distance is between the earth and the sun, moon, Jupiter (closest), Jupiter (far

Question

distance is between the earth and the sun, moon, Jupiter (closest), Jupiter (farthest) center of galaxy, and andromeda

Compare the gravitational attractie that each orthe following has on your body: a. The Sun b The Moon For distance, takes Jupiter c The planet Jupiler at is closest distance to the Sun and distance to the Sun d The planet Jupiter at its fardhest from Earth stance, take Jupiler' For distance the sun and add Earth's distance to the Sun e The mysterious center ofeur galaxy .assumed to be a black hole 3-million- times mat d localed 28,000 light years away massive than The Andromeda Galasy (100 billion times the mass ofour Sun, located 2.5 light years away. First, find all the relevant information (mass & distance), then compute the stren of gravity. object Grav. Field Mass (kilogram Distance (meters Jupiter (closest to d. Jupiter aarthest Earth center of galaxy f Andromeda Of the six objects listed, which has the greatest gravitational attraction to you? Which has the least gravitational attraction to you?

Explanation / Answer

Let the mass of the body = 70 kg, By applying the Newton's Universal law of gravitation

[a]

The Sun

Fyou-sun = G m* Msun/ r2= 6.67*10-11*70*2*1030/ (149.6*109)2 [ r is the distance is between the earth and the sun]

F you-sun = 0.42N

[b]

The Moon

Fyou-moon = G m* Mmoon/ r2= 6.67*10-11*70*7.35*1022/ (3.844*108)2 [ r is the distance is between the earth and the moon]

Fyou-moon = 0.0023N

[c]

The planet Jupiter [ as it is closest to Earth]

Fyou-jupiter = G m* Mjupiter / r2

Here; r = [distance of Jupiter- Sun] - [distance of Sun- Earth]

r = 778.5*109 - 149.6*109 =628.9 *109 m

Fyou-jupiter = G m* Mjupiter / r2= 6.67*10-11*70*1.9*1027/ (628.9*109)2 = 2.24*10-5 N

Fyou-jupiter = 2.24*10-5 N  [ as it is closest to Earth]

[d]

The planet Jupiter [ as it is farthest from Earth]

Fyou-jupiter = G m* Mjupiter / r2

Here; r = [distance of Jupiter- Sun] + [distance of Sun- Earth]

r = 778.5*109+ 149.6*109 =928.1 *109 m

Fyou-jupiter = G m* Mjupiter / r2= 6.67*10-11*70*1.9*1027/ (928.1*109)2 = 1.03*10-5 N

Fyou-jupiter =1 .03*10-5 N  [ as it is farthest from Earth]

[e]

Centre of gravity

FCentre of gravity = G m* Mblack hole / r2

Mblack hole = 3 *106 * M sun=3 *106 * 2*1030 kg= 6*1036 kg

r= 28,000 light years= 28*103* 9.5*1015 m = 266*1018 m [ 1 light year= 9.5*1015 m]

FCentre of gravity = G m* Mblack hole / r2 = 6.67*10-11*70*6*1036 / ( 266*1018 )2 = 3.96*10-13 N

FCentre of gravity = 3.96*10-13 N

[f]

Andromeda

FAndromeda = G m* MAndromeda/ r2

MAndromeda = 100 *109 * M sun= 1011 * 2*1030 kg= 2*1041 kg

r= 2.5 million light years= 2.5*106* 9.5*1015 m = 23.75*1021m [ 1 light year= 9.5*1015 m]

FAndromeda  = G m* MAndromeda/ r2 = 6.67*10-11*70*2*1041 / ( 23.75*1021 )2 = 1.66*10-12 N

FAndromeda=  1.66*10-12 N

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