(a) be pulled down to the surface of the Earth. Ignoring all air resistance, determine the speed with which the telescope would impact the Earth. Use mgh as the gravitational potential energy, where m is the mass of the telescope, g= 9.81 m/s² (the acceleration due to gravity at the surface of the Earth), and h is the distance If the Hubble space telescope were to come to an abrupt stop it would above the surface of the Earth.
(a) be pulled down to the surface of the Earth. Ignoring all air resistance, determine the speed with which the telescope would impact the Earth. Use mgh as the gravitational potential energy, where m is the mass of the telescope, g= 9.81 m/s² (the acceleration due to gravity at the surface of the Earth), and h is the distance If the Hubble space telescope were to come to an abrupt stop it would above the surface of the Earth.
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![# Problem 1: Hubble Space Telescope and Gravitational Potential Energy
The Hubble space telescope orbits the Earth at an altitude of approximately 600 kilometers and has a mass of \( 1.11 \times 10^4 \) kg.
### Part (a)
If the Hubble space telescope were to come to an abrupt stop, it would be pulled down to the surface of the Earth. Ignoring all air resistance, determine the speed with which the telescope would impact the Earth. Use \( mgh \) as the gravitational potential energy, where \( m \) is the mass of the telescope, \( g = 9.81 \, \text{m/s}^2 \) (the acceleration due to gravity at the surface of the Earth), and \( h \) is the distance above the surface of the Earth.
### Part (b)
Repeat the calculation from Part (a) using the **actual** expression for the gravitational potential energy,
\[ U_G = - \frac{GmM}{r} \]
where \( G \) is Newton’s gravitational constant, \( m \) is the mass of the telescope, \( M \) is the mass of the Earth, and \( r \) is the distance from the **center** of the Earth to the Hubble telescope.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F859743d5-9578-4a68-94b4-09f68a5c3500%2Ffadac686-fb16-418a-a68d-20823f7b60cf%2Fswaahun_processed.png&w=3840&q=75)
Transcribed Image Text:# Problem 1: Hubble Space Telescope and Gravitational Potential Energy
The Hubble space telescope orbits the Earth at an altitude of approximately 600 kilometers and has a mass of \( 1.11 \times 10^4 \) kg.
### Part (a)
If the Hubble space telescope were to come to an abrupt stop, it would be pulled down to the surface of the Earth. Ignoring all air resistance, determine the speed with which the telescope would impact the Earth. Use \( mgh \) as the gravitational potential energy, where \( m \) is the mass of the telescope, \( g = 9.81 \, \text{m/s}^2 \) (the acceleration due to gravity at the surface of the Earth), and \( h \) is the distance above the surface of the Earth.
### Part (b)
Repeat the calculation from Part (a) using the **actual** expression for the gravitational potential energy,
\[ U_G = - \frac{GmM}{r} \]
where \( G \) is Newton’s gravitational constant, \( m \) is the mass of the telescope, \( M \) is the mass of the Earth, and \( r \) is the distance from the **center** of the Earth to the Hubble telescope.
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