The gravitational potential energy of a low-Earth orbit satellite has been estimated at 1.5 million joules. If the satellite has a mass of 417 grams, and g=9.8ms-2, at what altitude (in meters) is the satellite orbiting? Give your answer to the nearest meter.
To find the altitude at which the satellite is orbiting, we need to use the formula for gravitational potential energy and then solve for the altitude.
Gravitational potential energy (PE) is given by the formula:
PE = mgh
where m is the mass of the satellite, g is the acceleration due to gravity, and h is the altitude.
We have been given the mass of the satellite as 417 grams (or 0.417 kg), the gravitational acceleration (g) as 9.8 m/s^2, and the gravitational potential energy (PE) as 1.5 million joules.
Substituting the given values into the formula, we get:
1.5 million = 0.417 * 9.8 * h
Now, let's solve for h:
h = 1.5 million / (0.417 * 9.8)
h ≈ 3766.94 meters
Therefore, the satellite is orbiting at an altitude of approximately 3767 meters. Rounded to the nearest meter, the answer is 3767 meters.