Lunar orbit question (calculating the mass ratio of earth and moon)

In summary, the conversation discusses calculating the ratio of the mass of the Earth with the mass of the moon and the acceleration of free fall on the Moon's surface. The constants used are also mentioned. There is some confusion about how the moon orbits the Earth and whether both planets orbit a center point. The conversation also explores the possibility of balancing centripetal forces and finding the center of mass of two stationary objects.
  • #1
jkena04
3
0
The problem I am struggling with is this . .

The centre of the Earth-Moon system is 4.7x10^3 km from the centre of the earth. Calculate;

i.the ratio of the mass of the Earth with the mass of the moon.
ii.The acceleration of free fall on the Moon's surface.

Constants
Distance between centre of mass of the Earth and centre of mass of moon - 3.8x10^5 km
Radius of Earth - 6.4x10^3 km
radius of moon - 1.7x10^3 km

Im a bit confused over how the moon actually orbits the earth. Do both planets orbit a centre point? If this is the case then for the Earth is in circular motion about a centre point, hence;

F(centripetal)=(m(earth)*v^2)/r = Gravitational force = (G*m(earth)*m(moon))/R^2

where R=distance between Earth and moon
r=radius of circular orbit

is this correct? also do the Earth and the moon also have the same tangential or angular speed?

Thank you in advance for your help!
 
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  • #2
You could go the route of balancing the centripetal forces as you began to do. If so, you might want to cast it in terms of angular velocity rather than tangential velocity, since the angular velocities of the Earth and Moon about their mutual center of gravity must be equal (and independent of their orbital radii about the center of mass).

Alternatively, suppose you were asked to find the center of mass (COM) of two stationary objects sitting in front of you. You're given their masses, m1 and m2, and the total distance between them, d, and you need to find the distance of the COM from the center of m1 in terms of the masses and distances given. How would you proceed?
 

1. How do we calculate the mass ratio of Earth and Moon?

The mass ratio of Earth and Moon can be calculated by using the formula: (Mass of Earth)/(Mass of Moon) = (Distance between Earth and Moon)^2 / (Period of Moon)^2. This formula is derived from Newton's Law of Universal Gravitation.

2. What is the current accepted value for the mass ratio of Earth and Moon?

The current accepted value for the mass ratio of Earth and Moon is approximately 81.3, meaning that Earth's mass is about 81.3 times greater than the Moon's mass.

3. How do we measure the distance between Earth and Moon?

The distance between Earth and Moon can be measured using a variety of techniques, including radar ranging, lunar laser ranging, and optical methods such as parallax measurements. These methods involve precise measurements of the time it takes for signals to travel between Earth and Moon.

4. How does the mass ratio of Earth and Moon affect lunar orbit?

The mass ratio of Earth and Moon affects lunar orbit by determining the strength of the gravitational pull between the two bodies. A higher mass ratio means that Earth's gravitational pull on the Moon is stronger, leading to a smaller orbital period and a closer orbit.

5. What other factors can affect the mass ratio of Earth and Moon?

The mass ratio of Earth and Moon can also be affected by the presence of other celestial bodies, such as the Sun and other planets. These bodies can exert gravitational forces on Earth and Moon, causing slight variations in their mass ratio over time.

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