Answer :
Final answer:
The work done to propel a six-ton satellite to heights of 100 and 400 miles above Earth is found by calculating the gravitational potential energy, using the formula W = mgh. The calculations involve the satellite's mass, the acceleration due to gravity, and the additional height above Earth's surface. More precise calculations would account for the change in gravity with altitude.
Explanation:
To determine the work done in propelling a six-ton satellite to specific heights above Earth, we use the concept of gravitational potential energy in physics. The formula to calculate the work done, assuming no air resistance and negligible weight of the propellant, is Work = gravitational potential energy (U) = mgh, where m is the mass of the satellite, g is the acceleration due to gravity (which we will approximate as constant at close distances like 100 or 400 miles), and h is the height to which the satellite is lifted.
The radius of Earth is given as 4000 miles. Therefore, for a height (h) of:
- (a) 100 miles above Earth, the work done is W = m * g * (radius of Earth + 100 miles)
- (b) 400 miles above Earth, the work done is W = m * g * (radius of Earth + 400 miles)
However, it's important to mention that as we move away from the surface of the Earth, the acceleration due to gravity decreases, so for more precise calculations, this should be taken into account.
The actual values require substituting the mass (m) in tons, the height (h) above the Earth in miles, and the acceleration due to gravity (g) measured in appropriate units that match the mass and distance units used.
Learn more about Gravitational Potential Energy here:
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