Question

1. What is the magnitude of the average gravitational force between the Sun and Mercury?
2. What is the magnitude of the average gravitational force between the Sun and Mercury if the orbital radius of Mercury was doubled?

(you will have to look up Newton's Universal Law of Gravitation and some values of mass and distance) and please list them with the solution.

Please answer in scientific notation and round to three significant figures.

Answer 1

(i) Magnitude of the average gravitational force between the Sun and Mercury which will be given by -

F_avg = G M m / r²

where, G = gravitational constant = 6.67 x 10^-11 Nm²/kg²

M = mass of the Sun = 1.9891 x 10³⁰ kg

m = mass of Mercury = 3.285 x 10²³ kg

r = distance from the Sun to Mercury = 57.91 x 10⁹ m

then, we get

F_avg = [(6.67 x 10^-11 Nm²/kg²) (1.9891 x 10³⁰ kg) (3.285 x 10²³ kg)] / (57.91 x 10⁹ m)²

F_avg = [(4.358 x 10⁴³ Nm²) / (3.353 x 10²¹ m²)]

F_avg = 1.2997 x 10²² N

F_avg 1.30 x 10²² N

If the orbital radius of Mercury was doubled, then the magnitude of average gravitational force between the Sun and Mercury which will be given by -

F_avg = G M m / R²

where, G = gravitational constant = 6.67 x 10^-11 Nm²/kg²

M = mass of the Sun = 1.9891 x 10³⁰ kg

m = mass of Mercury = 3.285 x 10²³ kg

R = radius of Mercury = 2439 km = 4878 km

then, we get

F_avg = [(6.67 x 10^-11 Nm²/kg²) (1.9891 x 10³⁰ kg) (3.285 x 10²³ kg)] / (4878 x 10³ m)²

F_avg = [(4.358 x 10⁴³ Nm²) / (2.379 x 10¹³ m²)]

F_avg = 1.83 x 10³⁰ N