a) The distance between the earth and the moon is 3.84 x
meters. The Mass of the moon is 7.348 ×
kilograms.
The Mass of the earth is 5.9722 ×
kilograms.
b) The gravitational force between the earth and the moon is approximately 1.982 ×
Newtons.
How scientific notation is written:
Using scientific notation, the distance between the earth and the moon from kilometers is converted to meters.
384,000 kilometers = 3.84 x
= 3.84 x
meters
Similarly, the mass of the moon in scientific notation = 7.348 ×
kg, and the mass of the earth can be written as 5.9722 ×
kg.
b. Gravitational force:
Using the formula F = G * (m1 * m2) / r^2 and plugging in the values, we have:
F = (6.674 × 10^-11 N*m^2/kg^2) * (5.9722 ×
kg) * (7.348 ×
kg) / (3.84 x
m)
Simplifying the equation:
F = 1.982 ×
N
Complete Question:
Newton's law of gravitational force (measured in Newtons) between two objects r meters apart with masses m1 kilograms and m2 kilograms is given by the formula F=Gr2m1m2, where G is a constant approximately equal to 6.674×10−11.
The earth and the moon are about 384,000 kilometers apart.
The mass of the moon is about 73,480,000,000,000,000,000,000 kg, and the mass of the earth is about 5,972,200,000,000,000,000,000,000 kg. a. The size of the numbers in this question make them hard to work with. Rewrite them using scientific notation. Don't forget to check the units and make any necessary conversions (hint: meters vs. kilometers). The distance between the earth and the moon:____ meters Mass of the moon: _--kilograms Mass of the earth: ____kilograms b. Calculate the gravitational force. Give your answer in scientific notation. Note: Since the number 384,000 only has three significant digits (numbers before trailing zeros), it is appropriate to round your final answer so that it also has three significant digits (2 decimal places, in scientific notation).____ Newtons