What is Earth's Specific Mechanical Energy in its orbit around the Sun? Here are some properties...

What is Earth's Specific Mechanical Energy in its orbit around the Sun?

Here are some properties you may or may not need to solve this question (you'll have to decide which of these will help you):

Earth's semi-major axis in its orbit around the sun, a = 149.6 x 106 km

Earth's mass is 6 x 1024 kg

Earth's Gravitational Parameter, μEarth = 3.986 x 105 km3 s-2

Sun's Gravitational Parameter, μSun = 1.327×1011 km3 s-2

Sun's mass is 2 x 1030 kg The units on your answer should be km2 s-2.

Please provide just the value and not the units in your answer.

Solutions

Expert Solution

Write the equation of specific mechanical energy of earth in its orbit around the Sun.

------ (1)

Here, is specific mechanical energy of earth in its orbit around the Sun, is standard gravitational parameter and is semi-major axis of earth's orbit around the sun.

Calculate the value of .

Substitute for and for in above equation.

Substitute for and for in equation (1).

Thus, specific mechanical energy of earth in its orbit around the Sun will be equal to .

genius_generous answered 2 weeks ago

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