Why is it necessary to know the distance to a planet in order to determine the planet's mass?

Question

Thanks!

It is for school.

Answer 1

Depending on how far away you are from the planet, the amount of acceleration you experience will vary.

Say you're 10,000 miles over Earth, not orbiting, but stationary... You will begin to "fall", and accelerate at a certain rate. That rate will increase as you near the Earth's center of mass.

Now, say you're 10,000 miles over the moon, also not orbiting. You'll begin to "Fall" again, but at a rate much less than that you experienced over the Earth.

If you know the rate at which you are accelerating, and the distance away you are from the planet's center of mass, you can calculate the amount of mass that planet consists of.

Answer 2

By observing the movements of the planets across the sky, it is possible to make an accurate model of the solar system, except for one thing: you don't know how big it is. You can know all the angles between all the objects in the solar system, but if you make everything uniformly bigger or smaller, all the angles stay the same.

The model of the solar system will even work perfectly well using Newtonian gravity, as long as all the masses of all the objects vary as you make the model bigger or smaller. The periods of all the orbits will remain the same as long as the density of each object remains the same while you vary its size. In other words, if the mass of each object varies as the cube of the size factor, all the orbits remain the same.

So, to determine the mass of anything in the solar system, you must be able to determine its size. Once you determine the distance to any solar system object, this sets the size and the mass of all the objects. This was first done in the 18th century, by observing transits of Venus across the face of the Sun from different parts of the Earth. Venus covered different parts of the Sun, and took different amounts of time to cross the sun, depending on where on Earth the observations were made. Using these measurements, it was then possible to compare the distance to Venus with distances on the Earth (which were known by that time by surveying techniques).

Answer 3

Hi Wanda -

It's only "necessary" if you're using the gravitational force exerted by the planet (given or measured by you in some way) to determine the planet's mass.

There are other ways to find its mass, for example by using it's orbital speed and distance from the sun.

I'm sure you're familiar with the Newtonian physics equations for each case. If not, you can go to:

www.wikipedia.org/wiki/Newton%27s_law_of_universal_gravitation

and follow the links to obtain all the relevant equations.

Have fun!

CQ

Answer 4

It is because by knowing the distance and gravitational effect upon our planet or nearby planet which we know we can calculate the mass of that planet

Answer 5

You don't need to know the distance to the planet from where you are but the distance to the sun.

Answer 6

So that you would know directly were it is and how far away from earth it is.

Answer 7

it is not mass = weight so size and density are all that is relevant.

Answer 8

Who said it was nessesary?

Answer 9

who even said it is necessary, i dont see the correlation

Answer 10

idk for sure, but i would bet it has something to do with gravitational pull or something