#### To determine

**a)**

**To find:**

The work to move the other body from r=a to r=b if one of the bodies is fixed

#### Answer

**W=Gm1m21a-1b**

#### Explanation

**1) Concept:**

The work is calculated by using the formula W=∫abf(x)dx

**2) Given:**

F=Gm1m2r2

m1, m2 are masses, G is the gravitational constant and r is the distance between bodies.

**3) Calculation:**

The work is calculated by using the formula:

W=∫abf(x)dx

The gravitational force is given by F(r)=Gm1m2r2 We need to find the work done when the position changes from r=a to r=b

Therefore,

W=∫abGm1m2r2dr

=Gm1m2∫ab1r2dr

=Gm1m2-1rab

=-Gm1m21b-1a

W=Gm1m21a-1b

**Conclusion:**

Thework done is W=Gm1m21a-1b

#### To determine

**b)**

**To compute:**

The work required to launch the satellite

#### Answer

**W=8.496×109**

#### Explanation

**1) Concept:**

The required work is calculated by using the formula W=Gm1m21a-1b

**2) Given:**

The mass of the earth is M=5.98×1024kg

Radius of the earth is R=6.37×106m

G=6.67×10-11 N·m2/kg2

Height of the satellite from earth’s surface is 1000km=1000000 m

The weight of the satellite m=1000kg

**3) Calculation:**

By using part a), the work done by the satellite is calculated by

W=Gm1m21a-1b

The satellite is 1,000,000 m from the earth’ssurface; therefore, the distance from the centre of the earth to the satellite is R+1,000,000 where R is the radius of the earth

W=GMm1R-1R+1,000,000

W=(6.67×10-11)(5.98×1024)(1000)16.37×106-16.37×106+1,000,000

W=(6.67×10-11)(5.98×1024)(103)16.37×106-16.37×106+106

W=(6.67×5.98×1016)16.37×106-17.37×106

W=6.67×5.98×10100.021

W=0.8496 ×1010

W=8.496×109

**Conclusion:**

The work required to launch the satellite is W=8.496×109