gravitational acceleration question?

Question

my phy proff forgot to post the class lectures online (we dont do lectures in class... long story) so i dont kno how to do any of the problems given on his online quiz... please help

A planet has a radius of 6.879 x10^6 m and a mass of 6.507 x10^24 kg. What is the gravitational acceleration close to its surface.

the answer is 9.17183053374108 but i need help on how to you get that answer

Answer 1

Gravitational force between two bodies of mass m1 and m2 with a separation d between their centre of mass is just

F = G * m1 *m2/d^2

where G is the universal gravitaional constant

If the mass m1 is a planet then we call the force the weight of m2

(weight = mg where g is the gravitational acceleration)


Therefore G * m1 * m2 /d^2 = m2g

Dividing both sides by m2 (m2 disappears)

g = G * m1/d^2

substitute the mass of the planet for m1,.
close to the surface, d = radius of planet,
use the value of G that you should have been given

Answer 2

Use the formula
g=GM/R^2,where g=gravitational acceleration
G=gravitational constant,6.67x10^-11
M=mass
R=radius

Answer 3

Start with Newton's Law of Universal Gravitation for the force of gravitation between two objects

F = G*(m1*m2/r^2) (eq. 1)

where m1 is the mass of the planet, m2 is the mass of an object close to its surface, r is the radius, and G is a constant (look it up)

Also, the gravitational force on an object is Fw = mg (let's make that m = m2 for an object near the planet. So Fw=m2*g (eq. 2)

Set Fw from eq.2 equal to F from (eq. 1)

Fw = F

So,

m2*g = G*(m1*m2)/r^2

m2 cancels from both sides

so we have g = (G*m1)/r^2

You have radius and mass, and G is constant. g is the answer your looking for.