What is the gtravitational potential energy of a 2.00e3 kg staellite that is in an orbit that has a radius of 9.90e6 m around the earth? Use gravitational potential energy=0 at r=�‡ (answer=-2.01e11J)
What is the work done against gravity on the satellite in the problem #1 in lifting it into it's orbit?
What is the change in the gravitational potential energy of the satellite in the problem #1 as it is lifted from the earth's surface to its orbit?
I will be happy to critique your thinking. Remember, the satellite at Earth's surface had PE, it was not zero.
To calculate the gravitational potential energy of a satellite in orbit, we can use the equation:
Gravitational potential energy = -G * (mass of satellite * mass of Earth) / radius of orbit
Here, G is the gravitational constant (approximately 6.67e-11 Nm²/kg²), the mass of the satellite is 2.00e3 kg, the mass of Earth is approximately 5.98e24 kg, and the radius of the orbit is 9.90e6 m.
Substituting the given values into the equation:
Gravitational potential energy = - (6.67e-11 Nm²/kg²) * (2.00e3 kg) * (5.98e24 kg) / (9.90e6 m)
Calculating this expression will give us the gravitational potential energy of the satellite in orbit.
To find the work done against gravity in lifting the satellite into its orbit, we need to know the height and vertical displacement involved. However, if we assume that the height is negligible compared to the radius of the orbit, we can approximate the work done as the change in gravitational potential energy.
So, the change in gravitational potential energy of the satellite is the difference between the gravitational potential energy in orbit and the gravitational potential energy when the satellite was at Earth's surface.
If the gravitational potential energy at the surface of the Earth is given as zero, then the change in gravitational potential energy is equal to the gravitational potential energy in orbit.
To find the change in gravitational potential energy, we can subtract the gravitational potential energy at the surface of the Earth from the gravitational potential energy in orbit.
To summarize:
1. Calculate the gravitational potential energy of the satellite in orbit using the given equation and values.
2. To find the work done against gravity, approximate it as the change in gravitational potential energy.
3. The change in gravitational potential energy is equal to the gravitational potential energy in orbit, so it can be found by subtracting the gravitational potential energy at the surface of the Earth from the gravitational potential energy in orbit.