# Keplers laws of motion - quick question on units

• channel1
In summary, the conversation is about finding the radius using an equation involving T (units: sec), G (units: m^3/(kg*s^2)), and M (units: kg). The question is about the units of the resulting radius, which should be in meters. The confusion is resolved when it is clarified that G in the equation is not an acceleration, but the gravitational constant with units m^3/(kg*s^2).
channel1

## Homework Statement

R3=((T2GM/(4∏2))1/3

## The Attempt at a Solution

simple enough, my only question is when I plug in T (units: sec) G (units: m/s^2) and M (units: kg) there is nothing to cancel out the kg so my R is not in units of meters...the equation is correct because we were given it in class but what's going on with the units?

channel1 said:

## Homework Statement

R3=((T2GM/(4∏2))1/3

## The Attempt at a Solution

simple enough, my only question is when I plug in T (units: sec) G (units: m/s^2) and M (units: kg) there is nothing to cancel out the kg so my R is not in units of meters...the equation is correct because we were given it in class but what's going on with the units?

## The Attempt at a Solution

G in this problem isn't an acceleration. It's the gravitational constant G. The units are m^3/(kg*s^2).

channel1 said:

## Homework Statement

R3=((T2GM/(4∏2))1/3

## The Attempt at a Solution

simple enough, my only question is when I plug in T (units: sec) G (units: m/s^2) and M (units: kg) there is nothing to cancel out the kg so my R is not in units of meters...the equation is correct because we were given it in class but what's going on with the units?

## Homework Statement

That's G, not g

EDIT: Beaten to the punch!

Ah hah! Thank you both!

Kepler's laws of motion are fundamental principles that describe the motion of objects in orbit around a central body. The equation you have provided is known as Kepler's third law, which relates the orbital period (T) of an object to its distance from the central body (R) and the mass of the central body (M). In order to get the correct units for R, you need to use the appropriate units for G and M as well. G should be in units of m^3/(kg*s^2) and M should be in units of kg. By using these units, the kg will cancel out and you will be left with R in units of meters, as expected. It is important to always pay attention to the units when working with equations in science, as they can provide valuable information and help ensure the accuracy of your calculations.

## 1. What are Kepler's laws of motion?

Kepler's laws of motion are a set of three scientific laws that describe the motion of planets and other celestial bodies around the sun. They were developed by Johannes Kepler in the early 17th century.

## 2. What is the first law of Kepler's laws of motion?

The first law, also known as the law of ellipses, states that all planets move in elliptical orbits around the sun, with the sun at one of the focal points of the ellipse.

## 3. What is the second law of Kepler's laws of motion?

The second law, also known as the law of equal areas, states that an imaginary line connecting a planet to the sun will sweep out equal areas in equal amounts of time, meaning that a planet moves faster when it is closer to the sun and slower when it is farther away.

## 4. What is the third law of Kepler's laws of motion?

The third law, also known as the law of harmonies, states that the square of a planet's orbital period is directly proportional to the cube of its average distance from the sun. In other words, the farther a planet is from the sun, the longer it takes to complete one orbit.

## 5. What is the importance of units when studying Kepler's laws of motion?

Units are important when studying Kepler's laws of motion because they allow scientists to accurately measure and compare the different aspects of orbital motion, such as distance, time, and velocity. Using consistent units also helps in making calculations and predictions based on these laws.

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