# Finding distance between Earth and Moon in gravitational fields

• Bolter
In summary, The first question involves finding the distance between the center of the Moon and the Earth assuming the Moon moves in a circular orbit with a period of 27.5 days and the mass of the Earth is 6.0 × 10^24 kg. The second question asks how high a person could jump on a planet with the same density as Earth but only half the radius, using the same effort as on Earth. The answer to the second question can be found by understanding the relationship between gravity and radius. Both questions involve using proportionality relationships and thinking like a physicist.
Bolter
Homework Statement
Calculate the distance between 2 masses in a gravitational field

Calculate the height reached when a person jumps on a planet
Relevant Equations
Orbital period
gravitational field strength
Here are 2 questions that I have tried to answer and was hoping if these are right ways to go about it?

Q1) Find the distance in meters (m) between centre of the Moon and the centre of the Earth, assuming that the Moon moves in a circular orbit with a period of 27.5 days. Take the mass of the Earth as 6.0 × 10^24 kg. Assume that the distance between the Earth and the Moon is much larger than the radii of both planets

Q2) If a person can jump a vertical height of 1.3 m on the Earth, how high could he jump (applying the same effort as on the Earth) on a planet with the same density as the Earth, but only half the radius.

Any help would be appreciated! Thanks

Your work looks good to me.

Bolter
gneill said:
Your work looks good to me.

Ok thank you so much

Looks good to me, too. Note that once you have the expression ##g = \frac{4}{3}G \pi \rho R## you can see that ##g## is just proportional to ##R## for fixed ##\rho##. So, you can see ##g_2## will be half of ##g_1##.

Bolter
TSny said:
Looks good to me, too. Note that once you have the expression ##g = \frac{4}{3}G \pi \rho R## you can see that ##g## is just proportional to ##R## for fixed ##\rho##. So, you can see ##g_2## will be half of ##g_1##.

Ah yes I can see this relationship, much easier to use the proportionality relationship then to identify how much bigger or smaller g1 will be to g

Bolter said:
Ah yes I can see this relationship, much easier to use the proportionality relationship then to identify how much bigger or smaller g1 will be to g
You are learning to think like a physicist.

## 1. How is the distance between Earth and Moon calculated in gravitational fields?

The distance between Earth and Moon is calculated using the equation for gravitational force, which takes into account the masses of the two objects and the distance between them. This distance is known as the orbital radius and can be calculated using the law of universal gravitation.

## 2. What tools are used to measure the distance between Earth and Moon in gravitational fields?

Scientists use a variety of tools to measure the distance between Earth and Moon, including radar, laser ranging, and spacecraft ranging. These methods allow for precise measurements of the distance between the two objects.

## 3. How does the distance between Earth and Moon change in different gravitational fields?

The distance between Earth and Moon can vary depending on the gravitational field they are in. For example, during a new moon, when the Moon is between the Earth and the Sun, the gravitational pull on the Moon is stronger, causing it to be slightly closer to Earth. On the other hand, during a full moon, when the Earth is between the Moon and the Sun, the gravitational pull on the Moon is weaker, causing it to be slightly farther from Earth.

## 4. How does the distance between Earth and Moon affect tides on Earth?

The distance between Earth and Moon plays a significant role in the tides on Earth. The gravitational pull of the Moon on the Earth's oceans causes the tides to rise and fall. When the Moon is closer to Earth, the gravitational pull is stronger, resulting in higher tides, known as spring tides. Conversely, when the Moon is farther from Earth, the gravitational pull is weaker, resulting in lower tides, known as neap tides.

## 5. How has our understanding of the distance between Earth and Moon in gravitational fields evolved over time?

Our understanding of the distance between Earth and Moon has evolved over time as technology and scientific advancements have allowed for more accurate measurements. Early estimates of the distance were based on observations and calculations, while modern methods, such as radar and spacecraft ranging, provide precise measurements. Additionally, our understanding of the effects of gravitational fields on the distance between Earth and Moon has also improved over time, thanks to advancements in the field of astrophysics.

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