How Do We Calculate Mercury's Gravitational Field Intensity?

[NeomiXD]

On Earth, the gravitational field intensity is 9.8 N/kg. Mercury has a mass of 3.28 x 1023 kg and a radius of 2.57 x 106 m. Calculate the gravitational field intensity on Mercury in N/kg.

Given:

g = 9.8 N/kg (on earth)
m = 3.28 x 10^23 Kg
d = 2.57 x 10^6m

Required:

g = ?

Solution:

?

I was just wondering what given would be used and what equation would you use to solve this question; F = Gm1m2 / d^2 or F = mg.

 

[Aimless]

I was just wondering what given would be used and what equation would you use to solve this question; F = Gm1m2 / d^2 or F = mg.

What is the definition of little g? What is the definition of big G? (I don't mean the value. I mean the definition from a conceptual sense.)

One of those two is universally applicable. The other is not. That should give you a clue as to which equation to use.

 

[NeomiXD]

G in the universal gravitational constant (6.67 x 10^-11 Nm^2/kg^2). So, I have to F = Gm1m2 / d^2 to solve this question...but isn't m2 (mass of Earth) not given?

 

[Aimless]

Why do you care about the mass of the Earth? Where are you performing this calculation?

Consider the units involved. The problem asks for the gravitational field intensity, which has units of N/kg. Is this the same thing as gravitational force? What are the units of gravitational force? What do you need to do to make the units match?

 

[rwisz]

I would like to clarify that the given information is incomplete for calculating the gravitational field intensity on Mercury. In order to calculate the gravitational field intensity, we need to know the mass of the object attracting Mercury (m1) and the distance between Mercury and that object (d). Without this information, we cannot accurately calculate the gravitational field intensity on Mercury.

Furthermore, the equation F = Gm1m2 / d^2 is used to calculate the force of gravity between two objects, not the gravitational field intensity. The equation g = F/m, or g = Gm1/d^2, is used to calculate the gravitational field intensity.

If we assume that the object attracting Mercury is the Sun, then we can use the equation g = Gm1/d^2, where m1 is the mass of the Sun (1.989 x 10^30 kg) and d is the distance between Mercury and the Sun (5.79 x 10^10 m). Plugging in these values, we get a gravitational field intensity of approximately 3.59 N/kg on Mercury, significantly lower than the value on Earth due to Mercury's smaller mass and distance from the Sun.

In conclusion, the given information is not sufficient to accurately calculate the gravitational field intensity on Mercury. More information is needed, such as the mass of the object attracting Mercury, to provide a precise answer.