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- anonymous

A newly discovered planet has a mass 1.5 times compared to that of the earth, and its diameter is 3 times compared to earth. What is the gravitational acceleration on this planet?

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- anonymous

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- IrishBoy123

we relate the idea of g at the earth's surface to Newton's law of universal gravitation, such that at the surface of our planet of radius \(R_e\), we can say:
\(\large F = \frac{GM_em}{R_e^2} = mg_e\)
so
\(\large g_e = \frac{GM_e}{R_e^2}\)
Then, noting that G is a universal constant, we can say that:
\(\large G = \frac{g_e \ R_e^2}{M_e}\)
such that, as between 2 different planets, earth and planet X:
\( \huge \frac{g_e \ R_e^2}{M_e} = \frac{g_x \ R_x^2}{M_x} \)
and so, to find \(g_x\) using the data provided in the question

- anonymous

what would be my Re and Me?

- anonymous

is it 8.42 x10 ^-23?

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- anonymous

- anonymous

is it 3.021 x 10-34?

- IrishBoy123

i was teasing. my apologies.
we know from above equations that:
\(\large g_x = g_e \times \frac{R_e^2}{Me} \times \frac{M_x}{R_x^2} = g_e \times (\frac{R_e}{R_x})^2 \times \frac{M_x}{M_e}\)
you have everything [ie the ratios!!] you need in the original question to do this.

- IrishBoy123

from the question:
.....**has a mass 1.5 times compared to that of the earth***..... ***diameter is 3 times compared to earth****
so you know \(\frac{M_x}{M_e}\) and \(\frac{R_x}{R_e}\)

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