# Gravitation and Gravitational Fields

• Mary1910
In summary: Yes, that formula would work for part c. You can use it to solve for the velocity of the satellite in its orbit. Just plug in the values for G, m1, and m2, and the radius of the orbit (which you calculated in part a) and solve for v. This will give you the speed at which the satellite must travel in order to maintain its orbit.
Mary1910

## Homework Statement

A satellite is designed to orbit Earth at an altitude above its surface that will place it in a gravitational field with a strength of 4.5 N/kg.

a) Calculate the distance above the surface of Earth at which the satellite must orbit

b) Assuming the orbit is circular, calculate the acceleration of the satellite and its direction

c) At what speed must the satellite travel in order to maintain this orbit?

## Homework Equations

F=G(m1)(m2)/(r)^2

v= √(G)(m) / (r)

## The Attempt at a Solution

a)
G=6.67 x 10^-11 N•m^2/kg^2
m=5.98 x 10^24 kg
F=4.5 N/kg

F=G(m1)(m2)/(r)^2

r^2=G(m1)(m2) / (F)

r^2=(6.67 x 10^-11 N•m^2/kg^2)(5.98 x 10^24 kg) / (4.5 N/kg)
r=^2√8.863688889 x 10^13
r=2.98 x 10^13m

∴The distance above the surface of the Earth that the satellite must orbit is 2.98 x 10^13m or 2.98 x 10^10kmb)

v= √(G)(m) / (r)

v=√(6.67 x 10^-11 N•m^2/kg^2)(5.98 x 10^24 kg) / (2.98 x 10^13m)
v=√(9.98866 x 10^14) / (2.98 x 10^13m)
v=3.66 m/s

I don't think that its possible that this could be correct, after looking up a little bit about satellites I found that satellites have a much greater orbital velocity than this. I also don't understand how I am supposed to calculate the direction of the satellite with the information that has been given.

c) And finally, for c) wouldn't my answer just be the same as part b) ? Since I am only maintaining orbit I don't think I need to be concerned about an escape velocity.
Help with these would be really appreciated. Thank you.

The second part asks you to find acceleration , not velocity .
Mary1910 said:
v= √(G)(m) / (r)
This is incorrect . Check the formula for ' v ' once again .

Hope this helps .

Qwertywerty said:
The second part asks you to find acceleration , not velocity .

This is incorrect . Check the formula for ' v ' once again .

Hope this helps .

I can't find any other formulas related to acceleration to solve this type of problem. Would it work if I solve for velocity and then divide velocity by time? Although, with this question I don't know if that would work either. Was part a) correct?

Do you know circular motion ?

Part A is fine .

Would a formula for planet/celestial orbit work for part c? Such as K=G(m1+m2) / (4π^2)

## What is gravitation?

Gravitation is a fundamental force of nature that causes objects with mass to attract each other. It is responsible for the motion of planets, stars, and other celestial bodies in the universe.

## What is a gravitational field?

A gravitational field is a region of space where a mass experiences a force due to the presence of another mass. The strength of the gravitational field is determined by the mass of the objects and their distance from each other.

## How does gravity affect objects?

Gravity causes objects to have weight and fall towards the center of the Earth. It also affects the motion of objects in space, such as the orbit of planets around the sun.

## What is the relationship between mass and gravity?

The greater the mass of an object, the stronger its gravitational pull. This means that objects with larger masses will attract each other with a greater force than objects with smaller masses.

## How does distance affect the strength of gravity?

The strength of gravity decreases as the distance between two objects increases. This is known as the inverse square law, where the force of gravity is inversely proportional to the square of the distance between the objects.

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