A setellite in Earth orbit has a mass of 91 kg and is at an altitude of 2.04 × 10 6 m. (Assume that U = 0 as r → ∞)(a) What is the potential energy of the satellite-Earth system?J(b) What is the magnitude of the gravitational force exerted by the Earth on the satellite?N(c) What force, if any, does the satellite exert on the Earth? (Enter the magnitude of the force, if there is no forN

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A setellite in Earth orbit has a mass of 91 kg and is at an altitude of   2.04  ×      10    6    m. (Assume that U = 0 as   r  →  ∞)(a) What is the potential energy of the satellite-Earth system?J(b) What is the magnitude of the gravitational force exerted by the Earth on the satellite?N(c) What force, if any, does the satellite exert on the Earth? (Enter the magnitude of the force, if there is no forN

Finnegan Zimmerman · Accepted Answer

Step 1Given that,Mass of satellite = 91 kgAltitude   h  =  2.04  ×      10    6       mStep 2We will use the formula of the potential energy at the altitudeThe formula of the potential energy is  U  =            −      G      M      m              r      +      h      Where M = mass of earth m = mass of the satelliteG = gravitational constanth = altituder = radius of the earthWe will use the formula of the gravitational force at the altitudeThe formula of the gravitational force is      F    g    =            G      M      m              (      r      +      h              )        2            Step 3(a). We need to calculate the potential energy of the satellite-earth systemUsing the formula of the potential energy  U  =            −      G      M      m              r      +      h      Put the value into the formula  U  =            −      6.67      ×              10                  −          11                    ×      5.97      ×              10                  24                    ×      91              6.37      ×              10        6            +      2.04      ×              10        6                U  =  −  4.30  ×      10    9       J(b). We need to calculate the magnitude of the gravitational force exerted by the earth on the satelliteUsing the formula of the gravitational force       F    g    =            G      M      m              (      r      +      h              )        2            Put the value into the formula      F    g    =            6.67      ×              10                  −          11                    ×              10                  24                    ×      91              (      6.37      ×              10        6            +      2.04      ×              10        6                    )        2                    F    g    =  512.3     N(c). We know that,According to Newton&#039;s third law,The gravitational force exerted by the earth on the satellite is equal and opposite to the gravitational force exerted by the satellite on the earth.We need to calculate the magnitude of the force exerted by the satellite on the earthUsing Newton&#039;s third law      F                  E        s              =  −      F          s      E      Put the value into the formula      F                  E        s              =  −  512.3     N        |        F                  E        s                  |    =  512.3     N

A setellite in Earth orbit has a mass of 91 kg and is at an altitude of 2.04 ×<!-- × -

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