KE = -PE
Now we can substitute the value of PE we calculated earlier to find the kinetic energy of the satellite:
KE = - (43 kg * 9.8 m/s^2 * 23,000,000 m)
After calculating the expression, you will find the kinetic energy of the satellite in joules.