The sun’s mass is about 2.7 x 107 times greater than the moon’s mass. The sun is about 400 times farther from Earth than the moon. How does the gravitational force exerted on Earth by the sun compare with the gravitational force exerted on Earth by the moon?
Amoon = g* Mmoon/Rmoon^2
Asun=G* Msun/Rsun^2= G*2.7*10^7*Mmoon /(4*10^2*Rmoon)^2
Asun/Amoon= 2.7*10^7/(4*10^2)^2=2.7*10^7/1.6*10^5=
1.69*10^2
To compare the gravitational force exerted on Earth by the sun and the moon, we can use the equation for gravitational force, which is given by:
F = G * (m1 * m2) / r^2
Where F is the gravitational force, G is the gravitational constant (approximately 6.67430 × 10^-11 N * (m/kg)^2), m1 and m2 are the masses of the objects, and r is the distance between them.
In this case, we have the following information:
Mass of the sun (Msun) = 2.7 x 10^7 * Mass of the moon (Mmoon)
Distance to sun (Rsun) = 400 * Distance to moon (Rmoon)
Now let's compare the gravitational force exerted on Earth by the sun and the moon.
First, we need to calculate the gravitational force exerted by the moon on Earth:
Fmoon = G * (Mmoon * Mearth) / Rmoon^2
Next, we can calculate the gravitational force exerted by the sun on Earth:
Fsun = G * (Msun * Mearth) / Rsun^2
Now, we can find the ratio of the gravitational forces:
Fsun / Fmoon = (G * (Msun * Mearth) / Rsun^2) / (G * (Mmoon * Mearth) / Rmoon^2)
The gravitational constant (G), mass of Earth (Mearth), and the distances from Earth to the sun and moon (Rsun and Rmoon) are constants, so they cancel out in the ratio calculation. We are left with:
Fsun / Fmoon = (Msun * Mearth) / (Mmoon * Mearth)
Simplifying further:
Fsun / Fmoon = Msun / Mmoon
Now, substituting the given values:
Fsun / Fmoon = 2.7 x 10^7
Therefore, the gravitational force exerted on Earth by the sun is approximately 2.7 x 10^7 times greater than the gravitational force exerted on Earth by the moon.