Gravitational pull on probe between the Sun and the Earth

[bearhug]

How far from Earth must a space probe be along a line toward the Sun so that the Sun's gravitational pull on the probe balances the Earth's pull?

I'm actually just confused as to how to set this up. I know that I need to consider d being the distance from the Earth to the sun and r being the distance from the Earth to the probe. And use (d-r). Any help as to how I should set this up would be greatly appreciated. Part of what I'm confused with is that when referring to pull I'm thinking that is a force right. I'm completely lost as to how to start this one.

 

[andrevdh]

Equate the gravitational attractive power on the probe by the Earth and the sun.

 

[kyle8921]

I can provide a response to this question. First, let's clarify that gravitational pull is indeed a force. It is the force of attraction between two objects due to their mass and distance from each other.

To set up this problem, we can use Newton's Law of Universal Gravitation, which states that the force of gravity between two objects is directly proportional to the product of their masses and inversely proportional to the square of the distance between them. Mathematically, this can be expressed as:

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

Where F is the force of gravity, G is the gravitational constant, m1 and m2 are the masses of the two objects, and r is the distance between them.

In this case, we can let m1 be the mass of the Sun, m2 be the mass of the space probe, and r be the distance from the Earth to the probe. We also know that the force of gravity between the Sun and the probe must be equal to the force of gravity between the Earth and the probe in order for them to balance each other out. So we can set up the following equation:

F(Sun-probe) = F(Earth-probe)

Using the formula above, we can rewrite this as:

G * (m1 * m2) / (d-r)^2 = G * (mEarth * m2) / r^2

Where d is the distance from the Earth to the Sun and mEarth is the mass of the Earth. Now we can solve for r by cross-multiplying and simplifying:

r = (d * mEarth) / (m1 + mEarth)

So, to balance the gravitational pull between the Sun and the Earth on the probe, it must be located at a distance of (d * mEarth) / (m1 + mEarth) from the Earth along the line towards the Sun.

I hope this helps in setting up and solving the problem. It is important to note that this is a simplified model and in reality, there may be other factors at play that can affect the balance of gravitational forces on the probe.