Question

On the ground the gravitional force on a satelite is W . whar iw the gravitational force on the satelite when at a height R/50?​

Answer 1

The gravitational force between two objects due to their masses is

F

=

G

m

1

m

2

r

2

where

F

=

force in newtons

m

1

=

mass of first object in kilograms

m

2

=

mass of second object in kilograms

r

=

distance between centres of the objects in metres

G

=

the "gravitational constant", approximately equal to

6.674

×

10

−

11

N

k

g

−

2

m

2

This idea was first formulated by Isaac Newton, and published by him in 1686.

In this problem, let

m

1

=

m

E

=

mass of the earth; let

m

2

=

m

S

=

mass of the satellite.

On the ground:

W

=

G

m

E

m

S

R

2

, where

R

is the radius of the earth.

In orbit:

F

=

G

m

E

m

S

(

R

+

R

50

)

2

=

G

m

E

m

S

(

51

R

50

)

2

where

F

is the force we're looking for.

Put the two together:

F

(

51

R

50

)

2

=

W

R

2

F

(

51

50

)

2

=

W

F

=

2500

2601

W