# Can this gravity problem be solved without using the Earth's mass

• hndalama
In summary, a geosynchronous satellite orbits the Earth with a period of 24 hours and stays above the same location on Earth at all times. The radius of its orbit can be calculated using the equation GM/r2 = v2/r = w2r, but the mass of Earth is needed. However, it is possible to solve for the radius using other equations and data tables, or express it as a fraction of the Earth's radius.
hndalama

## Homework Statement

A satellite orbits the Earth in a geosynchronous orbit around the equator, meaning that its period is 24 hours and it stays above the same location on Earth at all times. (G = 6.67 x 10⁻¹¹ Nm²/kg².) What is the radius of its orbit?

## Homework Equations

GM/r2 = v2/r = w2r

## The Attempt at a Solution

I can solve this if the mass of Earth is given but since it isn't I'd like to know if there is a way to solve this without using Earth's mass

Sometimes you may have to look things up.

hndalama said:

## Homework Statement

A satellite orbits the Earth in a geosynchronous orbit around the equator, meaning that its period is 24 hours and it stays above the same location on Earth at all times. (G = 6.67 x 10⁻¹¹ Nm²/kg².) What is the radius of its orbit?

## Homework Equations

GM/r2 = v2/r = w2r

## The Attempt at a Solution

I can solve this if the mass of Earth is given but since it isn't I'd like to know if there is a way to solve this without using Earth's mass

You know that g = GM/re2, rearrange this to give you the expression for M then go from there

lychette said:
You know that g = GM/re2, rearrange this to give you the expression for M then go from there
Sure, but then re needs to be looked up.

This is true enough and in general I think that re is given in data tables rather than M.(certainly in A level reference tables)
Also the combination GM usually crops up on both side of gravitational equations and therefore cancel out
In this example for the Earth gE = GME/rE2 and for the satellite gs = GME/rs2
This gives gErE2 = gsrs2
knowing that gs = v2/rs and further substitution enables rs to be calculated.
If re is not given then an answer can still be obtained in terms of re

lychette said:
If re is not given then an answer can still be obtained in terms of re
This is, of course, correct. Perhaps the problem should have asked
What is the radius of its orbit as a fraction of the Earth's radius?
to make things clear.

## 1. Can gravity exist without the Earth's mass?

Yes, gravity is a universal force that exists between any two objects with mass. It is not dependent on the Earth's mass alone.

## 2. How does the Earth's mass affect gravity?

The Earth's mass is one of the factors that determine the strength of gravity. The larger the mass of an object, the stronger its gravitational pull.

## 3. Is it possible to calculate gravity without accounting for the Earth's mass?

No, the Earth's mass is a crucial component in the calculation of gravity. Without it, the strength of gravity cannot be accurately determined.

## 4. Can we create artificial gravity without using the Earth's mass?

Yes, we can create artificial gravity through other means such as centrifugal force or electromagnetic force. However, these methods may not be as strong as the Earth's gravitational force.

## 5. How does the presence of other objects in the universe affect gravity without the Earth's mass?

The presence of other objects in the universe also contributes to the strength of gravity. The more massive an object is, the stronger its gravitational pull on other objects. Therefore, the Earth's mass is not the only factor influencing gravity in the universe.

• Introductory Physics Homework Help
Replies
1
Views
1K
• Introductory Physics Homework Help
Replies
2
Views
2K
• Introductory Physics Homework Help
Replies
11
Views
2K
• Introductory Physics Homework Help
Replies
5
Views
2K
• Introductory Physics Homework Help
Replies
5
Views
2K
• Introductory Physics Homework Help
Replies
3
Views
2K
• Introductory Physics Homework Help
Replies
7
Views
1K
• Introductory Physics Homework Help
Replies
2
Views
1K
• Introductory Physics Homework Help
Replies
17
Views
2K
• Introductory Physics Homework Help
Replies
21
Views
2K