Answers:
5) [tex]1.99(10)^{21} N[/tex]
6) [tex]1.37(10)^{18} N[/tex]
7) [tex]1.64(10)^{21} N[/tex]
8) [tex]4.29(10)^{10} N[/tex] more than Venus force of gravity on Pluto
Explanation:
According to Newton's law of Universal Gravitation, the force [tex]F[/tex] exerted between two bodies of masses [tex]M[/tex] and [tex]m[/tex] and separated by a distance [tex]R[/tex] is equal to the product of their masses and inversely proportional to the square of the distance:
[tex]F=G\frac{Mm}{R^{2}}[/tex] (1)
Where [tex]G=6.674(10)^{-11}\frac{m^{3}}{kgs^{2}}[/tex] is the Gravitational Constant
This is the equation we will use to solve each question in this problem.
5) Gravitational force between Earth and Moon
In this case we have:
[tex]F_{earth-moon}[/tex] is the gravitational force between Earth and Moon
[tex]M=5.97(10)^{24} kg[/tex] is the mass of the Earth
[tex]m=7.46(10)^{23} kg[/tex] is the mass of the Moon
[tex]R=3.86(10)^{8} m[/tex] is the distance between Earth and Moon
Solving:
[tex]F_{earth-moon}=6.674(10)^{-11}\frac{m^{3}}{kgs^{2}}\frac{(5.97(10)^{24} kg)(7.46(10)^{23} kg)}{(3.86(10)^{8} m)^{2}}[/tex] (2)
[tex]F_{earth-moon}=1.99(10)^{21} N[/tex] (3)
6) Gravitational force between Jupiter and Venus
Assuming for a moment that the planets are perfectly aligned and all are in the same orbital period, we can make a rough estimation of the distance between Jupiter and Venus, knowing the distance of each to the Sun:
distance between Sun and Jupiter - distance between Sun and Venus=distance between Jupiter and Venus=[tex]R_{jupiter-venus}[/tex] (4)
[tex]R_{jupiter-venus}=778.3(10)^{9} m - 108(10)^{9} m=6.703(10)^{11} m[/tex] (5)
Using this value in the Law of Universal Gravitation equation:
[tex]F_{jupiter-venus}=6.674(10)^{-11}\frac{m^{3}}{kgs^{2}}\frac{(1.90(10)^{27} kg)(4.87(10)^{24} kg)}{(6.703(10)^{11} m)^{2}}[/tex] (6)
[tex]F_{jupiter-venus}=1.37(10)^{18} N[/tex] (7)
7) Gravitational force between Saturn and Mars
Using the same assumption we made in the prior question:
distance between Sun and Saturn - distance between Sun and Mars=distance between Saturn and Mars=[tex]R_{saturn-mars}[/tex] (8)
[tex]R_{saturn-mars}=1427(10)^{9} m - 227.9(10)^{9} m=227.9(10)^{9} m[/tex] (9)
Using this value in the Law of Universal Gravitation equation:
[tex]F_{saturn-mars}=6.674(10)^{-11}\frac{m^{3}}{kgs^{2}}\frac{(1.989(10)^{30} kg)(6.42(10)^{23} kg)}{(227.9(10)^{9} m)^{2}}[/tex] (10)
[tex]F_{saturn-mars}=1.64(10)^{21} N[/tex] (11)
8) How much more is earths force of gravity on Pluto than Venus force of gravity on Pluto?
Firstly, we need to find [tex]F_{earth-pluto}[/tex] and then find [tex]F_{venus-pluto}[/tex] in order to find the difference.
For [tex]F_{earth-pluto}[/tex]:
[tex]M=5.97(10)^{24} kg[/tex] is the mass of the Earth
[tex]m=1.46(10)^{22} kg[/tex] is the mass of Pluto
[tex]R_{earth-pluto}=5.7504(10)^{12} m[/tex] is the distance between Earth and Pluto
[tex]F_{earth-pluto}=6.674(10)^{-11}\frac{m^{3}}{kgs^{2}}\frac{(5.97(10)^{24} kg)(1.46(10)^{22} kg)}{(5.7504(10)^{12} m)^{2}}[/tex] (12)
[tex]F_{earth-pluto}=1.759(10)^{11} N[/tex] (13) Force between Earth and Pluto
For [tex]F_{venus-pluto}[/tex]:
[tex]M=4.87(10)^{24} kg[/tex] is the mass of Venus
[tex]m=1.46(10)^{22} kg[/tex] is the mass of Pluto
[tex]R_{venus-pluto}=5.792(10)^{12} m[/tex] is the distance between Venus and Pluto
[tex]F_{venus-pluto}=6.674(10)^{-11}\frac{m^{3}}{kgs^{2}}\frac{(4.87(10)^{24} kg)1.46(10)^{22} kg)}{(5.792(10)^{12} m)^{2}}[/tex] (14)
[tex]F_{venus-pluto}=1.33(10)^{11} N[/tex] (15) Force between Venus and Pluto
Calculating the difference:
[tex]F_{earth-pluto}-F_{venus-pluto}=1.759(10)^{11} N-1.33(10)^{11} N[/tex]
Finally:
[tex]F_{earth-pluto}-F_{venus-pluto}=4.29(10)^{10} N[/tex] (16)
Hence:
Earths force of gravity on Pluto is [tex]4.29(10)^{10} N[/tex] than Venus force of gravity on Pluto.
