# Universal Gravitation Question

• Greywolfe1982
In summary, the conversation discusses the calculation of a planet's mass based on its orbital period and radius. The final calculation results in a mass close to that of the sun, but after further research, it is found that the mass of the sun is actually much larger. The correct mass for the planet is determined to be approximately 10^27 kg.
Greywolfe1982

## Homework Statement

Given: G = 6.67259 × 10^−11 Nm2/kg2
A small Moon of a planet has an orbital period of 2.08 days and an orbital radius of 5.04 × 10^5 km.
From these data, determine the mass of the planet. Answer in units of kg.

FG=FC
FG=Gm1m2/r^2
FC=mv^2/r

## The Attempt at a Solution

First step was to convert into meters/seconds:
2.08 days to 179712 seconds
5.04x10^5km to 5.04x10^8m

Use v=d/t (or v=2$$\pi$$r/T) and get a velocity of 17621.1m/s. Use Fg=Fc and simplify to Gm/r=v^2, rearrange to v^2r/G=m. I crunched out the numbers and get a mass that's nearly as large as the sun. The problem states it's a planet, so I'm assuming I'm doing something wrong...what is it?

I don't see any error in your calculation... What is your final number you get for mass? Note the mass of the sun is about 2*10^30 kg.

Doh, I guess I should have done half a second of research before I posted this topic.

For some reason I thought the Earth was ...x10^10, rather than x10^24. I got an answer of something (don't have the papers by me now)x10^27, which now seems fairly reasonable.

## 1. What is universal gravitation?

Universal gravitation is a physical law that states that any two objects with mass will be attracted to each other with a force that is directly proportional to their masses and inversely proportional to the square of the distance between them.

## 2. Who discovered universal gravitation?

Sir Isaac Newton is credited with discovering universal gravitation in 1687 through his famous publication "Philosophiæ Naturalis Principia Mathematica".

## 3. How does universal gravitation affect objects on Earth?

Universal gravitation is responsible for the force of gravity that keeps objects on Earth from floating away into space. It also determines the weight of an object, as the force of gravity between the object and the Earth determines how much the object will accelerate towards the Earth's center.

## 4. Is universal gravitation the same as Newton's law of gravity?

Yes, universal gravitation is often referred to as Newton's law of gravity, as it was first described by Sir Isaac Newton.

## 5. Can universal gravitation be observed in everyday life?

Yes, universal gravitation is constantly at work in our everyday lives. It is responsible for keeping objects on the ground and for the orbits of planets around the sun. It also plays a role in the tides and other phenomena on Earth.

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