Physics question

Question

If the mass of the Sun were suddenly doubled, its gravitational pull on Mars would be

A.The same as it was before

B.Twice as strong as before

C.Four times as strong as before

D. One-fourth as strong as before

Answer 1

Hi Jessica! For this problem we need to look at the Universal Law of Gravitation. I'll explain it here, but if you'd like to read more you can just hit this link: http://hyperphysics.phy-astr.gsu.edu/hbase/hframe.html

The equation for the Universal Law of Gravitation is as follows:

F = G*m₁*m₂/r²

The variables represent the following values:

F = force of gravitation

G = universal gravitational constant, which is 6.67*10^-11 N*m²/kg²

m1 = mass of body 1

m2 = mass of body 2

r = distance between the center of mass of each body

In this problem, m1 would be the mass of mars, m2 would be the mass of the sun, and r would be the distance between mars and the sun. Thankfully, we don't need to know the mass of mars or the distance between mars and the sun to solve this problem, as these values will remain constant. What the problem is asking is the ratio of the pull of gravity with the sun's mass doubled to the typical pull of gravity of the sun. In equation form:

ratio = (pull with sun's mass doubled) / (pull with sun's mass unchanged)

ratio = F₂/F₁

By calling the mass of the sun m_s, we know that when we double the mass of the sun we can substitute 2*m_s. Now, we will put these values into the force equation, writing an equation for F₂ and F₁:

(Note: m_m = mass of Mars)

F₁ = m_m*m_s*G/r²

F₂ = m_m*2*m_s*G/r²

Now we write the equation for F₂/F₁:

F₂/F₁ = (m_m*2*m_s*G/r²) / (m_m*m_s*G/r²)

You can probably tell that a lot of these terms will cancel

F₂/F₁ = (m_m*2*m_s*G/r²) / (m_m*m_s*G/r²)

After some simple algebra, we are left with:

F₂/F₁ = 2

Thus, if the mass of the sun suddenly doubled (heaven forbid), its gravitational pull on Mars would double.

Answer 2

You might recognize the equation for gravitational force between two masses as F = G*m*M/r^2

F = Force of Gravity

m = mass number 1 (often smaller than M)

M = mass number 2 (often bigger than m)

r = the distance between the two masses

So if the big mass M suddenly doubled, then what happens to F?

Well you look at the equation, and plugin 2*M, instead of M

F = G*m*2*M/r^2

Notice that now F is twice as big as it was before, so the answer is B