Gravitational force exerted by Jupiter on a baby

[tchls1]

Hi everyone, I'm a college student enrolled in an astronomy course, and simply put, science and math in general are both quite possibly the two things I'm worst at! Anyways, I have a test coming up and our professor gave us a practice test, and after a lot of studying, I was able to figure out most problems. This one, however, I have spent the past two ours trying to solve with no luck:

Suppose you wanted to calculate the gravitational force exerted by Jupiter on a 4.0-kg baby at the
moment of her birth. What is the minimum distance possible distance between the baby and Jupiter?
Under what circumstances would that occur? What would be the magnitude of the gravitational force
Jupiter exerts on the baby under those conditions?

It's from the chapter on Kepler's three laws, and I know that at some point this equation should be used:
Fg=G x mm (mass of two objects) divided by distance squared

As said before, this is a practice problem, so I'm not trying to get anyone to solve my homework for me, I was just hoping someone here could walk me through this! Thanks!

 

[jedishrfu]

Welcome to PF!

First you should use the homework template for your question and provide some work to show what you're thinking.

To start things off, I assume the baby is being born on the Earth and is being affected by Jupiter's gravity.

What is the closest distance that the Earth can be to Jupiter? You can find this online.

Given that then assume the Jupiter is directly overhead so that the baby is affected by Earth's gravity downward and Jupiter's gravity upward.

Does that help?

 

[Bandersnatch]

Given that then assume the Jupiter is directly overhead so that the baby is affected by Earth's gravity downward and Jupiter's gravity upward.

The question doesn't ask for the net force on the baby, just for the baby-Jupiter gravitational force.

tchls1, you've got the right equation there. Just plug the numbers in and you'll get the magnitude.

The other two questions don't require any math. Best to draw the orbits of Earth and Jupiter around the sun to help you visualise the situation and see the conditions under which the distance is the closest.
One other thing to consider would be what does treating the Earth as a point or as a sphere change in the picture, and if it's a change that matters.

 

[jedishrfu]

The question doesn't ask for the net force on the baby, just for the baby-Jupiter gravitational force.

Thanks for the clarification, I was simply trying to setup the scenario and let the op decide what to do next.

 

[HalfLostAndSearching]

Hi there,

Firstly, great job on studying and trying to solve this problem on your own! I can appreciate the determination and effort you have put into understanding this concept.

Now, let's break down the problem and see how we can solve it. We have a baby with a mass of 4.0 kg and Jupiter, a massive planet with a mass of approximately 1.9 x 10^27 kg. We are asked to find the minimum distance between the baby and Jupiter, and the corresponding gravitational force exerted by Jupiter on the baby.

To start, we can use the equation you mentioned, Fg = G x mm/d^2, where G is the gravitational constant (6.67 x 10^-11 Nm^2/kg^2), mm is the product of the masses of the two objects (in this case, 1.9 x 10^27 kg x 4.0 kg), and d is the distance between the two objects.

Now, let's try to find the minimum distance between the baby and Jupiter. According to Kepler's third law, the square of the orbital period (T) of a planet is directly proportional to the cube of its average distance (r) from the sun. In this case, we can use the same concept and apply it to the baby's distance from Jupiter. Since we are looking for the minimum distance, we can assume that the baby has just been born and is at the closest point in its orbit to Jupiter. This is known as the perijove distance, which is approximately 4.95 x 10^8 km for Jupiter.

Now, we can plug in the values in our equation, Fg = (6.67 x 10^-11 Nm^2/kg^2) x (1.9 x 10^27 kg x 4.0 kg)/ (4.95 x 10^8 km)^2. This gives us a value of approximately 6.83 x 10^-4 N. This is the magnitude of the gravitational force exerted by Jupiter on the baby at the moment of her birth.

In terms of circumstances, this would occur when the baby is at the perijove distance from Jupiter, which is the closest point in its orbit. However, it is important to note that this is a hypothetical scenario and it is not physically possible for a baby to be born in space, let alone at the