(1) Consider two objects of mass m1 and m2 respectively, whose distance apart is given by d. Newton’s Law of Universal Gravitation states that the force, F, attracting the two objects to each other varies with m1m2 d2 . (i) Write this situation as an equation with the constant of variation being G. (ii) If the units of mass are kilograms, the units of force are newtons, and the units of distance are metres, what are the units of G? (iii) The mass of Jupiter is 1.89 ×1027 kilograms. The distance from Jupiter to the Sun is 7.79 ×1011 metres. The mass of the Sun is 1.99 ×1030 kilograms. The gravitational force between Jupiter and the Sun is 4.13 ×1023 newtons. Use this information to determine the value of G, written in scientific notation and correct to 3 significant figures.
(1) Consider two objects of mass m1 and m2 respectively, whose distance apart
is given by d. Newton’s Law of Universal Gravitation states that the force, F,
attracting the two objects to each other varies with m1m2
d2 .
(i) Write this situation as an equation with the constant of variation being G.
(ii) If the units of mass are kilograms, the units of force are newtons, and the
units of distance are metres, what are the units of G?
(iii) The mass of Jupiter is 1.89 ×1027 kilograms. The distance from Jupiter to
the Sun is 7.79 ×1011 metres. The mass of the Sun is 1.99 ×1030 kilograms. The
gravitational force between Jupiter and the Sun is 4.13 ×1023 newtons. Use this
information to determine the value of G, written in scientific notation and correct
to 3 significant figures.
(iv) The distance from Alpha Centauri, the nearest star system to ours, is 4.37
light years. One light year is equivalent to 9.46 ×1015 metres. The mass of Alpha
Centauri A, the largest star in the system, is 1.1 times that of the Sun. What is
the gravitational force between the Sun and Alpha Centauri A?
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